The Scientific World Journal: Mathematical Analysis The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. On a New Class of -Valent Meromorphic Functions Defined in Conic Domains Tue, 26 Jul 2016 09:16:25 +0000 We define a new class of multivalent meromorphic functions using the generalised hypergeometric function. We derived this class related to conic domain. It is also shown that this new class of functions, under certain conditions, becomes a class of starlike functions. Some results on inclusion and closure properties are also derived. Mohammed Ali Alamri and Maslina Darus Copyright © 2016 Mohammed Ali Alamri and Maslina Darus. All rights reserved. A Rosenzweig-MacArthur (1963) Criterion for the Chemostat Mon, 18 Jul 2016 16:46:33 +0000 The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too. Torsten Lindström and Yuanji Cheng Copyright © 2016 Torsten Lindström and Yuanji Cheng. All rights reserved. Local Integral Estimates for Quasilinear Equations with Measure Data Tue, 17 May 2016 12:00:24 +0000 Local integral estimates as well as local nonexistence results for a class of quasilinear equations for and Hessian equations were established, where is a nonnegative locally integrable function or, more generally, a locally finite measure, is a positive Radon measure, and with and or . Qiaoyu Tian, Shengzhi Zhang, Yonglin Xu, and Jia Mu Copyright © 2016 Qiaoyu Tian et al. All rights reserved. Perturbational Blowup Solutions to the Two-Component Dullin-Gottwald-Holm System Thu, 31 Mar 2016 17:39:41 +0000 We construct a family of nonradially symmetric exact solutions for the two-component DGH system by the perturbational method. Depending on the parameters, the class of solutions includes both blowup type and global existence type. Ka Luen Cheung Copyright © 2016 Ka Luen Cheung. All rights reserved. On Vertex Covering Transversal Domination Number of Regular Graphs Tue, 29 Mar 2016 09:54:45 +0000 A simple graph is said to be -regular if each vertex of is of degree . The vertex covering transversal domination number is the minimum cardinality among all vertex covering transversal dominating sets of . In this paper, we analyse this parameter on different kinds of regular graphs especially for and . Also we provide an upper bound for of a connected cubic graph of order . Then we try to provide a more stronger relationship between and . R. Vasanthi and K. Subramanian Copyright © 2016 R. Vasanthi and K. Subramanian. All rights reserved. The Existence of Weak -Pullback Exponential Attractor for Nonautonomous Dynamical System Tue, 22 Mar 2016 13:31:59 +0000 First, for a process , we introduce a new concept, called the weak -pullback exponential attractor, which is a family of sets , for any , satisfying the following: (i) is compact, (ii) is positively invariant, that is, , and (iii) there exist such that ; that is, pullback exponential attracts . Then we give a method to obtain the existence of weak -pullback exponential attractors for a process. As an application, we obtain the existence of weak -pullback exponential attractor for reaction diffusion equation in with exponential growth of the external force. Yongjun Li, Xiaona Wei, and Yanhong Zhang Copyright © 2016 Yongjun Li et al. All rights reserved. Fuzzy - and Fuzzy Completely - Functions via Fuzzy e-Open Sets Tue, 08 Mar 2016 08:23:54 +0000 We introduced the notions of fuzzy - functions and fuzzy completely - functions via fuzzy e-open sets. Some properties and several characterization of these types of functions are investigated. V. Seenivasan and K. Kamala Copyright © 2016 V. Seenivasan and K. Kamala. All rights reserved. Blowup Phenomenon of Solutions for the IBVP of the Compressible Euler Equations in Spherical Symmetry Wed, 03 Feb 2016 12:41:02 +0000 The blowup phenomenon of solutions is investigated for the initial-boundary value problem (IBVP) of the -dimensional Euler equations with spherical symmetry. We first show that there are only trivial solutions when the velocity is of the form for any value of or any positive integer . Then, we show that blowup phenomenon occurs when and . As a corollary, the blowup properties of solutions with velocity of the form are obtained. Our analysis includes both the isentropic case and the isothermal case . Ka Luen Cheung and Sen Wong Copyright © 2016 Ka Luen Cheung and Sen Wong. All rights reserved. Numerical Algorithm for Delta of Asian Option Thu, 09 Jul 2015 08:28:26 +0000 We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of of Asian geometric option and use this analytical form as a control to numerically calculate of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. Boxiang Zhang, Yang Yu, and Weiguo Wang Copyright © 2015 Boxiang Zhang et al. All rights reserved. On Intuitionistic Fuzzy -Almost Compactness and -Nearly Compactness Tue, 07 Jul 2015 06:54:45 +0000 The concept of intuitionistic fuzzy β-almost compactness and intuitionistic fuzzy β-nearly compactness in intuitionistic fuzzy topological spaces is introduced and studied. Besides giving characterizations of these spaces, we study some of their properties. Also, we investigate the behavior of intuitionistic fuzzy β-compactness, intuitionistic fuzzy β-almost compactness, and intuitionistic fuzzy β-nearly compactness under several types of intuitionistic fuzzy continuous mappings. R. Renuka and V. Seenivasan Copyright © 2015 R. Renuka and V. Seenivasan. All rights reserved. Mathematical Problems for Complex Systems Wed, 24 Jun 2015 06:34:56 +0000 Haijun Jiang, Haibo He, Jianlong Qiu, Qiankun Song, and Jianquan Lu Copyright © 2015 Haijun Jiang et al. All rights reserved. Consensus of Nonlinear Complex Systems with Edge Betweenness Centrality Measure under Time-Varying Sampled-Data Protocol Thu, 18 Jun 2015 12:18:43 +0000 This paper proposes a new consensus criterion for nonlinear complex systems with edge betweenness centrality measure. By construction of a suitable Lyapunov-Krasovskii functional, the consensus criterion for such systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed methods. M. J. Park, O. M. Kwon, and E. J. Cha Copyright © 2015 M. J. Park et al. All rights reserved. Results for Two-Level Designs with General Minimum Lower-Order Confounding Tue, 16 Jun 2015 14:18:35 +0000 The general minimum lower-order confounding (GMC) criterion for two-level design not only reveals the confounding information of factor effects but also provides a good way to select the optimal design, which was proposed by Zhang et al. (2008). The criterion is based on the aliased effect-number pattern (AENP). Therefore, it is very important to study properties of AENP for two-level GMC design. According to the ordering of elements in the AENP, the confounding information between lower-order factor effects is more important than that of higher-order effects. For two-level GMC design, this paper mainly shows the interior principles to calculate the leading elements and in the AENP. Further, their mathematical formulations are obtained for every GMC design with according to two cases: (i) and (ii) . Zhi Ming Li and Run Chu Zhang Copyright © 2015 Zhi Ming Li and Run Chu Zhang. All rights reserved. A Learning Framework of Nonparallel Hyperplanes Classifier Tue, 16 Jun 2015 12:24:42 +0000 A novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem when different parameters or loss functions are chosen. Concretely, we discuss the linear and nonlinear cases of the framework, in which we select the hinge loss function as example. Moreover, we also give the primal problems of several extension versions of TWSVM’s deformation versions. It is worth mentioning that, in the decision function, the Euclidean distance is replaced by the absolute value , which keeps the consistency between the decision function and the optimization problem and reduces the computational cost particularly when the kernel function is introduced. The numerical experiments on several artificial and benchmark datasets indicate that our framework is not only fast but also shows good generalization. Zhi-Xia Yang, Yuan-Hai Shao, and Yao-Lin Jiang Copyright © 2015 Zhi-Xia Yang et al. All rights reserved. Description and Application of a Mathematical Method for the Analysis of Harmony Tue, 16 Jun 2015 08:10:36 +0000 Harmony issues are widespread in human society and nature. To analyze these issues, harmony theory has been proposed as the main theoretical approach for the study of interpersonal relationships and relationships between humans and nature. Therefore, it is of great importance to study harmony theory. After briefly introducing the basic concepts of harmony theory, this paper expounds the five elements that are essential for the quantitative description of harmony issues in water resources management: harmony participant, harmony objective, harmony regulation, harmony factor, and harmony action. A basic mathematical equation for the harmony degree, that is, a quantitative expression of harmony issues, is introduced in the paper: , where is the uniform degree, is the difference degree, is the harmony coefficient, and is the disharmony coefficient. This paper also discusses harmony assessment and harmony regulation and introduces some application examples. Qiting Zuo, Runfang Jin, Junxia Ma, and Guotao Cui Copyright © 2015 Qiting Zuo et al. All rights reserved. Comment on “On Soft -Open Sets and Soft -Continuous Functions” Thu, 28 May 2015 10:33:46 +0000 A. K. Mousa and A. Ghareeb Copyright © 2015 A. K. Mousa and A. Ghareeb. All rights reserved. Recent Theories and Applications in Approximation Theory Wed, 08 Apr 2015 07:00:13 +0000 Fazlollah Soleymani, Predrag S. Stanimirović, Juan R. Torregrosa, Hassan Saberi Nik, and Emran Tohidi Copyright © 2015 Fazlollah Soleymani et al. All rights reserved. The Mixed Finite Element Multigrid Method for Stokes Equations Tue, 07 Apr 2015 13:09:57 +0000 The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. K. Muzhinji, S. Shateyi, and S. S. Motsa Copyright © 2015 K. Muzhinji et al. All rights reserved. On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows Mon, 30 Mar 2015 07:58:04 +0000 A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. J. Venetis Copyright © 2015 J. Venetis. All rights reserved. On a Cubically Convergent Iterative Method for Matrix Sign Sun, 29 Mar 2015 08:32:23 +0000 We propose an iterative method for finding matrix sign function. It is shown that the scheme has global behavior with cubical rate of convergence. Examples are included to show the applicability and efficiency of the proposed scheme and its reciprocal. M. Sharifi, S. Karimi Vanani, F. Khaksar Haghani, M. Arab, and S. Shateyi Copyright © 2015 M. Sharifi et al. All rights reserved. New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations Thu, 26 Mar 2015 08:46:03 +0000 This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations. Mohamed S. Al-luhaibi Copyright © 2015 Mohamed S. Al-luhaibi. All rights reserved. Geometric Construction of Eighth-Order Optimal Families of Ostrowski’s Method Thu, 26 Mar 2015 08:06:08 +0000 Based on well-known fourth-order Ostrowski’s method, we proposed many new interesting optimal families of eighth-order multipoint methods without memory for obtaining simple roots. Its geometric construction consists in approximating at zn in such a way that its average with the known tangent slopes at xn and yn is the same as the known weighted average of secant slopes and then we apply weight function approach. The adaptation of this strategy increases the convergence order of Ostrowski's method from four to eight and its efficiency index from 1.587 to 1.682. Finally, a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal eighth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, it is also noted that larger basins of attraction belong to our methods although the other methods are slow and have darker basins while some of the methods are too sensitive upon the choice of the initial value. Ramandeep Behl and S. S. Motsa Copyright © 2015 Ramandeep Behl and S. S. Motsa. All rights reserved. Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions Wed, 25 Mar 2015 09:38:37 +0000 Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem. Yueqing Zhao, Rongfei Lin, Zdenek Šmarda, Yasir Khan, Jinbiao Chen, and Qingbiao Wu Copyright © 2015 Yueqing Zhao et al. All rights reserved. On a Derivative-Free Variant of King’s Family with Memory Wed, 25 Mar 2015 07:38:33 +0000 The aim of this paper is to construct a method with memory according to King’s family of methods without memory for nonlinear equations. It is proved that the proposed method possesses higher R-order of convergence using the same number of functional evaluations as King’s family. Numerical experiments are given to illustrate the performance of the constructed scheme. M. Sharifi, S. Karimi Vanani, F. Khaksar Haghani, M. Arab, and S. Shateyi Copyright © 2015 M. Sharifi et al. All rights reserved. Stabilities for Nonisentropic Euler-Poisson Equations Mon, 16 Mar 2015 14:30:46 +0000 We establish the stabilities and blowup results for the nonisentropic Euler-Poisson equations by the energy method. By analysing the second inertia, we show that the classical solutions of the system with attractive forces blow up in finite time in some special dimensions when the energy is negative. Moreover, we obtain the stabilities results for the system in the cases of attractive and repulsive forces. Ka Luen Cheung and Sen Wong Copyright © 2015 Ka Luen Cheung and Sen Wong. All rights reserved. A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube Thu, 19 Feb 2015 08:15:30 +0000 A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindrical coordinates and then simplified by employing the long wavelength and low Reynolds number assumptions. Exact solutions are derived for the velocity components, the axial pressure gradient, and the stream function. However, the expressions for the pressure rise and the volume flow rate are evaluated numerically. The features of the flow characteristics such as pumping and trapping are illustrated and discussed with the help of graphs. It is observed that the volume flow rate is influenced significantly by the width of plug flow region as well as the cilia length parameter . The analysis is also applied and compared with the estimated value of the volume flow rate of epididymal fluid in the ductus efferentes of the human male reproductive tract. A. M. Siddiqui, A. A. Farooq, and M. A. Rana Copyright © 2015 A. M. Siddiqui et al. All rights reserved. Recent Developments on Sequence Spaces and Compact Operators with Applications Thu, 29 Jan 2015 11:26:10 +0000 S. A. Mohiuddine, M. Mursaleen, Józef Banaś, Suthep Suantai, and Abdullah Alotaibi Copyright © 2015 S. A. Mohiuddine et al. All rights reserved. A General Class of Derivative Free Optimal Root Finding Methods Based on Rational Interpolation Wed, 28 Jan 2015 12:31:11 +0000 We construct a new general class of derivative free -point iterative methods of optimal order of convergence using rational interpolant. The special cases of this class are obtained. These methods do not need Newton’s iterate in the …first step of their iterative schemes. Numerical computations are presented to show that the new methods are efficient and can be seen as better alternates. Fiza Zafar, Nusrat Yasmin, Saima Akram, and Moin-ud-Din Junjua Copyright © 2015 Fiza Zafar et al. All rights reserved. Some New Sets of Sequences of Fuzzy Numbers with Respect to the Partial Metric Wed, 28 Jan 2015 12:18:19 +0000 In this paper, we essentially deal with Köthe-Toeplitz duals of fuzzy level sets defined using a partial metric. Since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct some classical notions. In this paper, we present the sets of bounded, convergent, and null series and the set of sequences of bounded variation of fuzzy level sets, based on the partial metric. We examine the relationships between these sets and their classical forms and give some properties including definitions, propositions, and various kinds of partial metric spaces of fuzzy level sets. Furthermore, we study some of their properties like completeness and duality. Finally, we obtain the Köthe-Toeplitz duals of fuzzy level sets with respect to the partial metric based on a partial ordering. Uğur Kadak and Muharrem Ozluk Copyright © 2015 Uğur Kadak and Muharrem Ozluk. All rights reserved. Relation of the Cyclotomic Equation with the Harmonic and Derived Series Thu, 22 Jan 2015 06:20:19 +0000 We associate some (old) convergent series related to definite integrals with the cyclotomic equation , for several natural numbers m; for example, for , leads to . In some cases, we express the results in terms of the Dirichlet characters. Generalizations for arbitrary m are well defined but do imply integrals and/or series summations rather involved. Luis J. Boya and Cristian Rivera Copyright © 2015 Luis J. Boya and Cristian Rivera. All rights reserved. -Almost Periodic Solutions of BAM Neural Networks with Time-Varying Delays on Time Scales Mon, 19 Jan 2015 09:33:40 +0000 On a new type of almost periodic time scales, a class of BAM neural networks is considered. By employing a fixed point theorem and differential inequality techniques, some sufficient conditions ensuring the existence and global exponential stability of -almost periodic solutions for this class of networks with time-varying delays are established. Two examples are given to show the effectiveness of the proposed method and results. Yongkun Li, Lili Zhao, and Li Yang Copyright © 2015 Yongkun Li et al. All rights reserved. The Diophantine Equation Wed, 14 Jan 2015 06:41:23 +0000 Let be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if , then the equation has no positive integer solutions ; (ii) if , then the equation has only the solutions , where is an odd prime with ; (iii) if and , then the equation has at most two positive integer solutions . Lan Qi and Xiaoxue Li Copyright © 2015 Lan Qi and Xiaoxue Li. All rights reserved. An Existence Theorem for Fractional -Difference Inclusions with Nonlocal Substrip Type Boundary Conditions Mon, 05 Jan 2015 13:42:35 +0000 By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractional -difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example. Ahmed Alsaedi, Sotiris K. Ntouyas, and Bashir Ahmad Copyright © 2015 Ahmed Alsaedi et al. All rights reserved. Fixed Point Theorems for Hybrid Mappings Mon, 05 Jan 2015 13:08:24 +0000 We obtain some fixed point theorems for two pairs of hybrid mappings using hybrid tangential property and quadratic type contractive condition. Our results generalize some results by Babu and Alemayehu and those contained therein. In the sequel, we introduce a new notion to generalize occasionally weak compatibility. Moreover, two concrete examples are established to illuminate the generality of our results. Maria Samreen, Tayyab Kamran, and Erdal Karapinar Copyright © 2015 Maria Samreen et al. All rights reserved. Dynamics of Nonlinear Systems Mon, 22 Dec 2014 11:25:07 +0000 Maoan Han, Zhen Jin, Yonghui Xia, and Haomin Zhou Copyright © 2014 Maoan Han et al. All rights reserved. Coefficient Bounds for Some Families of Starlike and Convex Functions of Reciprocal Order Mon, 24 Nov 2014 12:47:01 +0000 The aim of the present paper is to investigate coefficient estimates, Fekete-Szegő inequality, and upper bound of third Hankel determinant for some families of starlike and convex functions of reciprocal order. Muhammad Arif, Maslina Darus, Mohsan Raza, and Qaiser Khan Copyright © 2014 Muhammad Arif et al. All rights reserved. Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials Mon, 17 Nov 2014 06:45:45 +0000 In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. Hasib Khan, Hossein Jafari, Rahmat Ali Khan, Haleh Tajadodi, and Sarah Jane Johnston Copyright © 2014 Hasib Khan et al. All rights reserved. Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs Sun, 16 Nov 2014 00:00:00 +0000 The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed. A. Pirkhedri, H. H. S. Javadi, and H. R. Navidi Copyright © 2014 A. Pirkhedri et al. All rights reserved. On Some Growth Properties of Entire Functions Using Their Maximum Moduli Focusing th Relative Order Mon, 03 Nov 2014 06:40:25 +0000 We discuss some growth rates of composite entire functions on the basis of the definition of relative th order (relative th lower order) with respect to another entire function which improve some earlier results of Roy (2010) where and are any two positive integers. Luis Manuel Sanchez Ruiz, Sanjib Kumar Datta, Tanmay Biswas, and Golok Kumar Mondal Copyright © 2014 Luis Manuel Sanchez Ruiz et al. All rights reserved. Linear Discrete Pursuit Game with Phase Constraints Thu, 30 Oct 2014 00:00:00 +0000 We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Position of the evader satisfies phase constraints: , where is a subset of . We considered two cases: (1) controls of the players satisfy geometric constraints, and (2) controls of the players satisfy total constraints. Terminal set is a subset of and it is assumed to have a nonempty interior. Game is said to be completed if at some step ; thus, the evader has not the right to leave set . To construct the control of the pursuer, at each step , we use the value of the control parameter of the evader at the step . We obtain sufficient conditions of completion of pursuit from certain initial positions of the players in finite time interval and construct a control for the pursuer in explicit form. Asqar Raxmanov and Gafurjan Ibragimov Copyright © 2014 Asqar Raxmanov and Gafurjan Ibragimov. All rights reserved. Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems Thu, 16 Oct 2014 13:18:52 +0000 We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results. Hassan Saberi Nik and Paulo Rebelo Copyright © 2014 Hassan Saberi Nik and Paulo Rebelo. All rights reserved. New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems Tue, 14 Oct 2014 07:04:39 +0000 This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. W. M. Abd-Elhameed Copyright © 2014 W. M. Abd-Elhameed. All rights reserved. On the General Dedekind Sums and Two-Term Exponential Sums Tue, 14 Oct 2014 00:00:00 +0000 We use the analytic methods and the properties of Gauss sums to study the computational problem of one kind hybrid mean value involving the general Dedekind sums and the two-term exponential sums, and give an interesting computational formula for it. Junli Zhang and Wenpeng Zhang Copyright © 2014 Junli Zhang and Wenpeng Zhang. All rights reserved. Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations Sun, 12 Oct 2014 14:21:02 +0000 An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable. A. R. Seadawy and K. El-Rashidy Copyright © 2014 A. R. Seadawy and K. El-Rashidy. All rights reserved. Existence of Tripled Fixed Points for a Class of Condensing Operators in Banach Spaces Sun, 14 Sep 2014 12:48:26 +0000 We give some results concerning the existence of tripled fixed points for a class of condensing operators in Banach spaces. Further, as an application, we study the existence of solutions for a general system of nonlinear integral equations. Vatan Karakaya, Nour El Houda Bouzara, Kadri Doğan, and Yunus Atalan Copyright © 2014 Vatan Karakaya et al. All rights reserved. Certain Inequalities Involving Generalized Erdélyi-Kober Fractional -Integral Operators Thu, 11 Sep 2014 00:00:00 +0000 In recent years, a remarkably large number of inequalities involving the fractional -integral operators have been investigated in the literature by many authors. Here, we aim to present some new fractional integral inequalities involving generalized Erdélyi-Kober fractional -integral operator due to Gaulué, whose special cases are shown to yield corresponding inequalities associated with Kober type fractional -integral operators. The cases of synchronous functions as well as of functions bounded by integrable functions are considered. Praveen Agarwal, Soheil Salahshour, Sotiris K. Ntouyas, and Jessada Tariboon Copyright © 2014 Praveen Agarwal et al. All rights reserved. Modified Fractional Variational Iteration Method for Solving the Generalized Time-Space Fractional Schrödinger Equation Thu, 04 Sep 2014 00:00:00 +0000 Based on He’s variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations. Baojian Hong and Dianchen Lu Copyright © 2014 Baojian Hong and Dianchen Lu. All rights reserved. On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations Wed, 03 Sep 2014 07:33:03 +0000 A class of derivative-free methods without memory for approximating a simple zero of a nonlinear equation is presented. The proposed class uses four function evaluations per iteration with convergence order eight. Therefore, it is an optimal three-step scheme without memory based on Kung-Traub conjecture. Moreover, the proposed class has an accelerator parameter with the property that it can increase the convergence rate from eight to twelve without any new functional evaluations. Thus, we construct a with memory method that increases considerably efficiency index from to . Illustrations are also included to support the underlying theory. T. Lotfi, K. Mahdiani, Z. Noori, F. Khaksar Haghani, and S. Shateyi Copyright © 2014 T. Lotfi et al. All rights reserved. Global Practical Tracking by Output Feedback for Nonlinear Systems with Unknown Growth Rate and Time Delay Wed, 03 Sep 2014 00:00:00 +0000 This paper is the further investigation of work of Yan and Liu, 2011, and considers the global practical tracking problem by output feedback for a class of uncertain nonlinear systems with not only unmeasured states dependent growth but also time-varying time delay. Compared with the closely related works, the remarkableness of the paper is that the time-varying time delay and unmeasurable states are permitted in the system nonlinear growth. Motivated by the related tracking results and flexibly using the ideas and techniques of universal control and dead zone, an adaptive output-feedback tracking controller is explicitly designed with the help of a new Lyapunov-Krasovskii functional, to make the tracking error prescribed arbitrarily small after a finite time while keeping all the closed-loop signals bounded. A numerical example demonstrates the effectiveness of the results. Xuehua Yan and Xinmin Song Copyright © 2014 Xuehua Yan and Xinmin Song. All rights reserved. On the Convergence and Stability Results for a New General Iterative Process Tue, 02 Sep 2014 00:00:00 +0000 We put forward a new general iterative process. We prove a convergence result as well as a stability result regarding this new iterative process for weak contraction operators. Kadri Doğan and Vatan Karakaya Copyright © 2014 Kadri Doğan and Vatan Karakaya. All rights reserved. A New Look at the Coefficients of a Reciprocal Generating Function Thu, 28 Aug 2014 06:33:23 +0000 We study a special property of free cumulants. We prove that coefficients of a reciprocal generating function correspond to “free cumulants with the first two elements in the same block.” Wiktor Ejsmont Copyright © 2014 Wiktor Ejsmont. All rights reserved. On the Maximum Estrada Index of 3-Uniform Linear Hypertrees Thu, 28 Aug 2014 05:52:41 +0000 For a simple hypergraph on vertices, its Estrada index is defined as , where are the eigenvalues of its adjacency matrix. In this paper, we determine the unique 3-uniform linear hypertree with the maximum Estrada index. Faxu Li, Liang Wei, Jinde Cao, Feng Hu, and Haixing Zhao Copyright © 2014 Faxu Li et al. All rights reserved. On a Subclass of Meromorphic Close-to-Convex Functions Thu, 28 Aug 2014 00:00:00 +0000 The main purpose of this paper is to introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, inclusion relationship, distortion property, and radius of meromorphic convexity are derived. Ming-Liang Li, Lei Shi, and Zhi-Gang Wang Copyright © 2014 Ming-Liang Li et al. All rights reserved. Spectral Analysis of the Bounded Linear Operator in the Reproducing Kernel Space Thu, 28 Aug 2014 00:00:00 +0000 We first introduce some related definitions of the bounded linear operator in the reproducing kernel space . Then we show spectral analysis of and derive several property theorems. Lihua Guo, Songsong Li, Boying Wu, and Dazhi Zhang Copyright © 2014 Lihua Guo et al. All rights reserved. On a New Iterative Scheme without Memory with Optimal Eighth Order Thu, 28 Aug 2014 00:00:00 +0000 The purpose of this paper is to derive and discuss a three-step iterative expression for solving nonlinear equations. In fact, we derive a derivative-free form for one of the existing optimal eighth-order methods and preserve its convergence order. Theoretical results will be upheld by numerical experiments. M. Sharifi, S. Karimi Vanani, F. Khaksar Haghani, M. Arab, and S. Shateyi Copyright © 2014 M. Sharifi et al. All rights reserved. On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition Thu, 28 Aug 2014 00:00:00 +0000 We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the singular systems. It also allows us to obtain an estimate of convergence ball for inexact Newton method and some important special cases. Fangqin Zhou Copyright © 2014 Fangqin Zhou. All rights reserved. One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order Wed, 27 Aug 2014 08:52:46 +0000 Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in , one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order is considered. Numerical simulations show the validity and feasibility of the proposed scheme. Ping Zhou and Rongji Bai Copyright © 2014 Ping Zhou and Rongji Bai. All rights reserved. The Trigonometric Polynomial Like Bernstein Polynomial Wed, 27 Aug 2014 00:00:00 +0000 A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given. Xuli Han Copyright © 2014 Xuli Han. All rights reserved. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations Wed, 27 Aug 2014 00:00:00 +0000 This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. S. S. Motsa, V. M. Magagula, and P. Sibanda Copyright © 2014 S. S. Motsa et al. All rights reserved. Parameterized Hilbert-Type Integral Inequalities in the Whole Plane Tue, 19 Aug 2014 07:14:11 +0000 By the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the best possible. We also consider the equivalent forms, the reverses, and some particular cases in the homogeneous kernels. Qiliang Huang, Shanhe Wu, and Bicheng Yang Copyright © 2014 Qiliang Huang et al. All rights reserved. An Inversion-Free Method for Finding Positive Definite Solution of a Rational Matrix Equation Tue, 19 Aug 2014 00:00:00 +0000 A new iterative scheme has been constructed for finding minimal solution of a rational matrix equation of the form . The new method is inversion-free per computing step. The convergence of the method has been studied and tested via numerical experiments. Fazlollah Soleymani, Mahdi Sharifi, Solat Karimi Vanani, Farhad Khaksar Haghani, and Adem Kılıçman Copyright © 2014 Fazlollah Soleymani et al. All rights reserved. Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function Mon, 18 Aug 2014 13:02:14 +0000 The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings. Jinhong Zhang, Jianwen Jia, and Xinyu Song Copyright © 2014 Jinhong Zhang et al. All rights reserved. Oscillations for Neutral Functional Differential Equations Mon, 18 Aug 2014 12:33:51 +0000 We will consider a class of neutral functional differential equations. Some infinite integral conditions for the oscillation of all solutions are derived. Our results extend and improve some of the previous results in the literature. Fatima N. Ahmed, Rokiah R. Ahmad, Ummul K. S. Din, and Mohd S. M. Noorani Copyright © 2014 Fatima N. Ahmed et al. All rights reserved. On Some Approximation Theorems for Power -Bounded Operators on Locally Convex Vector Spaces Mon, 18 Aug 2014 08:32:02 +0000 This paper deals with the study of some operator inequalities involving the power -bounded operators along with the most known properties and results, in the more general framework of locally convex vector spaces. Ludovic Dan Lemle Copyright © 2014 Ludovic Dan Lemle. All rights reserved. Existence Results for a System of Coupled Hybrid Fractional Differential Equations Mon, 18 Aug 2014 06:31:13 +0000 This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations with Dirichlet boundary conditions. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example. Bashir Ahmad, Sotiris K. Ntouyas, and Ahmed Alsaedi Copyright © 2014 Bashir Ahmad et al. All rights reserved. New Conditions for Obtaining the Exact Solutions of the General Riccati Equation Mon, 18 Aug 2014 05:54:05 +0000 We propose a direct method for solving the general Riccati equation . We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions , and of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method. Lazhar Bougoffa Copyright © 2014 Lazhar Bougoffa. All rights reserved. Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model Sun, 17 Aug 2014 12:20:13 +0000 By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results. Zizhen Zhang and Huizhong Yang Copyright © 2014 Zizhen Zhang and Huizhong Yang. All rights reserved. On -Fibrations in Bitopological Semigroups Sun, 17 Aug 2014 12:11:49 +0000 We extend the path lifting property in homotopy theory for topological spaces to bitopological semigroups and we show and prove its role in the -fibration property. We give and prove the relationship between the -fibration property and an approximate fibration property. Furthermore, we study the pullback maps for -fibrations. Suliman Dawood and Adem Kılıçman Copyright © 2014 Suliman Dawood and Adem Kılıçman. All rights reserved. Generalized Contractive Mappings and Weakly -Admissible Pairs in -Metric Spaces Sun, 17 Aug 2014 00:00:00 +0000 The aim of this paper is to present some coincidence and common fixed point results for generalized (, )-contractive mappings using partially weakly --admissibility in the setup of -metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered -metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results. N. Hussain, V. Parvaneh, and S. J. Hoseini Ghoncheh Copyright © 2014 N. Hussain et al. All rights reserved. Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots Tue, 12 Aug 2014 10:55:38 +0000 We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton’s method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method. Fiza Zafar, Nawab Hussain, Zirwah Fatimah, and Athar Kharal Copyright © 2014 Fiza Zafar et al. All rights reserved. Applications of Normal S-Iterative Method to a Nonlinear Integral Equation Mon, 11 Aug 2014 11:50:20 +0000 It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven. Faik Gürsoy Copyright © 2014 Faik Gürsoy. All rights reserved. Convergence Analysis for a Modified SP Iterative Method Sun, 10 Aug 2014 13:09:59 +0000 We consider a new iterative method due to Kadioglu and Yildirim (2014) for further investigation. We study convergence analysis of this iterative method when applied to class of contraction mappings. Furthermore, we give a data dependence result for fi…xed point of contraction mappings with the help of the new iteration method. Fatma Öztürk Çeliker Copyright © 2014 Fatma Öztürk Çeliker. All rights reserved. A Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums Thu, 07 Aug 2014 11:39:03 +0000 The main purpose of this paper is using the analytic method, A. Weil’s classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the general exponential sums and give a sharp asymptotic formula for it. Jianghua Li and Tingting Wang Copyright © 2014 Jianghua Li and Tingting Wang. All rights reserved. Littlewood-Paley Operators on Morrey Spaces with Variable Exponent Thu, 07 Aug 2014 06:12:12 +0000 By applying the vector-valued inequalities for the Littlewood-Paley operators and their commutators on Lebesgue spaces with variable exponent, the boundedness of the Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley -functions and -functions, and their commutators generated by BMO functions, is obtained on the Morrey spaces with variable exponent. Shuangping Tao and Lijuan Wang Copyright © 2014 Shuangping Tao and Lijuan Wang. All rights reserved. The Adomian Decomposition Method for Solving a Moving Boundary Problem Arising from the Diffusion of Oxygen in Absorbing Tissue Mon, 04 Aug 2014 00:00:00 +0000 This paper begins by giving the results obtained by the Crank-Gupta method and Gupta-Banik method for the oxygen diffusion problem in absorbing tissue, and then we propose a new resolution method for this problem by the Adomian decomposition method. An approximate analytical solution is obtained, which is demonstrated to be quite accurate by comparison with the numerical and approximate solutions obtained by Crank and Gupta. The study confirms the accuracy and efficiency of the algorithm for analytic approximate solutions of this problem. Lazhar Bougoffa Copyright © 2014 Lazhar Bougoffa. 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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.