The Scientific World Journal: Mathematical Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Numerical Analysis of an -Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation Thu, 24 Jul 2014 12:04:57 +0000 http://www.hindawi.com/journals/tswj/2014/371413/ We discuss and analyze an -Galerkin mixed finite element (-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an -GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the -GMFE method. Based on the discussion on the theoretical error analysis in -norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in -norm. Moreover, we derive and analyze the stability of -GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. Jinfeng Wang, Meng Zhao, Min Zhang, Yang Liu, and Hong Li Copyright © 2014 Jinfeng Wang et al. All rights reserved. Some Hermite-Hadamard Type Inequalities for Harmonically s-Convex Functions Thu, 24 Jul 2014 11:53:31 +0000 http://www.hindawi.com/journals/tswj/2014/279158/ We establish some estimates of the right-hand side of Hermite-Hadamard type inequalities for functions whose derivatives absolute values are harmonically s-convex. Several Hermite-Hadamard type inequalities for products of two harmonically s-convex functions are also considered. Feixiang Chen and Shanhe Wu Copyright © 2014 Feixiang Chen and Shanhe Wu. All rights reserved. Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series Thu, 24 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/265031/ Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. Zhihua Zhang Copyright © 2014 Zhihua Zhang. All rights reserved. Analytical Approximate Solutions for a General Class of Nonlinear Delay Differential Equations Thu, 24 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/631416/ We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods. Bogdan Căruntu and Constantin Bota Copyright © 2014 Bogdan Căruntu and Constantin Bota. All rights reserved. Dynamics of a Delayed Model for the Transmission of Malicious Objects in Computer Network Wed, 23 Jul 2014 09:37:04 +0000 http://www.hindawi.com/journals/tswj/2014/194104/ An SEIQRS model for the transmission of malicious objects in computer network with two delays is investigated in this paper. We show that possible combination of the two delays can affect the stability of the model and make the model bifurcate periodic solutions under some certain conditions. For further investigation, properties of the periodic solutions are studied by using the normal form method and center manifold theory. Finally, some numerical simulations are given to justify the theoretical results. Zizhen Zhang and Huizhong Yang Copyright © 2014 Zizhen Zhang and Huizhong Yang. All rights reserved. A Novel Chaotic Map and an Improved Chaos-Based Image Encryption Scheme Sun, 20 Jul 2014 11:12:00 +0000 http://www.hindawi.com/journals/tswj/2014/713541/ In this paper, we present a novel approach to create the new chaotic map and propose an improved image encryption scheme based on it. Compared with traditional classic one-dimensional chaotic maps like Logistic Map and Tent Map, this newly created chaotic map demonstrates many better chaotic properties for encryption, implied by a much larger maximal Lyapunov exponent. Furthermore, the new chaotic map and Arnold’s Cat Map based image encryption method is designed and proved to be of solid robustness. The simulation results and security analysis indicate that such method not only can meet the requirement of imagine encryption, but also can result in a preferable effectiveness and security, which is usable for general applications. Xianhan Zhang and Yang Cao Copyright © 2014 Xianhan Zhang and Yang Cao. All rights reserved. On the Generalization of Lehmer Problem and High-Dimension Kloosterman Sums Wed, 16 Jul 2014 12:02:08 +0000 http://www.hindawi.com/journals/tswj/2014/726053/ For any fixed integer and integer with , it is clear that there exist k integers such that . Let denote the number of all such that and 2†. In this paper, we will use the analytic method and the estimate for high-dimension Kloosterman sums to study the asymptotic properties of and give two interesting asymptotic formulae for it. Guohui Chen and Han Zhang Copyright © 2014 Guohui Chen and Han Zhang. All rights reserved. A New Solution to the Matrix Equation Tue, 15 Jul 2014 12:00:16 +0000 http://www.hindawi.com/journals/tswj/2014/543610/ We investigate the matrix equation . For convenience, the matrix equation is named as Kalman-Yakubovich-conjugate matrix equation. The explicit solution is constructed when the above matrix equation has unique solution. And this solution is stated as a polynomial of coefficient matrices of the matrix equation. Moreover, the explicit solution is also expressed by the symmetric operator matrix, controllability matrix, and observability matrix. The proposed approach does not require the coefficient matrices to be in arbitrary canonical form. At the end of this paper, the numerical example is shown to illustrate the effectiveness of the proposed method. Caiqin Song Copyright © 2014 Caiqin Song. All rights reserved. Multicriteria Group Decision Making by Using Trapezoidal Valued Hesitant Fuzzy Sets Mon, 14 Jul 2014 14:23:59 +0000 http://www.hindawi.com/journals/tswj/2014/304834/ The concept of trapezoidal valued hesitant fuzzy set is introduced. Notion for distance between any two trapezoidal valued hesitant fuzzy elements is given. Using this proposed distance measure, we extend the technique for order preference by similarity to ideal solution for trapezoidal valued hesitant fuzzy sets. An example is constructed to show usefulness of this extension for multicriteria group decision making, where the opinions about the criteria values are expressed as trapezoidal valued hesitant fuzzy set. Tabasam Rashid and Syed Muhammad Husnine Copyright © 2014 Tabasam Rashid and Syed Muhammad Husnine. All rights reserved. The Smallest Spectral Radius of Graphs with a Given Clique Number Sun, 13 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/232153/ The first four smallest values of the spectral radius among all connected graphs with maximum clique size are obtained. Jing-Ming Zhang, Ting-Zhu Huang, and Ji-Ming Guo Copyright © 2014 Jing-Ming Zhang et al. All rights reserved. Generalized Equilibrium Problem with Mixed Relaxed Monotonicity Thu, 10 Jul 2014 07:57:30 +0000 http://www.hindawi.com/journals/tswj/2014/807324/ We extend the concept of relaxed -monotonicity to mixed relaxed --monotonicity. The concept of mixed relaxed --monotonicity is more general than many existing concepts of monotonicities. Finally, we apply this concept and well known KKM-theory to obtain the solution of generalized equilibrium problem. Haider Abbas Rizvi, Adem Kılıçman, and Rais Ahmad Copyright © 2014 Haider Abbas Rizvi et al. All rights reserved. Toughness Condition for a Graph to Be a Fractional -Critical Deleted Graph Wed, 09 Jul 2014 08:55:26 +0000 http://www.hindawi.com/journals/tswj/2014/369798/ A graph is called a fractional -deleted graph if admits a fractional -factor for any . A graph is called a fractional -critical deleted graph if, after deleting any vertices from , the resulting graph is still a fractional -deleted graph. The toughness, as the parameter for measuring the vulnerability of communication networks, has received significant attention in computer science. In this paper, we present the relationship between toughness and fractional -critical deleted graphs. It is determined that is fractional -critical deleted if . Wei Gao and Yun Gao Copyright © 2014 Wei Gao and Yun Gao. All rights reserved. Free Convection Nanofluid Flow in the Stagnation-Point Region of a Three-Dimensional Body Tue, 08 Jul 2014 08:54:35 +0000 http://www.hindawi.com/journals/tswj/2014/158269/ Analytical results are presented for a steady three-dimensional free convection flow in the stagnation point region over a general curved isothermal surface placed in a nanofluid. The momentum equations in x- and y-directions, energy balance equation, and nanoparticle concentration equation are reduced to a set of four fully coupled nonlinear differential equations under appropriate similarity transformations. The well known technique optimal homotopy analysis method (OHAM) is used to obtain the exact solution explicitly, whose convergence is then checked in detail. Besides, the effects of the physical parameters, such as the Lewis number, the Brownian motion parameter, the thermophoresis parameter, and the buoyancy ratio on the profiles of velocities, temperature, and concentration, are studied and discussed. Furthermore the local skin friction coefficients in x- and y-directions, the local Nusselt number, and the local Sherwood number are examined for various values of the physical parameters. Umer Farooq and Hang Xu Copyright © 2014 Umer Farooq and Hang Xu. All rights reserved. A Lower Bound on the Sinc Function and Its Application Tue, 08 Jul 2014 07:37:15 +0000 http://www.hindawi.com/journals/tswj/2014/571218/ A lower bound on the sinc function is given. Application for the sequence which related to Carleman inequality is given as well. Yue Hu and Cristinel Mortici Copyright © 2014 Yue Hu and Cristinel Mortici. All rights reserved. Riemann Boundary Value Problem for Triharmonic Equation in Higher Space Tue, 08 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/415052/ We mainly deal with the boundary value problem for triharmonic function with value in a universal Clifford algebra: , , , , , , , where    is a Lyapunov surface in , is the Dirac operator, and are unknown functions with values in a universal Clifford algebra Under some hypotheses, it is proved that the boundary value problem has a unique solution. Longfei Gu Copyright © 2014 Longfei Gu. All rights reserved. Temporal and Spatial Evolution Characteristics of Disturbance Wave in a Hypersonic Boundary Layer due to Single-Frequency Entropy Disturbance Sun, 06 Jul 2014 08:10:21 +0000 http://www.hindawi.com/journals/tswj/2014/517242/ By using a high-order accurate finite difference scheme, direct numerical simulation of hypersonic flow over an 8° half-wedge-angle blunt wedge under freestream single-frequency entropy disturbance is conducted; the generation and the temporal and spatial nonlinear evolution of boundary layer disturbance waves are investigated. Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer. Furthermore, the amplitudes of disturbance waves in the period phase are larger than that in the response phase and ablation phase and the frequency range in the boundary layer in the period phase is narrower than that in these two phases. In addition, the mode competition, dominant mode transformation, and disturbance energy transfer exist among different modes both in temporal and in spatial evolution. The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer. The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation. Zhenqing Wang, Xiaojun Tang, Hongqing Lv, and Jianqiang Shi Copyright © 2014 Zhenqing Wang et al. All rights reserved. Process Design of a Ball Joint, Considering Caulking and Pull-Out Strength Thu, 03 Jul 2014 06:33:48 +0000 http://www.hindawi.com/journals/tswj/2014/971679/ A ball joint for an automobile steering system is a pivot component which is connected to knuckle and lower control arm. The manufacturing process for its caulking comprises spinning and deforming. In this study, the process was simulated by flexible multibody dynamics. The caulking was evaluated qualitatively through numerical analysis and inspecting a plastically deformed shape. The structural responses of a ball joint, namely, pull-out strength and stiffness, are commonly investigated in the development process. Thus, following the caulking analysis, the structural responses were considered. In addition, three design variables related to the manufacturing process were defined, and the effects of design variables with respect to pull-out strength, caulking depth, and maximum stress were obtained by introducing the DOE using an L9 orthogonal array. Finally, the optimum design maximizing the pull-out strength was suggested. For the final design, the caulking quality and the pull-out strength were investigated by making six samples and their tests. Bong-Su Sin and Kwon-Hee Lee Copyright © 2014 Bong-Su Sin and Kwon-Hee Lee. All rights reserved. Radius Constants for Analytic Functions with Fixed Second Coefficient Tue, 01 Jul 2014 09:18:30 +0000 http://www.hindawi.com/journals/tswj/2014/898614/ Let be analytic in the unit disk with the second coefficient satisfying , . Sharp radius of Janowski starlikeness is obtained for functions whose th coefficient satisfies or . Other radius constants are also obtained for these functions, and connections with earlier results are made. Mahnaz M. Nargesi, Rosihan M. Ali, and V. Ravichandran Copyright © 2014 Mahnaz M. Nargesi et al. All rights reserved. Weighted -Statistical Convergence for Sequences of Positive Linear Operators Tue, 01 Jul 2014 07:56:18 +0000 http://www.hindawi.com/journals/tswj/2014/437863/ We introduce the notion of weighted -statistical convergence of a sequence, where represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted -statistical convergence. Further, we give a rate of weighted -statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our result. S. A. Mohiuddine, Abdullah Alotaibi, and Bipan Hazarika Copyright © 2014 S. A. Mohiuddine et al. All rights reserved. Eventually Periodic Solutions of a Max-Type Difference Equation Tue, 01 Jul 2014 07:50:04 +0000 http://www.hindawi.com/journals/tswj/2014/219437/ We study the following max-type difference equation , , where is a periodic sequence with period and with and , and the initial conditions are real numbers with . We show that if (or and is odd), then every well-defined solution of this equation is eventually periodic with period , which generalizes the results of (Elsayed and Stevi (2009), Iričanin and Elsayed (2010), Qin et al. (2012), and Xiao and Shi (2013)) to the general case. Besides, we construct an example with and being even which has a well-defined solution that is not eventually periodic. Taixiang Sun, Jing Liu, Qiuli He, Xin-He Liu, and Chunyan Tao Copyright © 2014 Taixiang Sun et al. All rights reserved. A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions Wed, 25 Jun 2014 12:36:38 +0000 http://www.hindawi.com/journals/tswj/2014/706296/ We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem. A. H. Bhrawy and M. A. Alghamdi Copyright © 2014 A. H. Bhrawy and M. A. Alghamdi. All rights reserved. Recent Development in Partial Differential Equations and Their Applications Wed, 25 Jun 2014 05:52:12 +0000 http://www.hindawi.com/journals/tswj/2014/243461/ Hossein Jafari, Chaudry M. Khalique, and Dumitru Baleanu Copyright © 2014 Hossein Jafari et al. All rights reserved. HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation Mon, 23 Jun 2014 13:44:09 +0000 http://www.hindawi.com/journals/tswj/2014/417486/ The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed method is independent of the basis function. In this method, a dynamic choice scheme of external grid points is proposed to eliminate the artifacts introduced by the partitioning technique. In order to decrease the calculation amount introduced by the change of the external grid points, the Newton interpolation technique is employed instead of the traditional Lagrange interpolation operator, and the condition number of the discretized matrix different equations is taken into account of the choice of the external grid points. Using the new numerical scheme, the time complexity of the sparse grid method for the image denoising is decreased to O(4J+2j) from O(43J), (). The experiment results show that the dynamic choice scheme of the external gird points can eliminate the boundary effect effectively and the efficiency can also be improved greatly comparing with the classical interval wavelets numerical methods. Shu-Li Mei and De-Hai Zhu Copyright © 2014 Shu-Li Mei and De-Hai Zhu. All rights reserved. Strongly Lacunary Ward Continuity in 2-Normed Spaces Mon, 23 Jun 2014 11:26:17 +0000 http://www.hindawi.com/journals/tswj/2014/479679/ A function defined on a subset of a 2-normed space is strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points in ; that is, is a strongly lacunary quasi-Cauchy sequence whenever () is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces. Hüseyin Çakalli and Sibel Ersan Copyright © 2014 Hüseyin Çakalli and Sibel Ersan. All rights reserved. Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field Thu, 19 Jun 2014 07:37:19 +0000 http://www.hindawi.com/journals/tswj/2014/705818/ In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the field and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets over to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples. Uğur Kadak and Hakan Efe Copyright © 2014 Uğur Kadak and Hakan Efe. All rights reserved. Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field Mon, 16 Jun 2014 05:28:36 +0000 http://www.hindawi.com/journals/tswj/2014/438924/ The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983), Grossman and Katz (1978), and Grossman (1979). Following Grossman and Katz, in the present paper, we introduce the sets of bounded, convergent, null series and p-bounded variation of sequences over the complex field and prove that these are complete. We propose a quite concrete approach based on the notion of Köthe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Köthe space and solidness. Uğur Kadak Copyright © 2014 Uğur Kadak. All rights reserved. Exact Multisoliton Solutions of General Nonlinear Schrödinger Equation with Derivative Thu, 12 Jun 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/593983/ Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota’s approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions. Qi Li, Qiu-yuan Duan, and Jian-bing Zhang Copyright © 2014 Qi Li et al. All rights reserved. On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings Wed, 11 Jun 2014 08:57:53 +0000 http://www.hindawi.com/journals/tswj/2014/374501/ The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined. Jing-Ming Zhang, Ting-Zhu Huang, and Ji-Ming Guo Copyright © 2014 Jing-Ming Zhang et al. All rights reserved. Theory, Methods, and Applications of Fractional Calculus Mon, 09 Jun 2014 09:14:45 +0000 http://www.hindawi.com/journals/tswj/2014/249717/ Abdon Atangana, Adem Kiliçman, Suares Clovis Oukouomi Noutchie, Aydin Secer, Santanu Saha Ray, and Ahmed M. A. El-Sayed Copyright © 2014 Abdon Atangana et al. All rights reserved. Implicit Contractive Mappings in Modular Metric and Fuzzy Metric Spaces Thu, 05 Jun 2014 10:54:40 +0000 http://www.hindawi.com/journals/tswj/2014/981578/ The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper we investigate the existence of fixed points of generalized -admissible modular contractive mappings in modular metric spaces. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and new fixed point theorems for integral contractions. In last section, we develop an important relation between fuzzy metric and modular metric and deduce certain new fixed point results in triangular fuzzy metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results. N. Hussain and P. Salimi Copyright © 2014 N. Hussain and P. Salimi. All rights reserved. Approximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method Tue, 03 Jun 2014 12:14:01 +0000 http://www.hindawi.com/journals/tswj/2014/721865/ The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results. Constantin Bota and Bogdan Căruntu Copyright © 2014 Constantin Bota and Bogdan Căruntu. All rights reserved. Continuous Hesitant Fuzzy Aggregation Operators and Their Application to Decision Making under Interval-Valued Hesitant Fuzzy Setting Sun, 25 May 2014 12:42:06 +0000 http://www.hindawi.com/journals/tswj/2014/897304/ Interval-valued hesitant fuzzy set (IVHFS), which is the further generalization of hesitant fuzzy set, can overcome the barrier that the precise membership degrees are sometimes hard to be specified and permit the membership degrees of an element to a set to have a few different interval values. To efficiently and effectively aggregate the interval-valued hesitant fuzzy information, in this paper, we investigate the continuous hesitant fuzzy aggregation operators with the aid of continuous OWA operator; the C-HFOWA operator and C-HFOWG operator are presented and their essential properties are studied in detail. Then, we extend the C-HFOW operators to aggregate multiple interval-valued hesitant fuzzy elements and then develop the weighted C-HFOW (WC-HFOWA and WC-HFOWG) operators, the ordered weighted C-HFOW (OWC-HFOWA and OWC-HFOWG) operators, and the synergetic weighted C-HFOWA (SWC-HFOWA and SWC-HFOWG) operators; some properties are also discussed to support them. Furthermore, a SWC-HFOW operators-based approach for multicriteria decision making problem is developed. Finally, a practical example involving the evaluation of service quality of high-tech enterprises is carried out and some comparative analyses are performed to demonstrate the applicability and effectiveness of the developed approaches. Ding-Hong Peng, Tie-Dan Wang, Chang-Yuan Gao, and Hua Wang Copyright © 2014 Ding-Hong Peng et al. All rights reserved. Output Feedback Fractional-Order Nonsingular Terminal Sliding Mode Control of Underwater Remotely Operated Vehicles Sun, 25 May 2014 11:59:49 +0000 http://www.hindawi.com/journals/tswj/2014/838019/ For the 4-DOF (degrees of freedom) trajectory tracking control problem of underwater remotely operated vehicles (ROVs) in the presence of model uncertainties and external disturbances, a novel output feedback fractional-order nonsingular terminal sliding mode control (FO-NTSMC) technique is introduced in light of the equivalent output injection sliding mode observer (SMO) and TSMC principle and fractional calculus technology. The equivalent output injection SMO is applied to reconstruct the full states in finite time. Meanwhile, the FO-NTSMC algorithm, based on a new proposed fractional-order switching manifold, is designed to stabilize the tracking error to equilibrium points in finite time. The corresponding stability analysis of the closed-loop system is presented using the fractional-order version of the Lyapunov stability theory. Comparative numerical simulation results are presented and analyzed to demonstrate the effectiveness of the proposed method. Finally, it is noteworthy that the proposed output feedback FO-NTSMC technique can be used to control a broad range of nonlinear second-order dynamical systems in finite time. Yaoyao Wang, Jiawang Chen, and Linyi Gu Copyright © 2014 Yaoyao Wang et al. All rights reserved. On Certain Subclass of Meromorphic Spirallike Functions Involving the Hypergeometric Function Sun, 25 May 2014 10:49:08 +0000 http://www.hindawi.com/journals/tswj/2014/541371/ We introduce and investigate a new subclass of meromorphic spirallike functions. Such results as integral representations, convolution properties, and coefficient estimates are proved. The results presented here would provide extensions of those given in earlier works. Several other results are also obtained. Lei Shi and Zhi-Gang Wang Copyright © 2014 Lei Shi and Zhi-Gang Wang. All rights reserved. Some Common Fixed Point Theorems in Complex Valued -Metric Spaces Sun, 25 May 2014 09:26:23 +0000 http://www.hindawi.com/journals/tswj/2014/587825/ Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. Rao et al. (2013) introduce the notion of complex valued -metric spaces. In this paper, we generalize the results of Azam et al. (2011), and Bhatt et al. (2011), by improving the conditions of contraction to establish the existence and uniqueness of common fixed point for two self-mappings on complex valued -metric spaces. Some examples are given to illustrate the main results. Aiman A. Mukheimer Copyright © 2014 Aiman A. Mukheimer. All rights reserved. On the Solution of NBVP for Multidimensional Hyperbolic Equations Sun, 25 May 2014 08:24:42 +0000 http://www.hindawi.com/journals/tswj/2014/841602/ We are interested in studying multidimensional hyperbolic equations with nonlocal integral and Neumann or nonclassical conditions. For the approximate solution of this problem first and second order of accuracy difference schemes are presented. Stability estimates for the solution of these difference schemes are established. Some numerical examples illustrating applicability of these methods to hyperbolic problems are given. Allaberen Ashyralyev and Necmettin Aggez Copyright © 2014 Allaberen Ashyralyev and Necmettin Aggez. All rights reserved. A New Sum Analogous to Gauss Sums and Its Fourth Power Mean Wed, 21 May 2014 11:15:56 +0000 http://www.hindawi.com/journals/tswj/2014/139725/ The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it. Shaofeng Ru and Wenpeng Zhang Copyright © 2014 Shaofeng Ru and Wenpeng Zhang. All rights reserved. The Unique Range Set of Meromorphic Functions in an Angular Domain Thu, 15 May 2014 11:39:37 +0000 http://www.hindawi.com/journals/tswj/2014/564640/ By using Tsuji's characteristic, we investigate uniqueness of meromorphic functions in an angular domain dealing with the shared set, which is different from the set of the paper (Lin et al., 2006) and obtain a series of results about the unique range set of meromorphic functions in angular domain. Hong-Yan Xu, Zu-Xing Xuan, and Hua Wang Copyright © 2014 Hong-Yan Xu et al. All rights reserved. Behavior of a Competitive System of Second-Order Difference Equations Thu, 15 May 2014 11:02:14 +0000 http://www.hindawi.com/journals/tswj/2014/283982/ We study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations: , , where the parameters , , , and for and initial conditions , , , and are positive real numbers. Some numerical examples are given to verify our theoretical results. Q. Din, T. F. Ibrahim, and K. A. Khan Copyright © 2014 Q. Din et al. All rights reserved. Infinitely Many Homoclinic Solutions for Second Order Nonlinear Difference Equations with -Laplacian Wed, 14 May 2014 09:40:23 +0000 http://www.hindawi.com/journals/tswj/2014/276372/ We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discrete -Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations. Guowei Sun and Ali Mai Copyright © 2014 Guowei Sun and Ali Mai. All rights reserved. On Generalized Difference Hahn Sequence Spaces Tue, 13 May 2014 14:05:14 +0000 http://www.hindawi.com/journals/tswj/2014/398203/ We construct some generalized difference Hahn sequence spaces by mean of sequence of modulus functions. The topological properties and some inclusion relations of spaces are investigated. Also we compute the dual of these spaces, and some matrix transformations are characterized. Kuldip Raj and Adem Kiliçman Copyright © 2014 Kuldip Raj and Adem Kiliçman. All rights reserved. Fixed Point Theorems for Generalized α-β-Weakly Contraction Mappings in Metric Spaces and Applications Wed, 07 May 2014 15:47:52 +0000 http://www.hindawi.com/journals/tswj/2014/784207/ We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized --weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph. Abdul Latif, Chirasak Mongkolkeha, and Wutiphol Sintunavarat Copyright © 2014 Abdul Latif et al. All rights reserved. Fixed Point Results for --Contractive Maps with Application to Boundary Value Problems Wed, 07 May 2014 11:26:52 +0000 http://www.hindawi.com/journals/tswj/2014/585964/ We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results. Nawab Hussain, Vahid Parvaneh, and Jamal Rezaei Roshan Copyright © 2014 Nawab Hussain et al. All rights reserved. An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs Wed, 07 May 2014 08:51:00 +0000 http://www.hindawi.com/journals/tswj/2014/525207/ This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable. Jianqiang Guo and Wansheng Wang Copyright © 2014 Jianqiang Guo and Wansheng Wang. All rights reserved. New Proofs of Some -Summation and -Transformation Formulas Wed, 07 May 2014 08:37:14 +0000 http://www.hindawi.com/journals/tswj/2014/940358/ We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of -series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts. Xian-Fang Liu, Ya-Qing Bi, and Qiu-Ming Luo Copyright © 2014 Xian-Fang Liu et al. All rights reserved. Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition Sun, 04 May 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/641705/ Let be a singular integral operator with its kernel satisfying , , where and are appropriate functions and and are positive constants. For with , the multilinear commutator generated by and is formally defined by . In this paper, the weighted -boundedness and the weighted weak type estimate for the multilinear commutator are established. Pu Zhang and Daiqing Zhang Copyright © 2014 Pu Zhang and Daiqing Zhang. All rights reserved. Analytic Approximate Solution for Falkner-Skan Equation Wed, 30 Apr 2014 12:16:40 +0000 http://www.hindawi.com/journals/tswj/2014/617453/ This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration. Vasile Marinca, Remus-Daniel Ene, and Bogdan Marinca Copyright © 2014 Vasile Marinca et al. All rights reserved. Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators Wed, 30 Apr 2014 06:44:34 +0000 http://www.hindawi.com/journals/tswj/2014/454865/ We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated. K. Zhukovsky Copyright © 2014 K. Zhukovsky. All rights reserved. The Dynamic Mutation Characteristics of Thermonuclear Reaction in Tokamak Tue, 29 Apr 2014 10:44:20 +0000 http://www.hindawi.com/journals/tswj/2014/841891/ The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations are transformed to the average equations with the method of multiple scales and the average equations turn to be a -symmetric perturbed polynomial Hamiltonian system of degree 5. Then, with the bifurcations theory and method of detection function, the qualitative behavior of the unperturbed system and the number of the limit cycles of the perturbed system for certain groups of parameter are analyzed. At last, the stability of the limit cycles is studied and the physical meaning of Tokamak equations under these parameter groups is given. Jing Li, Tingting Quan, Wei Zhang, and Wei Deng Copyright © 2014 Jing Li et al. All rights reserved. Cluster Synchronization for a Class of Neutral Complex Dynamical Networks with Markovian Switching Sun, 27 Apr 2014 10:03:53 +0000 http://www.hindawi.com/journals/tswj/2014/785706/ cluster synchronization problem for a class of neutral complex dynamical networks (NCDNs) with Markovian switching is investigated in this paper. Both the retarded and neutral delays are considered to be interval mode dependent and time varying. The concept of cluster synchronization is proposed to quantify the attenuation level of synchronization error dynamics against the exogenous disturbance of the NCDNs. Based on a novel Lyapunov functional, by employing some integral inequalities and the nature of convex combination, mode delay-range-dependent cluster synchronization criteria are derived in the form of linear matrix inequalities which depend not only on the disturbance attenuation but also on the initial values of the NCDNs. Finally, numerical examples are given to demonstrate the feasibility and effectiveness of the proposed theoretical results. Xinghua Liu Copyright © 2014 Xinghua Liu. All rights reserved. New Type Continuities via Abel Convergence Sun, 27 Apr 2014 08:52:27 +0000 http://www.hindawi.com/journals/tswj/2014/398379/ We investigate the concept of Abel continuity. A function defined on a subset of , the set of real numbers, is Abel continuous if it preserves Abel convergent sequences. Some other types of continuities are also studied and interesting result is obtained. It turned out that uniform limit of a sequence of Abel continuous functions is Abel continuous and the set of Abel continuous functions is a closed subset of continuous functions. Huseyin Cakalli and Mehmet Albayrak Copyright © 2014 Huseyin Cakalli and Mehmet Albayrak. All rights reserved. Identifiability and Identification of Trace Continuous Pollutant Source Sun, 27 Apr 2014 07:54:02 +0000 http://www.hindawi.com/journals/tswj/2014/215104/ Accidental pollution events often threaten people’s health and lives, and a pollutant source is very necessary so that prompt remedial actions can be taken. In this paper, a trace continuous pollutant source identification method is developed to identify a sudden continuous emission pollutant source in an enclosed space. The location probability model is set up firstly, and then the identification method is realized by searching a global optimal objective value of the location probability. In order to discuss the identifiability performance of the presented method, a conception of a synergy degree of velocity fields is presented in order to quantitatively analyze the impact of velocity field on the identification performance. Based on this conception, some simulation cases were conducted. The application conditions of this method are obtained according to the simulation studies. In order to verify the presented method, we designed an experiment and identified an unknown source appearing in the experimental space. The result showed that the method can identify a sudden trace continuous source when the studied situation satisfies the application conditions. Hongquan Qu, Shouwen Liu, Liping Pang, and Tao Hu Copyright © 2014 Hongquan Qu et al. All rights reserved. Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death Sun, 27 Apr 2014 06:52:41 +0000 http://www.hindawi.com/journals/tswj/2014/409730/ Based on Codeço’s cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder’s fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the prior estimate of exponential decrease of traveling wave solutions is needed. For this aim, a new method is proposed, which can be applied to reaction-diffusion systems consisting of more than three equations. Tianran Zhang and Qingming Gou Copyright © 2014 Tianran Zhang and Qingming Gou. All rights reserved. 1-Quasiconformal Mappings and CR Mappings on Goursat Groups Thu, 24 Apr 2014 09:38:19 +0000 http://www.hindawi.com/journals/tswj/2014/930571/ We show that 1-quasiconformal mappings on Goursat groups are CR or anti-CR mappings. This can reduce the determination of 1-quasiconformal mappings to the determination of CR automorphisms of CR manifolds, which is a fundamental problem in the theory of several complex variables. Qing Yan Wu and Zun Wei Fu Copyright © 2014 Qing Yan Wu and Zun Wei Fu. All rights reserved. Analysis of Fractional Dynamic Systems Wed, 23 Apr 2014 09:07:06 +0000 http://www.hindawi.com/journals/tswj/2014/760634/ Fawang Liu, Richard Magin, Changpin Li, Alla Sikorskii, and Santos Bravo Yuste Copyright © 2014 Fawang Liu et al. All rights reserved. The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays Wed, 16 Apr 2014 16:12:57 +0000 http://www.hindawi.com/journals/tswj/2014/965376/ We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at . Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Han Xu and Yinlai Jin Copyright © 2014 Han Xu and Yinlai Jin. All rights reserved. Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues Wed, 16 Apr 2014 09:36:17 +0000 http://www.hindawi.com/journals/tswj/2014/716082/ By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the bifurcation problems of nontwisted heteroclinic loop with resonant eigenvalues. The existence, numbers, and existence regions of 1-heteroclinic loop, 1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two 1-periodic orbits are obtained. Meanwhile, we give the corresponding bifurcation surfaces. Yinlai Jin, Xiaowei Zhu, Zheng Guo, Han Xu, Liqun Zhang, and Benyan Ding Copyright © 2014 Yinlai Jin et al. All rights reserved. Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative Tue, 15 Apr 2014 13:02:29 +0000 http://www.hindawi.com/journals/tswj/2014/402373/ Although there have existed some numerical algorithms for the fractional differential equations, developing high-order methods (i.e., with convergence order greater than or equal to 2) is just the beginning. Lubich has ever proposed the high-order schemes when he studied the fractional linear multistep methods, where he constructed the th order schemes for the th order Riemann-Liouville integral and th order Riemann-Liouville derivative. In this paper, we study such a problem and develop recursion formulas to compute these coefficients in the higher-order schemes. The coefficients of higher-order schemes are also obtained. We first find that these coefficients are oscillatory, which is similar to Runge’s phenomenon. So, they are not suitable for numerical calculations. Finally, several numerical examples are implemented to testify the efficiency of the numerical schemes for . Rifang Wu, Hengfei Ding, and Changpin Li Copyright © 2014 Rifang Wu et al. All rights reserved. On Fourier Series of Fuzzy-Valued Functions Thu, 10 Apr 2014 12:46:20 +0000 http://www.hindawi.com/journals/tswj/2014/782652/ Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh’s Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We derive uniform convergence of a fuzzy-valued function sequences and series with level sets. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, Fourier series of periodic fuzzy-valued functions is defined and its complex form is given via sine and cosine fuzzy coefficients with an illustrative example. Finally, by using the Dirichlet kernel and its properties, we especially examine the convergence of Fourier series of fuzzy-valued functions at each point of discontinuity, where one-sided limits exist. Uğur Kadak and Feyzi Başar Copyright © 2014 Uğur Kadak and Feyzi Başar. All rights reserved. Implementation of Steiner Point of Fuzzy Set Wed, 09 Apr 2014 12:01:44 +0000 http://www.hindawi.com/journals/tswj/2014/593065/ This paper deals with the implementation of Steiner point of fuzzy set. Some definitions and properties of Steiner point are investigated and extended to fuzzy set. This paper focuses on establishing efficient methods to compute Steiner point of fuzzy set. Two strategies of computing Steiner point of fuzzy set are proposed. One is called linear combination of Steiner points computed by a series of crisp α-cut sets of the fuzzy set. The other is an approximate method, which is trying to find the optimal α-cut set approaching the fuzzy set. Stability analysis of Steiner point of fuzzy set is also studied. Some experiments on image processing are given, in which the two methods are applied for implementing Steiner point of fuzzy image, and both strategies show their own advantages in computing Steiner point of fuzzy set. Jiuzhen Liang and Dejiang Wang Copyright © 2014 Jiuzhen Liang and Dejiang Wang. All rights reserved. Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation Mon, 07 Apr 2014 09:49:53 +0000 http://www.hindawi.com/journals/tswj/2014/716740/ The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on , and . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation . Lastly, numerical simulations in order to verify the analytical results are given. Daewook Kim, Dojin Kim, Keum-Shik Hong, and Il Hyo Jung Copyright © 2014 Daewook Kim et al. All rights reserved. Leapfrog/Finite Element Method for Fractional Diffusion Equation Thu, 03 Apr 2014 13:43:57 +0000 http://www.hindawi.com/journals/tswj/2014/982413/ We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an -error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis. Zhengang Zhao and Yunying Zheng Copyright © 2014 Zhengang Zhao and Yunying Zheng. All rights reserved. Limit of Riemann Solutions to the Nonsymmetric System of Keyfitz-Kranzer Type Thu, 03 Apr 2014 09:37:17 +0000 http://www.hindawi.com/journals/tswj/2014/287256/ The limit of Riemann solutions to the nonsymmetric system of Keyfitz-Kranzer type with a scaled pressure is considered for both polytropic gas and generalized Chaplygin gas. In the former case, the delta shock wave can be obtained as the limit of shock wave and contact discontinuity when and the parameter tends to zero. The point is, the delta shock wave is not the one of transport equations, which is obviously different from cases of some other systems such as Euler equations or relativistic Euler equations. For the generalized Chaplygin gas, unlike the polytropic or isothermal gas, there exists a certain critical value depending only on the Riemann initial data, such that when drops to , the delta shock wave appears as , which is actually a delta solution of the same system in one critical case. Then as becomes smaller and goes to zero at last, the delta shock wave solution is the exact one of transport equations. Furthermore, the vacuum states and contact discontinuities can be obtained as the limit of Riemann solutions when and , respectively. Lihui Guo and Gan Yin Copyright © 2014 Lihui Guo and Gan Yin. All rights reserved. Monotone Data Visualization Using Rational Trigonometric Spline Interpolation Thu, 03 Apr 2014 09:35:38 +0000 http://www.hindawi.com/journals/tswj/2014/602453/ Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically. Farheen Ibraheem, Maria Hussain, and Malik Zawwar Hussain Copyright © 2014 Farheen Ibraheem et al. All rights reserved. Anticontrol of Hopf Bifurcation and Control of Chaos for a Finance System through Washout Filters with Time Delay Thu, 03 Apr 2014 09:29:51 +0000 http://www.hindawi.com/journals/tswj/2014/983034/ A controlled model for a financial system through washout-filter-aided dynamical feedback control laws is developed, the problem of anticontrol of Hopf bifurcation from the steady state is studied, and the existence, stability, and direction of bifurcated periodic solutions are discussed in detail. The obtained results show that the delay on price index has great influences on the financial system, which can be applied to suppress or avoid the chaos phenomenon appearing in the financial system. Huitao Zhao, Mengxia Lu, and Junmei Zuo Copyright © 2014 Huitao Zhao et al. All rights reserved. Two Different Methods for Numerical Solution of the Modified Burgers’ Equation Thu, 03 Apr 2014 08:56:09 +0000 http://www.hindawi.com/journals/tswj/2014/780269/ A numerical solution of the modified Burgers’ equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing and error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM. Seydi Battal Gazi Karakoç, Ali Başhan, and Turabi Geyikli Copyright © 2014 Seydi Battal Gazi Karakoç et al. All rights reserved. Sinc-Chebyshev Collocation Method for a Class of Fractional Diffusion-Wave Equations Tue, 01 Apr 2014 08:16:23 +0000 http://www.hindawi.com/journals/tswj/2014/143983/ This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed. Zhi Mao, Aiguo Xiao, Zuguo Yu, and Long Shi Copyright © 2014 Zhi Mao et al. All rights reserved. Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order Tue, 01 Apr 2014 06:42:02 +0000 http://www.hindawi.com/journals/tswj/2014/147801/ The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods. Y. H. Cong and C. X. Jiang Copyright © 2014 Y. H. Cong and C. X. Jiang. All rights reserved. Recent Progress on Nonlinear Schrödinger Systems with Quadratic Interactions Mon, 31 Mar 2014 14:01:31 +0000 http://www.hindawi.com/journals/tswj/2014/214821/ The study of nonlinear Schrödinger systems with quadratic interactions has attracted much attention in the recent years. In this paper, we summarize time decay estimates of small solutions to the systems under the mass resonance condition in 2-dimensional space. We show the existence of wave operators and modified wave operators of the systems under some mass conditions in -dimensional space, where . The existence of scattering operators and finite time blow-up of the solutions for the systems in higher space dimensions is also shown. Chunhua Li and Nakao Hayashi Copyright © 2014 Chunhua Li and Nakao Hayashi. All rights reserved. On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations Mon, 31 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/379897/ Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters. Yuhai Wu and Jingjing Zhou Copyright © 2014 Yuhai Wu and Jingjing Zhou. All rights reserved. Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions Sun, 30 Mar 2014 11:40:54 +0000 http://www.hindawi.com/journals/tswj/2014/580871/ We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in . For time , we can define a functional associated with the solution of the equations and some testing function . When the pressure function of the governing equations is of the form , where is the density function, is a constant, and , we can show that the nontrivial solutions with nonslip boundary condition will blow up in finite time if satisfies some initial functional conditions defined by the integrals of . Examples of the testing functions include , , , , and . The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given. Sen Wong and Manwai Yuen Copyright © 2014 Sen Wong and Manwai Yuen. All rights reserved. Discontinuous Mixed Covolume Methods for Parabolic Problems Sun, 30 Mar 2014 08:51:28 +0000 http://www.hindawi.com/journals/tswj/2014/867863/ We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuous and first-order error estimate in . Ailing Zhu and Ziwen Jiang Copyright © 2014 Ailing Zhu and Ziwen Jiang. All rights reserved. Fixed Points of Contractive Mappings in -Metric-Like Spaces Sun, 30 Mar 2014 07:44:55 +0000 http://www.hindawi.com/journals/tswj/2014/471827/ We discuss topological structure of -metric-like spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results in -metric-like spaces are obtained. Two examples are presented in order to verify the effectiveness and applicability of our main results. Nawab Hussain, Jamal Rezaei Roshan, Vahid Parvaneh, and Zoran Kadelburg Copyright © 2014 Nawab Hussain et al. All rights reserved. A Time Delay Predator-Prey System with Three-Stage-Structure Thu, 27 Mar 2014 07:19:14 +0000 http://www.hindawi.com/journals/tswj/2014/512838/ A predator-prey system was studied that has a discrete delay, stage-structure, and Beddington-DeAngelis functional response, where predator species has three stages, immature, mature, and old age stages. By using of Mawhin's continuous theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution. Qiaoqin Gao and Zhen Jin Copyright © 2014 Qiaoqin Gao and Zhen Jin. All rights reserved. The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems Wed, 26 Mar 2014 08:02:41 +0000 http://www.hindawi.com/journals/tswj/2014/705703/ We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in . Yanan Jiang, Maoan Han, and Dongmei Xiao Copyright © 2014 Yanan Jiang et al. All rights reserved. An Analysis on Local Convergence of Inexact Newton-Gauss Method for Solving Singular Systems of Equations Wed, 26 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/752673/ We study the local convergence properties of inexact Newton-Gauss method for singular systems of equations. Unified estimates of radius of convergence balls for one kind of singular systems of equations with constant rank derivatives are obtained. Application to the Smale point estimate theory is provided and some important known results are extended and/or improved. Fangqin Zhou Copyright © 2014 Fangqin Zhou. All rights reserved. Upper Semicontinuity of Pullback Attractors for the 3D Nonautonomous Benjamin-Bona-Mahony Equations Wed, 26 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/853139/ We will study the upper semicontinuity of pullback attractors for the 3D nonautonomouss Benjamin-Bona-Mahony equations with external force perturbation terms. Under some regular assumptions, we can prove the pullback attractors of equation , converge to the global attractor of the above-mentioned equation with for any . Xinguang Yang, Xiaosong Wang, Juntao Li, and Lingrui Zhang Copyright © 2014 Xinguang Yang et al. All rights reserved. Bifurcation Analysis in Models for Vector-Borne Diseases with Logistic Growth Tue, 25 Mar 2014 12:00:50 +0000 http://www.hindawi.com/journals/tswj/2014/195864/ We establish and study vector-borne models with logistic and exponential growth of vector and host populations, respectively. We discuss and analyses the existence and stability of equilibria. The model has backward bifurcation and may have no, one, or two positive equilibria when the basic reproduction number is less than one and one, two, or three endemic equilibria when is greater than one under different conditions. Furthermore, we prove that the disease-free equilibrium is stable if is less than 1, it is unstable otherwise. At last, by numerical simulation, we find rich dynamical behaviors in the model. By taking the natural death rate of host population as a bifurcation parameter, we find that the system may undergo a backward bifurcation, saddle-node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation, and cusp bifurcation with the saturation parameter varying. The natural death rate of host population is a crucial parameter. If the natural death rate is higher, then the host population and the disease will die out. If it is smaller, then the host and vector population will coexist. If it is middle, the period solution will occur. Thus, with the parameter varying, the disease will spread, occur periodically, and finally become extinct. Guihua Li and Zhen Jin Copyright © 2014 Guihua Li and Zhen Jin. All rights reserved. Numerical Modeling of the Photothermal Processing for Bubble Forming around Nanowire in a Liquid Mon, 24 Mar 2014 12:20:29 +0000 http://www.hindawi.com/journals/tswj/2014/794630/ An accurate computation of the temperature is an important factor in determining the shape of a bubble around a nanowire immersed in a liquid. The study of the physical phenomenon consists in solving a photothermic coupled problem between light and nanowire. The numerical multiphysic model is used to study the variations of the temperature and the shape of the created bubble by illumination of the nanowire. The optimization process, including an adaptive remeshing scheme, is used to solve the problem through a finite element method. The study of the shape evolution of the bubble is made taking into account the physical and geometrical parameters of the nanowire. The relation between the sizes and shapes of the bubble and nanowire is deduced. Anis Chaari, Laurence Giraud-Moreau, Thomas Grosges, and Dominique Barchiesi Copyright © 2014 Anis Chaari et al. All rights reserved. Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria Sun, 23 Mar 2014 13:05:40 +0000 http://www.hindawi.com/journals/tswj/2014/585609/ The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip and an inclination flip. When the nonhyperbolic equilibrium does not undergo a transcritical bifurcation, we establish the coexistence and noncoexistence of the periodic orbits and homoclinic orbits. While the nonhyperbolic equilibrium undergoes the transcritical bifurcation, we obtain the noncoexistence of the periodic orbits and homoclinic orbits and the existence of two or three heteroclinic orbits. Fengjie Geng and Junfang Zhao Copyright © 2014 Fengjie Geng and Junfang Zhao. All rights reserved. Existence and Uniqueness Theorems for Impulsive Fractional Differential Equations with the Two-Point and Integral Boundary Conditions Sun, 23 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/918730/ We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case . M. J. Mardanov, N. I. Mahmudov, and Y. A. Sharifov Copyright © 2014 M. J. Mardanov et al. All rights reserved. A Maximal Element Theorem in FWC-Spaces and Its Applications Thu, 20 Mar 2014 09:11:18 +0000 http://www.hindawi.com/journals/tswj/2014/890696/ A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. Haishu Lu, Qingwen Hu, and Yulin Miao Copyright © 2014 Haishu Lu et al. All rights reserved. Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary Thu, 20 Mar 2014 07:17:04 +0000 http://www.hindawi.com/journals/tswj/2014/826125/ This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier. Chubing Zhang Copyright © 2014 Chubing Zhang. All rights reserved. On the Shape of Limit Cycles That Bifurcate from Isochronous Center Wed, 19 Mar 2014 14:18:03 +0000 http://www.hindawi.com/journals/tswj/2014/320406/ New idea and algorithm are proposed to compute asymptotic expression of limit cycles bifurcated from the isochronous center. Compared with known inverse integrating factor method, new algorithm to analytically computing shape of limit cycle proposed in this paper is simple and easy to apply. The applications of new algorithm to some examples are also given. Guang Chen and Yuhai Wu Copyright © 2014 Guang Chen and Yuhai Wu. All rights reserved. Dynamic Properties of the Solow Model with Bounded Technological Progress and Time-to-Build Technology Wed, 19 Mar 2014 13:44:04 +0000 http://www.hindawi.com/journals/tswj/2014/908629/ We introduce a time-to-build technology in a Solow model with bounded technological progress. Our analysis shows that the system may be asymptotically stable, or it can produce stability switches and Hopf bifurcations when time delay varies. The direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. Numerical simulations confirms the theoretical results. Luca Guerrini and Mauro Sodini Copyright © 2014 Luca Guerrini and Mauro Sodini. All rights reserved. A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation Wed, 19 Mar 2014 09:01:53 +0000 http://www.hindawi.com/journals/tswj/2014/681707/ The computational complexity of one-dimensional time fractional reaction-diffusion equation is compared with for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM) embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, parallel computations. A domain decomposition algorithm for time fractional reaction-diffusion equation with implicit finite difference method is proposed. The domain decomposition algorithm keeps the same parallelism but needs much fewer iterations, compared with Jacobi iteration in each time step. Numerical experiments are used to verify the efficiency of the obtained algorithm. Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang, and Jie Liu Copyright © 2014 Chunye Gong et al. All rights reserved. On Hardy-Pachpatte-Copson's Inequalities Tue, 18 Mar 2014 07:08:21 +0000 http://www.hindawi.com/journals/tswj/2014/607347/ We establish new inequalities similar to Hardy-Pachpatte-Copson’s type inequalities. These results in special cases yield some of the recent results. Chang-Jian Zhao and Wing-Sum Cheung Copyright © 2014 Chang-Jian Zhao and Wing-Sum Cheung. All rights reserved. A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach Mon, 17 Mar 2014 08:26:34 +0000 http://www.hindawi.com/journals/tswj/2014/109128/ In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed. Taha Aziz and F. M. Mahomed Copyright © 2014 Taha Aziz and F. M. Mahomed. All rights reserved. A Novel Iterative Scheme and Its Application to Differential Equations Sun, 16 Mar 2014 12:46:14 +0000 http://www.hindawi.com/journals/tswj/2014/605376/ The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method. Yasir Khan, F. Naeem, and Zdeněk Šmarda Copyright © 2014 Yasir Khan et al. All rights reserved. Some Refinements and Generalizations of I. Schur Type Inequalities Sun, 16 Mar 2014 11:23:21 +0000 http://www.hindawi.com/journals/tswj/2014/709358/ Recently, extensive researches on estimating the value of e have been studied. In this paper, the structural characteristics of I. Schur type inequalities are exploited to generalize the corresponding inequalities by variable parameter techniques. Some novel upper and lower bounds for the I. Schur inequality have also been obtained and the upper bounds may be obtained with the help of Maple and automated proving package (Bottema). Numerical examples are employed to demonstrate the reliability of the approximation of these new upper and lower bounds, which improve some known results in the recent literature. Xian-Ming Gu, Ting-Zhu Huang, Wei-Ru Xu, Hou-Biao Li, Liang Li, and Xi-Le Zhao Copyright © 2014 Xian-Ming Gu et al. All rights reserved. Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators Sun, 16 Mar 2014 08:06:43 +0000 http://www.hindawi.com/journals/tswj/2014/306214/ Let be a Musielak-Orlicz function and an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, , via the grand maximal function. The authors then obtain some real-variable characterizations of in terms of the radial, the nontangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy space with and are new even for its weighted variant. Finally, the authors characterize these spaces by anisotropic atomic decompositions. The authors also obtain the finite atomic decomposition characterization of , and, as an application, the authors prove that, for a given admissible triplet , if is a sublinear operator and maps all -atoms with (or all continuous -atoms with ) into uniformly bounded elements of some quasi-Banach spaces , then uniquely extends to a bounded sublinear operator from to . These results are new even for anisotropic Orlicz-Hardy spaces on . Baode Li, Dachun Yang, and Wen Yuan Copyright © 2014 Baode Li et al. All rights reserved. Nonoscillatory Solutions for System of Neutral Dynamic Equations on Time Scales Sun, 16 Mar 2014 07:33:49 +0000 http://www.hindawi.com/journals/tswj/2014/768215/ We will discuss nonoscillatory solutions to the -dimensional functional system of neutral type dynamic equations on time scales. We will establish some sufficient conditions for nonoscillatory solutions with the property . Zhanhe Chen, Taixiang Sun, Qi Wang, and Hongjian Xi Copyright © 2014 Zhanhe Chen et al. All rights reserved. On the Iterative Methods of Linearization, Decrease of Order and Dimension of the Karman-Type PDEs Sun, 16 Mar 2014 07:12:17 +0000 http://www.hindawi.com/journals/tswj/2014/792829/ Iterative methods to achieve a suitable linearization as well as a decrease of the order and dimension of nonlinear partial differential equations of the eighth order into the biharmonic and Poisson-type differential equations with their simultaneous linearization are proposed in this work. Validity and reliability of the obtained results are discussed using computer programs developed by the authors. A. V. Krysko, J. Awrejcewicz, S. P. Pavlov, M. V. Zhigalov, and V. A. Krysko Copyright © 2014 A. V. Krysko et al. All rights reserved. On Ulam's Type Stability of the Cauchy Additive Equation Sun, 16 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/540164/ We prove a general result on Ulam's type stability of the functional equation , in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias. Janusz Brzdęk Copyright © 2014 Janusz Brzdęk. All rights reserved. A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time Thu, 13 Mar 2014 12:21:34 +0000 http://www.hindawi.com/journals/tswj/2014/182508/ In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function of finding the walker at position at time is completely determined by the Laplace transform of the probability density function of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived. Long Shi, Zuguo Yu, Zhi Mao, and Aiguo Xiao Copyright © 2014 Long Shi et al. All rights reserved. Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces Thu, 13 Mar 2014 08:17:18 +0000 http://www.hindawi.com/journals/tswj/2014/493450/ We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators. Habtu Zegeye and Naseer Shahzad Copyright © 2014 Habtu Zegeye and Naseer Shahzad. All rights reserved. A Parallel Algorithm for the Two-Dimensional Time Fractional Diffusion Equation with Implicit Difference Method Wed, 12 Mar 2014 12:53:01 +0000 http://www.hindawi.com/journals/tswj/2014/219580/ It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is . In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future. Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang, and Jie Liu Copyright © 2014 Chunye Gong et al. All rights reserved. An Osgood Type Regularity Criterion for the 3D Boussinesq Equations Tue, 11 Mar 2014 09:26:20 +0000 http://www.hindawi.com/journals/tswj/2014/563084/ We consider the three-dimensional Boussinesq equations, and obtain an Osgood type regularity criterion in terms of the velocity gradient. Qiang Wu, Lin Hu, and Guili Liu Copyright © 2014 Qiang Wu et al. All rights reserved. Minimal Solution of Singular LR Fuzzy Linear Systems Tue, 11 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/517218/ In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated. M. Nikuie and M. Z. Ahmad Copyright © 2014 M. Nikuie and M. Z. Ahmad. All rights reserved. Contractive Maps in Locally Transitive Relational Metric Spaces Mon, 10 Mar 2014 13:49:53 +0000 http://www.hindawi.com/journals/tswj/2014/169358/ Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al. (2014) are also being discussed. Mihai Turinici Copyright © 2014 Mihai Turinici. All rights reserved. Improved Delay-Dependent Stability Conditions for MIMO Networked Control Systems with Nonlinear Perturbations Mon, 10 Mar 2014 13:06:10 +0000 http://www.hindawi.com/journals/tswj/2014/196927/ This paper provides improved time delay-dependent stability criteria for multi-input and multi-output (MIMO) network control systems (NCSs) with nonlinear perturbations. Without the stability assumption on the neutral operator after the descriptor approach, the new proposed stability theory is less conservative than the existing stability condition. Theoretical proof is given in this paper to demonstrate the effectiveness of the proposed stability condition. Jiuwen Cao Copyright © 2014 Jiuwen Cao. All rights reserved. On the Higher Power Sums of Reciprocal Higher-Order Sequences Mon, 10 Mar 2014 09:57:08 +0000 http://www.hindawi.com/journals/tswj/2014/521358/ Let be a higher-order linear recursive sequence. In this paper, we use the properties of error estimation and the analytic method to study the reciprocal sums of higher power of higher-order sequences. Then we establish several new and interesting identities relating to the infinite and finite sums. Zhengang Wu and Jin Zhang Copyright © 2014 Zhengang Wu and Jin Zhang. All rights reserved. A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations Mon, 10 Mar 2014 08:31:38 +0000 http://www.hindawi.com/journals/tswj/2014/489495/ We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. Özkan Güner and Adem C. Cevikel Copyright © 2014 Özkan Güner and Adem C. Cevikel. All rights reserved. A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations Sun, 09 Mar 2014 11:16:03 +0000 http://www.hindawi.com/journals/tswj/2014/141467/ A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple space replacing the complex space. Some a priori error estimates in -norm for the scalar unknown and in -norm for its gradient . Moreover, we also discuss a priori error estimates in -norm for the scalar unknown . Yang Liu, Hong Li, Wei Gao, Siriguleng He, and Zhichao Fang Copyright © 2014 Yang Liu et al. All rights reserved. An Inequality of Meromorphic Functions and Its Application Thu, 06 Mar 2014 08:07:33 +0000 http://www.hindawi.com/journals/tswj/2014/242851/ By applying Ahlfors theory of covering surface, we establish a fundamental inequality of meromorphic function dealing with multiple values in an angular domain. As an application, we prove the existence of some new singular directions for a meromorphic function , namely a Bloch direction and a pseudo-T direction for . Zhaojun Wu, Yuxian Chen, and Zuxing Xuan Copyright © 2014 Zhaojun Wu et al. All rights reserved. Homotopic Approximate Solutions for the Perturbed CKdV Equation with Variable Coefficients Wed, 05 Mar 2014 16:41:24 +0000 http://www.hindawi.com/journals/tswj/2014/593642/ This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation are also induced. Dianchen Lu, Tingting Chen, and Baojian Hong Copyright © 2014 Dianchen Lu et al. All rights reserved. On a New Efficient Steffensen-Like Iterative Class by Applying a Suitable Self-Accelerator Parameter Mon, 03 Mar 2014 08:39:12 +0000 http://www.hindawi.com/journals/tswj/2014/769758/ It is attempted to present an efficient and free derivative class of Steffensen-like methods for solving nonlinear equations. To this end, firstly, we construct an optimal eighth-order three-step uniparameter without memory of iterative methods. Then the self-accelerator parameter is estimated using Newton’s interpolation in such a way that it improves its convergence order from 8 to 12 without any extra function evaluation. Therefore, its efficiency index is increased from 81/4 to 121/4 which is the main feature of this class. To show applicability of the proposed methods, some numerical illustrations are presented. Taher Lotfi and Elahe Tavakoli Copyright © 2014 Taher Lotfi and Elahe Tavakoli. All rights reserved. Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian Sun, 02 Mar 2014 14:22:57 +0000 http://www.hindawi.com/journals/tswj/2014/920537/ We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem. Dorota Bors Copyright © 2014 Dorota Bors. All rights reserved. VIM-Based Dynamic Sparse Grid Approach to Partial Differential Equations Thu, 27 Feb 2014 16:28:30 +0000 http://www.hindawi.com/journals/tswj/2014/390148/ Combining the variational iteration method (VIM) with the sparse grid theory, a dynamic sparse grid approach for nonlinear PDEs is proposed in this paper. In this method, a multilevel interpolation operator is constructed based on the sparse grids theory firstly. The operator is based on the linear combination of the basic functions and independent of them. Second, by means of the precise integration method (PIM), the VIM is developed to solve the nonlinear system of ODEs which is obtained from the discretization of the PDEs. In addition, a dynamic choice scheme on both of the inner and external grid points is proposed. It is different from the traditional interval wavelet collocation method in which the choice of both of the inner and external grid points is dynamic. The numerical experiments show that our method is better than the traditional wavelet collocation method, especially in solving the PDEs with the Nuemann boundary conditions. Shu-Li Mei Copyright © 2014 Shu-Li Mei. All rights reserved. Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays Thu, 27 Feb 2014 13:53:19 +0000 http://www.hindawi.com/journals/tswj/2014/932395/ This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results. Xuling Wang, Xiaodi Li, and Gani Tr. Stamov Copyright © 2014 Xuling Wang et al. All rights reserved. On Positive Radial Solutions for a Class of Elliptic Equations Tue, 25 Feb 2014 07:18:10 +0000 http://www.hindawi.com/journals/tswj/2014/507312/ A class of elliptic boundary value problem in an exterior domain is considered under some conditions concerning the first eigenvalue of the relevant linear operator, where the variables of nonlinear term need not to be separated. Several new theorems on the existence and multiplicity of positive radial solutions are obtained by means of fixed point index theory. Our conclusions are essential improvements of the results in Lan and Webb (1998), Lee (1997), Mao and Xue (2002), Stańczy (2000), and Han and Wang (2006). Ying Wu and Guodong Han Copyright © 2014 Ying Wu and Guodong Han. All rights reserved. Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method Mon, 24 Feb 2014 09:32:29 +0000 http://www.hindawi.com/journals/tswj/2014/308205/ This paper proposes a new technique based on double parametric form of fuzzy numbers to handle the uncertain vibration equation for very large membrane for different particular cases. Uncertainties present in the initial condition and the wave velocity of free vibration are modelled through Gaussian convex normalised fuzzy set. Using the single parametric form of fuzzy number, the original fuzzy vibration equation is converted first to an interval fuzzy vibration equation. Next this equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same governing equation is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds. The present methods are very simple and effective. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the present analysis. Results obtained by the methods with new techniques are compared with existing results in special cases. Smita Tapaswini and S. Chakraverty Copyright © 2014 Smita Tapaswini and S. Chakraverty. All rights reserved. Multiple Control Strategies for Prevention of Avian Influenza Pandemic Mon, 24 Feb 2014 08:12:47 +0000 http://www.hindawi.com/journals/tswj/2014/949718/ We present the prevention of avian influenza pandemic by adjusting multiple control functions in the human-to-human transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and numerical techniques, we investigate the cost-effective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method. Roman Ullah, Gul Zaman, and Saeed Islam Copyright © 2014 Roman Ullah et al. All rights reserved. Analysis of Eyring-Powell Fluid in Helical Screw Rheometer Mon, 24 Feb 2014 08:07:51 +0000 http://www.hindawi.com/journals/tswj/2014/143968/ This paper aims to study the flow of an incompressible, isothermal Eyring-Powell fluid in a helical screw rheometer. The complicated geometry of the helical screw rheometer is simplified by “unwrapping or flattening” the channel, lands, and the outside rotating barrel, assuming the width of the channel is larger as compared to the depth. The developed second order nonlinear differential equations are solved by using Adomian decomposition method. Analytical expressions are obtained for the velocity profiles, shear stresses, shear at wall, force exerted on fluid, volume flow rates, and average velocity. The effect of non-Newtonian parameters, pressure gradients, and flight angle on the velocity profiles is noticed with the help of graphical representation. The observation confirmed the vital role of involved parameters during the extrusion process. A. M. Siddiqui, T. Haroon, and M. Zeb Copyright © 2014 A. M. Siddiqui et al. All rights reserved. A Gauss-Kuzmin Theorem for Continued Fractions Associated with Nonpositive Integer Powers of an Integer Sun, 23 Feb 2014 13:57:39 +0000 http://www.hindawi.com/journals/tswj/2014/984650/ We consider a family of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from , we solve a Gauss-Kuzmin-type problem. Dan Lascu Copyright © 2014 Dan Lascu. All rights reserved. Control Problems for Semilinear Neutral Differential Equations in Hilbert Spaces Sun, 23 Feb 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/431978/ We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied. Jin-Mun Jeong and Seong Ho Cho Copyright © 2014 Jin-Mun Jeong and Seong Ho Cho. All rights reserved. Some New Type Sigma Convergent Sequence Spaces and Some New Inequalities Thu, 20 Feb 2014 13:38:49 +0000 http://www.hindawi.com/journals/tswj/2014/589765/ We have discussed some important problems about the spaces and of Cesàro sigma convergent and Cesàro null sequence. Kuddusi Kayaduman and Mehmet Şengönül Copyright © 2014 Kuddusi Kayaduman and Mehmet Şengönül. All rights reserved. Definition and Properties of the Libera Operator on Mixed Norm Spaces Thu, 20 Feb 2014 11:14:48 +0000 http://www.hindawi.com/journals/tswj/2014/590656/ We consider the action of the operator on a class of “mixed norm” spaces of analytic functions on the unit disk, , defined by the requirement , where , , , and is a nonnegative integer. This class contains Besov spaces, weighted Bergman spaces, Dirichlet type spaces, Hardy-Sobolev spaces, and so forth. The expression need not be defined for analytic in the unit disk, even for . A sufficient, but not necessary, condition is that . We identify the indices , , , and for which is well defined on , acts from to , the implication holds. Assertion extends some known results, due to Siskakis and others, and contains some new ones. As an application of we have a generalization of Bernstein’s theorem on absolute convergence of power series that belong to a Hölder class. Miroslav Pavlovic Copyright © 2014 Miroslav Pavlovic. All rights reserved. Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology Thu, 20 Feb 2014 08:54:44 +0000 http://www.hindawi.com/journals/tswj/2014/945872/ We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples. Randhir Singh, Jitendra Kumar, and Gnaneshwar Nelakanti Copyright © 2014 Randhir Singh et al. All rights reserved. Strong Convergence Algorithm for Split Equilibrium Problems and Hierarchical Fixed Point Problems Thu, 20 Feb 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/390956/ The purpose of this paper is to investigate the problem of finding the approximate element of the common set of solutions of a split equilibrium problem and a hierarchical fixed point problem in a real Hilbert space. We establish the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Our main result extends and improves some well-known results in the literature. Abdellah Bnouhachem Copyright © 2014 Abdellah Bnouhachem. All rights reserved. New Stabilization for Dynamical System with Two Additive Time-Varying Delays Tue, 18 Feb 2014 14:51:18 +0000 http://www.hindawi.com/journals/tswj/2014/315817/ This paper provides a new delay-dependent stabilization criterion for systems with two additive time-varying delays. The novel functional is constructed, a tighter upper bound of the derivative of the Lyapunov functional is obtained. These results have advantages over some existing ones because the combination of the delay decomposition technique and the reciprocally convex approach. Two examples are provided to demonstrate the less conservatism and effectiveness of the results in this paper. Lianglin Xiong, Fan Yang, and Xiaozhou Chen Copyright © 2014 Lianglin Xiong et al. All rights reserved. A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation Tue, 18 Feb 2014 13:07:49 +0000 http://www.hindawi.com/journals/tswj/2014/297825/ We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in -norm for the scalar unknown and a priori error estimates in -norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in -norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. Jinfeng Wang, Yang Liu, Hong Li, and Zhichao Fang Copyright © 2014 Jinfeng Wang et al. All rights reserved. Local Generalized ()-Derivations Sun, 16 Feb 2014 15:25:18 +0000 http://www.hindawi.com/journals/tswj/2014/805780/ We study local generalized ()-derivations on algebras generated by their idempotents and give some important applications of our results. Ajda Fošner Copyright © 2014 Ajda Fošner. All rights reserved. A Class of Nonlocal Coupled Semilinear Parabolic System with Nonlocal Boundaries Sun, 16 Feb 2014 13:21:03 +0000 http://www.hindawi.com/journals/tswj/2014/912356/ We investigate the positive solutions of the semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary conditions. The blow-up and global existence criteria are obtained. Hong Liu and Haihua Lu Copyright © 2014 Hong Liu and Haihua Lu. All rights reserved. High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations Thu, 13 Feb 2014 16:07:21 +0000 http://www.hindawi.com/journals/tswj/2014/642989/ A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space derivative. The spectral stability and the Fourier stability analysis of the difference scheme are shown. Finally a detailed numerical analysis, including tables, figures, and error comparison, is given to demonstrate the theoretical results and high accuracy of the proposed scheme. Ibrahim Karatay and Serife R. Bayramoglu Copyright © 2014 Ibrahim Karatay and Serife R. Bayramoglu. All rights reserved. About Positivity of Green's Functions for Nonlocal Boundary Value Problems with Impulsive Delay Equations Thu, 13 Feb 2014 09:22:53 +0000 http://www.hindawi.com/journals/tswj/2014/978519/ The impulsive delay differential equation is considered with nonlocal boundary condition Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained. Alexander Domoshnitsky and Irina Volinsky Copyright © 2014 Alexander Domoshnitsky and Irina Volinsky. All rights reserved. Stability, Boundedness, and Lagrange Stability of Fractional Differential Equations with Initial Time Difference Wed, 12 Feb 2014 06:55:23 +0000 http://www.hindawi.com/journals/tswj/2014/939027/ Differential inequalities, comparison results, and sufficient conditions on initial time difference stability, boundedness, and Lagrange stability for fractional differential systems have been evaluated. Muhammed Çiçek, Coşkun Yakar, and Bülent Oğur Copyright © 2014 Muhammed Çiçek et al. All rights reserved. Some New Traveling Wave Exact Solutions of the (2+1)-Dimensional Boiti-Leon-Pempinelli Equations Tue, 11 Feb 2014 11:44:48 +0000 http://www.hindawi.com/journals/tswj/2014/743254/ We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions and simply periodic solutions which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results. Jian-ming Qi, Fu Zhang, Wen-jun Yuan, and Zi-feng Huang Copyright © 2014 Jian-ming Qi et al. All rights reserved. Fixed Point Results for Generalized Chatterjea Type Contractive Conditions in Partially Ordered -Metric Spaces Tue, 11 Feb 2014 09:16:01 +0000 http://www.hindawi.com/journals/tswj/2014/341751/ In the framework of ordered -metric spaces, fixed points of maps that satisfy the generalized -Chatterjea type contractive conditions are obtained. The results presented in the paper generalize and extend several well known comparable results in the literature. Safeer Hussain Khan, Mujahid Abbas, and Talat Nazir Copyright © 2014 Safeer Hussain Khan et al. All rights reserved. A Study of Frontier and Semifrontier in Intuitionistic Fuzzy Topological Spaces Tue, 11 Feb 2014 06:39:22 +0000 http://www.hindawi.com/journals/tswj/2014/674171/ Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms. Athar Kharal Copyright © 2014 Athar Kharal. All rights reserved. Approximation of Bivariate Functions via Smooth Extensions Mon, 10 Feb 2014 13:53:22 +0000 http://www.hindawi.com/journals/tswj/2014/102062/ For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained. Zhihua Zhang Copyright © 2014 Zhihua Zhang. All rights reserved. Some Properties of Solutions of a Functional-Differential Equation of Second Order with Delay Mon, 10 Feb 2014 13:05:29 +0000 http://www.hindawi.com/journals/tswj/2014/878395/ Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov’s fixed point theorem and weakly Picard operator theory. Veronica Ana Ilea and Diana Otrocol Copyright © 2014 Veronica Ana Ilea and Diana Otrocol. All rights reserved. Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces Mon, 10 Feb 2014 09:05:32 +0000 http://www.hindawi.com/journals/tswj/2014/272479/ We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well. Ezzat R. Hassan, M. Sh. Alhuthali, and M. M. Al-Ghanmi Copyright © 2014 Ezzat R. Hassan et al. All rights reserved. On -Statistical Convergence of Order Sun, 09 Feb 2014 09:48:44 +0000 http://www.hindawi.com/journals/tswj/2014/535419/ The idea of -convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of -statistical convergence of order and strong -Cesàro summability of order of real sequences and investigated their relationship. Mikail Et, Abdullah Alotaibi, and S. A. Mohiuddine Copyright © 2014 Mikail Et et al. All rights reserved. On the Singular Perturbations for Fractional Differential Equation Sun, 09 Feb 2014 07:47:10 +0000 http://www.hindawi.com/journals/tswj/2014/752371/ The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. Abdon Atangana Copyright © 2014 Abdon Atangana. All rights reserved. A New High-Order Stable Numerical Method for Matrix Inversion Thu, 06 Feb 2014 17:06:47 +0000 http://www.hindawi.com/journals/tswj/2014/830564/ A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples. F. Khaksar Haghani and F. Soleymani Copyright © 2014 F. Khaksar Haghani and F. Soleymani. All rights reserved. -Fuzzy Fixed Points Theorems for -Fuzzy Mappings via -Admissible Pair Wed, 05 Feb 2014 11:43:34 +0000 http://www.hindawi.com/journals/tswj/2014/853032/ We define the concept of -admissible for a pair of -fuzzy mappings and establish the existence of common -fuzzy fixed point theorem. Our result generalizes some useful results in the literature. We provide an example to support our result. Maliha Rashid, Akbar Azam, and Nayyar Mehmood Copyright © 2014 Maliha Rashid et al. All rights reserved. Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations Tue, 04 Feb 2014 11:20:53 +0000 http://www.hindawi.com/journals/tswj/2014/497393/ Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. I. Amirali, G. M. Amiraliyev, M. Cakir, and E. Cimen Copyright © 2014 I. Amirali et al. All rights reserved. Coefficient Inequalities for a Subclass of p-Valent Analytic Functions Tue, 04 Feb 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/801751/ The aim of this paper is to study the problem of coefficient bounds for a newly defined subclass of p-valent analytic functions. Many known results appear as special consequences of our work. Muhammad Arif, Janusz Sokół, and Muhammad Ayaz Copyright © 2014 Muhammad Arif et al. All rights reserved. On the Long Time Simulation of Reaction-Diffusion Equations with Delay Mon, 03 Feb 2014 06:42:28 +0000 http://www.hindawi.com/journals/tswj/2014/186802/ For a consistent numerical method to be practically useful, it is widely accepted that it must preserve the asymptotic stability of the original continuous problem. However, in this study, we show that it may lead to unreliable numerical solutions in long time simulation even if a classical numerical method gives a larger stability region than that of the original continuous problem. Some numerical experiments on the reaction-diffusion equations with delay are presented to confirm our findings. Finally, some open problems on the subject are proposed. Dongfang Li and Chengjian Zhang Copyright © 2014 Dongfang Li and Chengjian Zhang. All rights reserved. Dynamics of a Diffusive Predator-Prey Model with General Nonlinear Functional Response Mon, 03 Feb 2014 06:29:19 +0000 http://www.hindawi.com/journals/tswj/2014/721403/ We study a diffusive predator-prey model with nonconstant death rate and general nonlinear functional response. Firstly, stability analysis of the equilibrium for reduced ODE system is discussed. Secondly, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we show that there are no nontrivial steady state solutions for certain parameter configuration. Wensheng Yang Copyright © 2014 Wensheng Yang. All rights reserved. PPF Dependent Fixed Point Results for Triangular -Admissible Mappings Sun, 02 Feb 2014 08:35:09 +0000 http://www.hindawi.com/journals/tswj/2014/673647/ We introduce the concept of triangular -admissible mappings (pair of mappings) with respect to nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular -admissible mappings (pair of mappings) with respect to nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given. Ljubomir Ćirić, Saud M. Alsulami, Peyman Salimi, and Pasquale Vetro Copyright © 2014 Ljubomir Ćirić et al. All rights reserved. Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology Sun, 02 Feb 2014 07:20:04 +0000 http://www.hindawi.com/journals/tswj/2014/837021/ We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions. Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Amir, and Ihsanul Haq Copyright © 2014 Suheel Abdullah Malik et al. All rights reserved. The Non-Relativistic Limit for the e-MHD Equations Thu, 30 Jan 2014 09:36:27 +0000 http://www.hindawi.com/journals/tswj/2014/261082/ We investigate the non-relativistic limit for the e-MHD equations in a three-dimension unit periodic torus. With the prepared initial data, our result shows that the small parameter problems have unique solutions existing in the finite time interval where the corresponding limit problems (incompressible Euler equations) have smooth solutions. Moreover, the formal limit is rigorously justified. Hongli Wang and Jie Zhao Copyright © 2014 Hongli Wang and Jie Zhao. All rights reserved. Milloux Inequality of E-Valued Meromorphic Function Thu, 30 Jan 2014 08:29:18 +0000 http://www.hindawi.com/journals/tswj/2014/861573/ The main purpose of this paper is to establish the Milloux inequality of -valued meromorphic function from the complex plane to an infinite dimensional complex Banach space with a Schauder basis. As an application, we study the Borel exceptional values of an -valued meromorphic function and those of its derivatives; results are obtained to extend some related results for meromorphic scalar-valued function of Singh, Gopalakrishna, and Bhoosnurmath. Zhaojun Wu and Zuxing Xuan Copyright © 2014 Zhaojun Wu and Zuxing Xuan. All rights reserved. -Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation Wed, 29 Jan 2014 13:09:12 +0000 http://www.hindawi.com/journals/tswj/2014/534063/ -expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. Ali Filiz, Mehmet Ekici, and Abdullah Sonmezoglu Copyright © 2014 Ali Filiz et al. All rights reserved. Partial Rectangular Metric Spaces and Fixed Point Theorems Wed, 29 Jan 2014 09:59:44 +0000 http://www.hindawi.com/journals/tswj/2014/756298/ The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results. Satish Shukla Copyright © 2014 Satish Shukla. All rights reserved. High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils Wed, 29 Jan 2014 06:55:21 +0000 http://www.hindawi.com/journals/tswj/2014/142907/ We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils. Keijo Kalervo Mattila, Luiz Adolfo Hegele Júnior, and Paulo Cesar Philippi Copyright © 2014 Keijo Kalervo Mattila et al. All rights reserved. -Sumudu Transforms of -Analogues of Bessel Functions Wed, 29 Jan 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/327019/ The main purpose of this paper is to evaluate -Sumudu transforms of a product of -Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of -Sumudu transforms to the solutions of the -integrodifferential equations involving -Bessel functions. The results may help to extend the -theory of orthogonal functions. Faruk Uçar Copyright © 2014 Faruk Uçar. All rights reserved. On -Algebras of Holomorphic Functions Tue, 28 Jan 2014 10:53:35 +0000 http://www.hindawi.com/journals/tswj/2014/901726/ We consider the classes of holomorphic functions on the open unit disk in the complex plane. These classes are in fact generalizations of the class introduced by Kim (1986). The space equipped with the topology given by the metric defined by , with and , becomes an -space. By a result of Stoll (1977), the Privalov space with the topology given by the Stoll metric is an -algebra. By using these two facts, we prove that the spaces and coincide and have the same topological structure. Consequently, we describe a general form of continuous linear functionals on (with respect to the metric ). Furthermore, we give a characterization of bounded subsets of the spaces . Moreover, we give the examples of bounded subsets of that are not relatively compact. Romeo Meštrović Copyright © 2014 Romeo Meštrović. All rights reserved. Spaces of Ideal Convergent Sequences Tue, 28 Jan 2014 09:25:12 +0000 http://www.hindawi.com/journals/tswj/2014/134534/ In the present paper, we introduce some sequence spaces using ideal convergence and Musielak-Orlicz function . We also examine some topological properties of the resulting sequence spaces. M. Mursaleen and Sunil K. Sharma Copyright © 2014 M. Mursaleen and Sunil K. Sharma. All rights reserved. Existence of Limit Cycles in the Solow Model with Delayed-Logistic Population Growth Tue, 28 Jan 2014 09:15:41 +0000 http://www.hindawi.com/journals/tswj/2014/207806/ This paper is devoted to the existence and stability analysis of limit cycles in a delayed mathematical model for the economy growth. Specifically the Solow model is further improved by inserting the time delay into the logistic population growth rate. Moreover, by choosing the time delay as a bifurcation parameter, we prove that the system loses its stability and a Hopf bifurcation occurs when time delay passes through critical values. Finally, numerical simulations are carried out for supporting the analytical results. Carlo Bianca and Luca Guerrini Copyright © 2014 Carlo Bianca and Luca Guerrini. All rights reserved. Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities Tue, 28 Jan 2014 07:25:00 +0000 http://www.hindawi.com/journals/tswj/2014/278305/ The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results. Xian Liu, Jiajia Du, and Qing Gao Copyright © 2014 Xian Liu et al. All rights reserved. An Analytical Study for (2 + 1)-Dimensional Schrödinger Equation Mon, 27 Jan 2014 08:30:17 +0000 http://www.hindawi.com/journals/tswj/2014/438345/ In this paper, the homotopy analysis method has been applied to solve (2 + 1)-dimensional Schrödinger equations. The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms. The results obtained by homotopy analysis method have been compared with those of exact solutions. The main objective is to propose alternative methods of finding a solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results show that the solution of homotopy analysis method is in a good agreement with the exact solution. Behzad Ghanbari Copyright © 2014 Behzad Ghanbari. All rights reserved. Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems Mon, 27 Jan 2014 07:59:19 +0000 http://www.hindawi.com/journals/tswj/2014/309264/ Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made. Waleed M. Abd-Elhameed, Eid H. Doha, and Mahmoud A. Bassuony Copyright © 2014 Waleed M. Abd-Elhameed et al. All rights reserved. Stability of a Quartic Functional Equation Thu, 23 Jan 2014 16:26:11 +0000 http://www.hindawi.com/journals/tswj/2014/752146/ We obtain the general solution of the generalized quartic functional equation + for a fixed positive integer . We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces. Abasalt Bodaghi Copyright © 2014 Abasalt Bodaghi. All rights reserved. A New Sixth Order Method for Nonlinear Equations in R Thu, 23 Jan 2014 12:31:16 +0000 http://www.hindawi.com/journals/tswj/2014/890138/ A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton’s method and other sixth order methods considered. Sukhjit Singh and D. K. Gupta Copyright © 2014 Sukhjit Singh and D. K. Gupta. All rights reserved. A Hybrid Common Fixed Point Theorem under Certain Recent Properties Thu, 23 Jan 2014 11:16:01 +0000 http://www.hindawi.com/journals/tswj/2014/860436/ We prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings via common limit range property. Our result improves some results from the existing literature, especially the ones contained in Sintunavarat and Kumam (2009). Some illustrative and interesting examples to highlight the realized improvements are also furnished. Zoran Kadelburg, Sunny Chauhan, and Mohammad Imdad Copyright © 2014 Zoran Kadelburg et al. All rights reserved. Generalized Ulam-Hyers Stability, Well-Posedness, and Limit Shadowing of Fixed Point Problems for α-β-Contraction Mapping in Metric Spaces Thu, 23 Jan 2014 10:58:09 +0000 http://www.hindawi.com/journals/tswj/2014/569174/ We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle. Wutiphol Sintunavarat Copyright © 2014 Wutiphol Sintunavarat. All rights reserved. Roughness of -Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces Thu, 23 Jan 2014 09:15:01 +0000 http://www.hindawi.com/journals/tswj/2014/819046/ In this paper we study the roughness of -nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinite-dimensional spaces. An explicit form is given for each of the dichotomy constants of the perturbed equation in terms of the original ones. We emphasize that we do not assume any boundedness condition on the coefficients. Nicolae Lupa Copyright © 2014 Nicolae Lupa. All rights reserved. Feedback Control in a General Almost Periodic Discrete System of Plankton Allelopathy Thu, 23 Jan 2014 06:45:09 +0000 http://www.hindawi.com/journals/tswj/2014/824801/ We study the properties of almost periodic solutions for a general discrete system of plankton allelopathy with feedback controls and establish a theorem on the uniformly asymptotic stability of almost periodic solutions. Wenshuang Yin Copyright © 2014 Wenshuang Yin. All rights reserved. Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations Thu, 23 Jan 2014 06:42:27 +0000 http://www.hindawi.com/journals/tswj/2014/817542/ By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by where is the standard Riemann-Liouville fractional derivative, for and , subject to the boundary conditions , for , and , for , or , for , and , , for , Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result. Chengbo Zhai and Mengru Hao Copyright © 2014 Chengbo Zhai and Mengru Hao. All rights reserved. Some Inequalities for the -Analogue of the Classical Riemann Zeta Functions and the -Polygamma Functions Wed, 22 Jan 2014 10:20:05 +0000 http://www.hindawi.com/journals/tswj/2014/543593/ We present the generalizations on some inequalities for the -analogue of the classical Riemann zeta functions and the -polygamma functions. Banyat Sroysang Copyright © 2014 Banyat Sroysang. All rights reserved. Approximate Solution of Time-Fractional Advection-Dispersion Equation via Fractional Variational Iteration Method Wed, 22 Jan 2014 10:04:11 +0000 http://www.hindawi.com/journals/tswj/2014/769713/ This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie’s modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs. Birol İbiş and Mustafa Bayram Copyright © 2014 Birol İbiş and Mustafa Bayram. All rights reserved. Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach Tue, 21 Jan 2014 13:08:50 +0000 http://www.hindawi.com/journals/tswj/2014/935163/ The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology. Ricardo Aguilar-López, Rafael Martínez-Guerra, and Juan L. Mata-Machuca Copyright © 2014 Ricardo Aguilar-López et al. All rights reserved. A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications Tue, 21 Jan 2014 11:22:06 +0000 http://www.hindawi.com/journals/tswj/2014/194346/ We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models. Yuji Liu and Bashir Ahmad Copyright © 2014 Yuji Liu and Bashir Ahmad. All rights reserved. Dynamic Behavior of Positive Solutions for a Leslie Predator-Prey System with Mutual Interference and Feedback Controls Mon, 20 Jan 2014 13:51:11 +0000 http://www.hindawi.com/journals/tswj/2014/637026/ We consider a Leslie predator-prey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee the existence, uniqueness, and stability of a positive periodic solution. Cong Zhang, Nan-jing Huang, and Chuan-xian Deng Copyright © 2014 Cong Zhang et al. All rights reserved. Controllability and Observability of Fractional Linear Systems with Two Different Orders Mon, 20 Jan 2014 13:51:02 +0000 http://www.hindawi.com/journals/tswj/2014/618162/ This paper is concerned with the controllability and observability for a class of fractional linear systems with two different orders. The sufficient and necessary conditions for state controllability and state observability of such systems are established. The results obtained extend some existing results of controllability and observability for fractional dynamical systems. Dengguo Xu, Yanmei Li, and Weifeng Zhou Copyright © 2014 Dengguo Xu et al. All rights reserved. Practical Stability in terms of Two Measures for Set Differential Equations on Time Scales Mon, 20 Jan 2014 10:13:21 +0000 http://www.hindawi.com/journals/tswj/2014/241034/ We present a new comparison principle by introducing a notion of upper quasi-monotone nondecreasing and obtain the practical stability criteria for set valued differential equations in terms of two measures on time scales by using the vector Lyapunov function together with the new comparison principle. Peiguang Wang and Weiwei Sun Copyright © 2014 Peiguang Wang and Weiwei Sun. All rights reserved. Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method Mon, 20 Jan 2014 06:48:33 +0000 http://www.hindawi.com/journals/tswj/2014/150483/ We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method. Randhir Singh, Gnaneshwar Nelakanti, and Jitendra Kumar Copyright © 2014 Randhir Singh et al. All rights reserved. On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations Sun, 19 Jan 2014 12:22:31 +0000 http://www.hindawi.com/journals/tswj/2014/272949/ The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub’s conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of this class are shown and implemented numerically, showing their applicability and efficiency. Taher Lotfi, Alicia Cordero, Juan R. Torregrosa, Morteza Amir Abadi, and Maryam Mohammadi Zadeh Copyright © 2014 Taher Lotfi et al. All rights reserved. Modified Projection Algorithms for Solving the Split Equality Problems Sun, 19 Jan 2014 11:58:25 +0000 http://www.hindawi.com/journals/tswj/2014/328787/ The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed. Qiao-Li Dong and Songnian He Copyright © 2014 Qiao-Li Dong and Songnian He. All rights reserved. Fixed Points of Difference Operator of Meromorphic Functions Sun, 19 Jan 2014 07:00:51 +0000 http://www.hindawi.com/journals/tswj/2014/103249/ Let f be a transcendental meromorphic function of order less than one. The authors prove that the exact difference has infinitely many fixed points, if and are Borel exceptional values (or Nevanlinna deficiency values) of f. These results extend the related results obtained by Chen and Shon. Zhaojun Wu and Hongyan Xu Copyright © 2014 Zhaojun Wu and Hongyan Xu. All rights reserved. On Fractional Model Reference Adaptive Control Thu, 16 Jan 2014 11:57:53 +0000 http://www.hindawi.com/journals/tswj/2014/521625/ This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology. Bao Shi, Jian Yuan, and Chao Dong Copyright © 2014 Bao Shi et al. All rights reserved. Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation Thu, 16 Jan 2014 09:30:21 +0000 http://www.hindawi.com/journals/tswj/2014/819290/ By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: , where , and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions. M. R. S. Kulenović, Z. Nurkanović, and E. Pilav Copyright © 2014 M. R. S. Kulenović et al. All rights reserved. Interpolation by Hankel Translates of a Basis Function: Inversion Formulas and Polynomial Bounds Thu, 16 Jan 2014 09:11:05 +0000 http://www.hindawi.com/journals/tswj/2014/242750/ For , the authors have developed elsewhere a scheme for interpolation by Hankel translates of a basis function in certain spaces of continuous functions () depending on a weight . The functions and are connected through the distributional identity , where denotes the generalized Hankel transform of order . In this paper, we use the projection operators associated with an appropriate direct sum decomposition of the Zemanian space in order to derive explicit representations of the derivatives and their Hankel transforms, the former ones being valid when is restricted to a suitable interval for which is continuous. Here, denotes the th iterate of the Bessel differential operator if , while is the identity operator. These formulas, which can be regarded as inverses of generalizations of the equation , will allow us to get some polynomial bounds for such derivatives. Corresponding results are obtained for the members of the interpolation space . Cristian Arteaga and Isabel Marrero Copyright © 2014 Cristian Arteaga and Isabel Marrero. All rights reserved. Generalizations on Some Hermite-Hadamard Type Inequalities for Differentiable Convex Functions with Applications to Weighted Means Thu, 16 Jan 2014 06:44:35 +0000 http://www.hindawi.com/journals/tswj/2014/717164/ Some new Hermite-Hadamard type inequalities for differentiable convex functions were presented by Xi and Qi. In this paper, we present new generalizations on the Xi-Qi inequalities. Banyat Sroysang Copyright © 2014 Banyat Sroysang. All rights reserved. On Conformal Conic Mappings of Spherical Domains Tue, 14 Jan 2014 12:51:36 +0000 http://www.hindawi.com/journals/tswj/2014/840280/ The problem of the generation of homogeneous grids for spherical domains is considered in the class of conformal conic mappings. The equivalence between secant and tangent projections is shown and splitting the set of conformal conic mappings into equivalence classes is presented. The problem of minimization of the mapping factor variation is solved in the class of conformal conic mappings. Obtained results can be used in applied sciences, such as geophysical fluid dynamics and cartography, where the flattening of the Earth surface is required. Andrei Bourchtein and Ludmila Bourchtein Copyright © 2014 Andrei Bourchtein and Ludmila Bourchtein. All rights reserved. Infinitely Many Weak Solutions of the -Laplacian Equation with Nonlinear Boundary Conditions Tue, 14 Jan 2014 06:31:41 +0000 http://www.hindawi.com/journals/tswj/2014/194310/ We study the following -Laplacian equation with nonlinear boundary conditions: and where is a bounded domain in with smooth boundary . We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and do not need to satisfy the or condition. Feng-Yun Lu and Gui-Qian Deng Copyright © 2014 Feng-Yun Lu and Gui-Qian Deng. All rights reserved. Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument Sun, 12 Jan 2014 13:10:32 +0000 http://www.hindawi.com/journals/tswj/2014/514854/ We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green’s function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results. Kuo-Shou Chiu Copyright © 2014 Kuo-Shou Chiu. All rights reserved. Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators Sun, 12 Jan 2014 07:13:55 +0000 http://www.hindawi.com/journals/tswj/2014/519814/ The nonlocal boundary value problem for the parabolic differential equation in an arbitrary Banach space with the dependent linear positive operator is investigated. The well-posedness of this problem is established in Banach spaces of all -valued continuous functions on satisfying a Hölder condition with a weight . New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established. Allaberen Ashyralyev and Asker Hanalyev Copyright © 2014 Allaberen Ashyralyev and Asker Hanalyev. All rights reserved. On the Fourth Power Mean of the Two-Term Exponential Sums Sun, 12 Jan 2014 06:42:55 +0000 http://www.hindawi.com/journals/tswj/2014/724840/ The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of two-term exponential sums and give an interesting identity and asymptotic formula for it. Han Zhang and Wenpeng Zhang Copyright © 2014 Han Zhang and Wenpeng Zhang. All rights reserved. The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear Volterra-Fredholm Integrodifferential Equations Sun, 12 Jan 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/465951/ We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations. Behzad Ghanbari Copyright © 2014 Behzad Ghanbari. All rights reserved. Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials Sun, 12 Jan 2014 00:00:00 +0000 http://www.hindawi.com/journals/tswj/2014/413623/ A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. S. Mashayekhi, M. Razzaghi, and O. Tripak Copyright © 2014 S. Mashayekhi et al. All rights reserved. Analysis of Rattleback Chaotic Oscillations Wed, 08 Jan 2014 12:03:05 +0000 http://www.hindawi.com/journals/tswj/2014/569386/ Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback’s chaotic dynamics are studied by applying Kane’s model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors’ invariant parameters. Michael Hanias, Stavros G. Stavrinides, and Santo Banerjee Copyright © 2014 Michael Hanias et al. All rights reserved. Equivalent Conditions of Generalized Convex Fuzzy Mappings Wed, 08 Jan 2014 09:52:16 +0000 http://www.hindawi.com/journals/tswj/2014/412534/ We obtain some equivalent conditions of (strictly) pseudoconvex and quasiconvex fuzzy mappings. These results will be useful to present some characterizations of solutions for fuzzy mathematical programming. Xue Wen Liu and Dou He Copyright © 2014 Xue Wen Liu and Dou He. All rights reserved. Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations Sun, 05 Jan 2014 13:37:31 +0000 http://www.hindawi.com/journals/tswj/2014/928765/ We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. Fukang Yin, Junqiang Song, Hongze Leng, and Fengshun Lu Copyright © 2014 Fukang Yin et al. All rights reserved. Weighted Multilinear Hardy Operators on Herz Type Spaces Sun, 05 Jan 2014 08:16:48 +0000 http://www.hindawi.com/journals/tswj/2014/420408/ This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained results to the product Morrey-Herz spaces. Shuli Gong, Zunwei Fu, and Bolin Ma Copyright © 2014 Shuli Gong et al. All rights reserved. The S-Transform of Distributions Thu, 02 Jan 2014 16:14:44 +0000 http://www.hindawi.com/journals/tswj/2014/623294/ Parseval’s formula and inversion formula for the S-transform are given. A relation between the S-transform and pseudodifferential operators is obtained. The S-transform is studied on the spaces and . Sunil Kumar Singh Copyright © 2014 Sunil Kumar Singh. All rights reserved. Stability Analysis of Distributed Order Fractional Chen System Sun, 29 Dec 2013 18:16:39 +0000 http://www.hindawi.com/journals/tswj/2013/645080/ We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. H. Aminikhah, A. Refahi Sheikhani, and H. Rezazadeh Copyright © 2013 H. Aminikhah et al. All rights reserved. Coefficient Estimates for Initial Taylor-Maclaurin Coefficients for a Subclass of Analytic and Bi-Univalent Functions Defined by Al-Oboudi Differential Operator Sun, 29 Dec 2013 11:54:09 +0000 http://www.hindawi.com/journals/tswj/2013/171039/ We introduce and investigate an interesting subclass of analytic and bi-univalent functions in the open unit disk . For functions belonging to the class , we obtain estimates on the first two Taylor-Maclaurin coefficients and . Serap Bulut Copyright © 2013 Serap Bulut. All rights reserved. An Interval-Valued Intuitionistic Fuzzy TOPSIS Method Based on an Improved Score Function Wed, 25 Dec 2013 15:11:29 +0000 http://www.hindawi.com/journals/tswj/2013/879089/ This paper proposes an improved score function for the effective ranking order of interval-valued intuitionistic fuzzy sets (IVIFSs) and an interval-valued intuitionistic fuzzy TOPSIS method based on the score function to solve multicriteria decision-making problems in which all the preference information provided by decision-makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by IVIFS value and the information about criterion weights is known. We apply the proposed score function to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s) can be selected in the decision-making process. Finally, two illustrative examples for multicriteria fuzzy decision-making problems of alternatives are used as a demonstration of the applications and the effectiveness of the proposed decision-making method. Zhi-yong Bai Copyright © 2013 Zhi-yong Bai. All rights reserved. Cotton-Type and Joint Invariants for Linear Elliptic Systems Wed, 25 Dec 2013 08:32:29 +0000 http://www.hindawi.com/journals/tswj/2013/540705/ Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results. A. Aslam and F. M. Mahomed Copyright © 2013 A. Aslam and F. M. Mahomed. All rights reserved. Explicit Solutions of a Gravity-Induced Film Flow along a Convectively Heated Vertical Wall Wed, 25 Dec 2013 07:55:33 +0000 http://www.hindawi.com/journals/tswj/2013/475939/ The gravity-driven film flow has been analyzed along a vertical wall subjected to a convective boundary condition. The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly by using homotopy analysis method (HAM). The resulting solutions are investigated for heat transfer effects on velocity and temperature profiles. Ammarah Raees and Hang Xu Copyright © 2013 Ammarah Raees and Hang Xu. All rights reserved. Multiple Solutions for Nonhomogeneous Neumann Differential Inclusion Problems by the -Laplacian Tue, 24 Dec 2013 15:56:35 +0000 http://www.hindawi.com/journals/tswj/2013/753262/ A class of nonlinear Neumann problems driven by -Laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper is the variational method for locally Lipschitz functions. More precisely, Weierstrass theorem and Mountain Pass theorem are used to prove the existence of at least two nontrivial solutions. Qing-Mei Zhou Copyright © 2013 Qing-Mei Zhou. All rights reserved. An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations Sun, 22 Dec 2013 18:35:13 +0000 http://www.hindawi.com/journals/tswj/2013/837243/ We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior. Fazlollah Soleymani, Stanford Shateyi, and Gülcan Özkum Copyright © 2013 Fazlollah Soleymani et al. All rights reserved. The Oscillation on Solutions of Some Classes of Linear Differential Equations with Meromorphic Coefficients of Finite -Order Mon, 16 Dec 2013 09:07:23 +0000 http://www.hindawi.com/journals/tswj/2013/243873/ This paper considers the oscillation on meromorphic solutions of the second-order linear differential equations with the form where is a meromorphic function with -order. We obtain some theorems which are the improvement and generalization of the results given by Bank and Laine, Cao and Li, Kinnunen, and others. Hong-Yan Xu, Jin Tu, and Zu-Xing Xuan Copyright © 2013 Hong-Yan Xu et al. All rights reserved. Sufficient Condition on the Fractional Integral for the Convergence of a Function Sun, 15 Dec 2013 16:17:45 +0000 http://www.hindawi.com/journals/tswj/2013/428428/ A sufficient condition on the fractional integral of the absolute value of a function is given in this paper, which allows to assure the convergence of the function to zero. This result can be useful to assure the convergence of a function when it is hard to know its exact evolution, but conditions on its fractional integral can be stated. Manuel A. Duarte-Mermoud, Norelys Aguila-Camacho, and Javier A. Gallegos Copyright © 2013 Manuel A. Duarte-Mermoud et al. All rights reserved. Analysis of a Fractional-Order Couple Model with Acceleration in Feelings Thu, 12 Dec 2013 16:56:23 +0000 http://www.hindawi.com/journals/tswj/2013/730736/ A fractional-order nonlinear dynamical model of couple has been introduced. Upper bounds are obtained for a fractional-order nonlinear dynamical model. Also different from other models, a model with the order 2α is discussed. We are expecting an acceleration in feelings; that is why we increase the order of the derivative between . Stability analysis of the fractional-order nonlinear dynamical model of involving two persons is studied using the fractional Routh-Hurwitz criteria. By using stability analysis on fractional-order system, we obtain sufficient condition on the parameters for the locally asymptotic stability of equilibrium points. Finally, numerical simulations are presented to verify the obtained results. Ilknur Koca and Nuri Ozalp Copyright © 2013 Ilknur Koca and Nuri Ozalp. All rights reserved. New Result of Analytic Functions Related to Hurwitz Zeta Function Thu, 12 Dec 2013 16:55:45 +0000 http://www.hindawi.com/journals/tswj/2013/475643/ By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed. F. Ghanim and M. Darus Copyright © 2013 F. Ghanim and M. Darus. All rights reserved.