The Scientific World Journal: Mathematical Analysis The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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. About Positivity of Green's Functions for Nonlocal Boundary Value Problems with Impulsive Delay Equations Thu, 13 Feb 2014 09:22:53 +0000 The impulsive delay differential equation is considered with nonlocal boundary condition Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained. Alexander Domoshnitsky and Irina Volinsky Copyright © 2014 Alexander Domoshnitsky and Irina Volinsky. All rights reserved. Stability, Boundedness, and Lagrange Stability of Fractional Differential Equations with Initial Time Difference Wed, 12 Feb 2014 06:55:23 +0000 Differential inequalities, comparison results, and sufficient conditions on initial time difference stability, boundedness, and Lagrange stability for fractional differential systems have been evaluated. Muhammed Çiçek, Coşkun Yakar, and Bülent Oğur Copyright © 2014 Muhammed Çiçek et al. All rights reserved. Some New Traveling Wave Exact Solutions of the (2+1)-Dimensional Boiti-Leon-Pempinelli Equations Tue, 11 Feb 2014 11:44:48 +0000 We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions and simply periodic solutions which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results. Jian-ming Qi, Fu Zhang, Wen-jun Yuan, and Zi-feng Huang Copyright © 2014 Jian-ming Qi et al. All rights reserved. Fixed Point Results for Generalized Chatterjea Type Contractive Conditions in Partially Ordered -Metric Spaces Tue, 11 Feb 2014 09:16:01 +0000 In the framework of ordered -metric spaces, fixed points of maps that satisfy the generalized -Chatterjea type contractive conditions are obtained. The results presented in the paper generalize and extend several well known comparable results in the literature. Safeer Hussain Khan, Mujahid Abbas, and Talat Nazir Copyright © 2014 Safeer Hussain Khan et al. All rights reserved. A Study of Frontier and Semifrontier in Intuitionistic Fuzzy Topological Spaces Tue, 11 Feb 2014 06:39:22 +0000 Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms. Athar Kharal Copyright © 2014 Athar Kharal. All rights reserved. Approximation of Bivariate Functions via Smooth Extensions Mon, 10 Feb 2014 13:53:22 +0000 For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained. Zhihua Zhang Copyright © 2014 Zhihua Zhang. All rights reserved. Some Properties of Solutions of a Functional-Differential Equation of Second Order with Delay Mon, 10 Feb 2014 13:05:29 +0000 Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov’s fixed point theorem and weakly Picard operator theory. Veronica Ana Ilea and Diana Otrocol Copyright © 2014 Veronica Ana Ilea and Diana Otrocol. All rights reserved. Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces Mon, 10 Feb 2014 09:05:32 +0000 We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well. Ezzat R. Hassan, M. Sh. Alhuthali, and M. M. Al-Ghanmi Copyright © 2014 Ezzat R. Hassan et al. All rights reserved. On -Statistical Convergence of Order Sun, 09 Feb 2014 09:48:44 +0000 The idea of -convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of -statistical convergence of order and strong -Cesàro summability of order of real sequences and investigated their relationship. Mikail Et, Abdullah Alotaibi, and S. A. Mohiuddine Copyright © 2014 Mikail Et et al. All rights reserved. On the Singular Perturbations for Fractional Differential Equation Sun, 09 Feb 2014 07:47:10 +0000 The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. Abdon Atangana Copyright © 2014 Abdon Atangana. All rights reserved. A New High-Order Stable Numerical Method for Matrix Inversion Thu, 06 Feb 2014 17:06:47 +0000 A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples. F. Khaksar Haghani and F. Soleymani Copyright © 2014 F. Khaksar Haghani and F. Soleymani. All rights reserved. -Fuzzy Fixed Points Theorems for -Fuzzy Mappings via -Admissible Pair Wed, 05 Feb 2014 11:43:34 +0000 We define the concept of -admissible for a pair of -fuzzy mappings and establish the existence of common -fuzzy fixed point theorem. Our result generalizes some useful results in the literature. We provide an example to support our result. Maliha Rashid, Akbar Azam, and Nayyar Mehmood Copyright © 2014 Maliha Rashid et al. All rights reserved. Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations Tue, 04 Feb 2014 11:20:53 +0000 Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. I. Amirali, G. M. Amiraliyev, M. Cakir, and E. Cimen Copyright © 2014 I. Amirali et al. All rights reserved. Coefficient Inequalities for a Subclass of p-Valent Analytic Functions Tue, 04 Feb 2014 00:00:00 +0000 The aim of this paper is to study the problem of coefficient bounds for a newly defined subclass of p-valent analytic functions. Many known results appear as special consequences of our work. Muhammad Arif, Janusz Sokół, and Muhammad Ayaz Copyright © 2014 Muhammad Arif et al. All rights reserved. On the Long Time Simulation of Reaction-Diffusion Equations with Delay Mon, 03 Feb 2014 06:42:28 +0000 For a consistent numerical method to be practically useful, it is widely accepted that it must preserve the asymptotic stability of the original continuous problem. However, in this study, we show that it may lead to unreliable numerical solutions in long time simulation even if a classical numerical method gives a larger stability region than that of the original continuous problem. Some numerical experiments on the reaction-diffusion equations with delay are presented to confirm our findings. Finally, some open problems on the subject are proposed. Dongfang Li and Chengjian Zhang Copyright © 2014 Dongfang Li and Chengjian Zhang. All rights reserved. Dynamics of a Diffusive Predator-Prey Model with General Nonlinear Functional Response Mon, 03 Feb 2014 06:29:19 +0000 We study a diffusive predator-prey model with nonconstant death rate and general nonlinear functional response. Firstly, stability analysis of the equilibrium for reduced ODE system is discussed. Secondly, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we show that there are no nontrivial steady state solutions for certain parameter configuration. Wensheng Yang Copyright © 2014 Wensheng Yang. All rights reserved. PPF Dependent Fixed Point Results for Triangular -Admissible Mappings Sun, 02 Feb 2014 08:35:09 +0000 We introduce the concept of triangular -admissible mappings (pair of mappings) with respect to nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular -admissible mappings (pair of mappings) with respect to nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given. Ljubomir Ćirić, Saud M. Alsulami, Peyman Salimi, and Pasquale Vetro Copyright © 2014 Ljubomir Ćirić et al. All rights reserved. Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology Sun, 02 Feb 2014 07:20:04 +0000 We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions. Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Amir, and Ihsanul Haq Copyright © 2014 Suheel Abdullah Malik et al. All rights reserved. The Non-Relativistic Limit for the e-MHD Equations Thu, 30 Jan 2014 09:36:27 +0000 We investigate the non-relativistic limit for the e-MHD equations in a three-dimension unit periodic torus. With the prepared initial data, our result shows that the small parameter problems have unique solutions existing in the finite time interval where the corresponding limit problems (incompressible Euler equations) have smooth solutions. Moreover, the formal limit is rigorously justified. Hongli Wang and Jie Zhao Copyright © 2014 Hongli Wang and Jie Zhao. All rights reserved. Milloux Inequality of E-Valued Meromorphic Function Thu, 30 Jan 2014 08:29:18 +0000 The main purpose of this paper is to establish the Milloux inequality of -valued meromorphic function from the complex plane to an infinite dimensional complex Banach space with a Schauder basis. As an application, we study the Borel exceptional values of an -valued meromorphic function and those of its derivatives; results are obtained to extend some related results for meromorphic scalar-valued function of Singh, Gopalakrishna, and Bhoosnurmath. Zhaojun Wu and Zuxing Xuan Copyright © 2014 Zhaojun Wu and Zuxing Xuan. All rights reserved. -Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation Wed, 29 Jan 2014 13:09:12 +0000 -expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. Ali Filiz, Mehmet Ekici, and Abdullah Sonmezoglu Copyright © 2014 Ali Filiz et al. All rights reserved. Partial Rectangular Metric Spaces and Fixed Point Theorems Wed, 29 Jan 2014 09:59:44 +0000 The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results. Satish Shukla Copyright © 2014 Satish Shukla. All rights reserved. High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils Wed, 29 Jan 2014 06:55:21 +0000 We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils. Keijo Kalervo Mattila, Luiz Adolfo Hegele Júnior, and Paulo Cesar Philippi Copyright © 2014 Keijo Kalervo Mattila et al. All rights reserved. -Sumudu Transforms of -Analogues of Bessel Functions Wed, 29 Jan 2014 00:00:00 +0000 The main purpose of this paper is to evaluate -Sumudu transforms of a product of -Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of -Sumudu transforms to the solutions of the -integrodifferential equations involving -Bessel functions. The results may help to extend the -theory of orthogonal functions. Faruk Uçar Copyright © 2014 Faruk Uçar. All rights reserved. On -Algebras of Holomorphic Functions Tue, 28 Jan 2014 10:53:35 +0000 We consider the classes of holomorphic functions on the open unit disk in the complex plane. These classes are in fact generalizations of the class introduced by Kim (1986). The space equipped with the topology given by the metric defined by , with and , becomes an -space. By a result of Stoll (1977), the Privalov space with the topology given by the Stoll metric is an -algebra. By using these two facts, we prove that the spaces and coincide and have the same topological structure. Consequently, we describe a general form of continuous linear functionals on (with respect to the metric ). Furthermore, we give a characterization of bounded subsets of the spaces . Moreover, we give the examples of bounded subsets of that are not relatively compact. Romeo Meštrović Copyright © 2014 Romeo Meštrović. All rights reserved. Spaces of Ideal Convergent Sequences Tue, 28 Jan 2014 09:25:12 +0000 In the present paper, we introduce some sequence spaces using ideal convergence and Musielak-Orlicz function . We also examine some topological properties of the resulting sequence spaces. M. Mursaleen and Sunil K. Sharma Copyright © 2014 M. Mursaleen and Sunil K. Sharma. All rights reserved. Existence of Limit Cycles in the Solow Model with Delayed-Logistic Population Growth Tue, 28 Jan 2014 09:15:41 +0000 This paper is devoted to the existence and stability analysis of limit cycles in a delayed mathematical model for the economy growth. Specifically the Solow model is further improved by inserting the time delay into the logistic population growth rate. Moreover, by choosing the time delay as a bifurcation parameter, we prove that the system loses its stability and a Hopf bifurcation occurs when time delay passes through critical values. Finally, numerical simulations are carried out for supporting the analytical results. Carlo Bianca and Luca Guerrini Copyright © 2014 Carlo Bianca and Luca Guerrini. All rights reserved. Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities Tue, 28 Jan 2014 07:25:00 +0000 The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results. Xian Liu, Jiajia Du, and Qing Gao Copyright © 2014 Xian Liu et al. All rights reserved. An Analytical Study for (2 + 1)-Dimensional Schrödinger Equation Mon, 27 Jan 2014 08:30:17 +0000 In this paper, the homotopy analysis method has been applied to solve (2 + 1)-dimensional Schrödinger equations. The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms. The results obtained by homotopy analysis method have been compared with those of exact solutions. The main objective is to propose alternative methods of finding a solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results show that the solution of homotopy analysis method is in a good agreement with the exact solution. Behzad Ghanbari Copyright © 2014 Behzad Ghanbari. All rights reserved. Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems Mon, 27 Jan 2014 07:59:19 +0000 Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made. Waleed M. Abd-Elhameed, Eid H. Doha, and Mahmoud A. Bassuony Copyright © 2014 Waleed M. Abd-Elhameed et al. All rights reserved. Stability of a Quartic Functional Equation Thu, 23 Jan 2014 16:26:11 +0000 We obtain the general solution of the generalized quartic functional equation + for a fixed positive integer . We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces. Abasalt Bodaghi Copyright © 2014 Abasalt Bodaghi. All rights reserved. A New Sixth Order Method for Nonlinear Equations in R Thu, 23 Jan 2014 12:31:16 +0000 A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton’s method and other sixth order methods considered. Sukhjit Singh and D. K. Gupta Copyright © 2014 Sukhjit Singh and D. K. Gupta. All rights reserved. A Hybrid Common Fixed Point Theorem under Certain Recent Properties Thu, 23 Jan 2014 11:16:01 +0000 We prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings via common limit range property. Our result improves some results from the existing literature, especially the ones contained in Sintunavarat and Kumam (2009). Some illustrative and interesting examples to highlight the realized improvements are also furnished. Zoran Kadelburg, Sunny Chauhan, and Mohammad Imdad Copyright © 2014 Zoran Kadelburg et al. All rights reserved. Generalized Ulam-Hyers Stability, Well-Posedness, and Limit Shadowing of Fixed Point Problems for α-β-Contraction Mapping in Metric Spaces Thu, 23 Jan 2014 10:58:09 +0000 We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle. Wutiphol Sintunavarat Copyright © 2014 Wutiphol Sintunavarat. All rights reserved. Roughness of -Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces Thu, 23 Jan 2014 09:15:01 +0000 In this paper we study the roughness of -nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinite-dimensional spaces. An explicit form is given for each of the dichotomy constants of the perturbed equation in terms of the original ones. We emphasize that we do not assume any boundedness condition on the coefficients. Nicolae Lupa Copyright © 2014 Nicolae Lupa. All rights reserved. Feedback Control in a General Almost Periodic Discrete System of Plankton Allelopathy Thu, 23 Jan 2014 06:45:09 +0000 We study the properties of almost periodic solutions for a general discrete system of plankton allelopathy with feedback controls and establish a theorem on the uniformly asymptotic stability of almost periodic solutions. Wenshuang Yin Copyright © 2014 Wenshuang Yin. All rights reserved. Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations Thu, 23 Jan 2014 06:42:27 +0000 By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by where is the standard Riemann-Liouville fractional derivative, for and , subject to the boundary conditions , for , and , for , or , for , and , , for , Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result. Chengbo Zhai and Mengru Hao Copyright © 2014 Chengbo Zhai and Mengru Hao. All rights reserved. Some Inequalities for the -Analogue of the Classical Riemann Zeta Functions and the -Polygamma Functions Wed, 22 Jan 2014 10:20:05 +0000 We present the generalizations on some inequalities for the -analogue of the classical Riemann zeta functions and the -polygamma functions. Banyat Sroysang Copyright © 2014 Banyat Sroysang. All rights reserved. Approximate Solution of Time-Fractional Advection-Dispersion Equation via Fractional Variational Iteration Method Wed, 22 Jan 2014 10:04:11 +0000 This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie’s modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs. Birol İbiş and Mustafa Bayram Copyright © 2014 Birol İbiş and Mustafa Bayram. All rights reserved. Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach Tue, 21 Jan 2014 13:08:50 +0000 The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology. Ricardo Aguilar-López, Rafael Martínez-Guerra, and Juan L. Mata-Machuca Copyright © 2014 Ricardo Aguilar-López et al. All rights reserved. A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications Tue, 21 Jan 2014 11:22:06 +0000 We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models. Yuji Liu and Bashir Ahmad Copyright © 2014 Yuji Liu and Bashir Ahmad. All rights reserved. Dynamic Behavior of Positive Solutions for a Leslie Predator-Prey System with Mutual Interference and Feedback Controls Mon, 20 Jan 2014 13:51:11 +0000 We consider a Leslie predator-prey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee the existence, uniqueness, and stability of a positive periodic solution. Cong Zhang, Nan-jing Huang, and Chuan-xian Deng Copyright © 2014 Cong Zhang et al. All rights reserved. Controllability and Observability of Fractional Linear Systems with Two Different Orders Mon, 20 Jan 2014 13:51:02 +0000 This paper is concerned with the controllability and observability for a class of fractional linear systems with two different orders. The sufficient and necessary conditions for state controllability and state observability of such systems are established. The results obtained extend some existing results of controllability and observability for fractional dynamical systems. Dengguo Xu, Yanmei Li, and Weifeng Zhou Copyright © 2014 Dengguo Xu et al. All rights reserved. Practical Stability in terms of Two Measures for Set Differential Equations on Time Scales Mon, 20 Jan 2014 10:13:21 +0000 We present a new comparison principle by introducing a notion of upper quasi-monotone nondecreasing and obtain the practical stability criteria for set valued differential equations in terms of two measures on time scales by using the vector Lyapunov function together with the new comparison principle. Peiguang Wang and Weiwei Sun Copyright © 2014 Peiguang Wang and Weiwei Sun. All rights reserved. Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method Mon, 20 Jan 2014 06:48:33 +0000 We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method. Randhir Singh, Gnaneshwar Nelakanti, and Jitendra Kumar Copyright © 2014 Randhir Singh et al. All rights reserved. On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations Sun, 19 Jan 2014 12:22:31 +0000 The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub’s conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of this class are shown and implemented numerically, showing their applicability and efficiency. Taher Lotfi, Alicia Cordero, Juan R. Torregrosa, Morteza Amir Abadi, and Maryam Mohammadi Zadeh Copyright © 2014 Taher Lotfi et al. All rights reserved. Modified Projection Algorithms for Solving the Split Equality Problems Sun, 19 Jan 2014 11:58:25 +0000 The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed. Qiao-Li Dong and Songnian He Copyright © 2014 Qiao-Li Dong and Songnian He. All rights reserved. Fixed Points of Difference Operator of Meromorphic Functions Sun, 19 Jan 2014 07:00:51 +0000 Let f be a transcendental meromorphic function of order less than one. The authors prove that the exact difference has infinitely many fixed points, if and are Borel exceptional values (or Nevanlinna deficiency values) of f. These results extend the related results obtained by Chen and Shon. Zhaojun Wu and Hongyan Xu Copyright © 2014 Zhaojun Wu and Hongyan Xu. All rights reserved. On Fractional Model Reference Adaptive Control Thu, 16 Jan 2014 11:57:53 +0000 This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology. Bao Shi, Jian Yuan, and Chao Dong Copyright © 2014 Bao Shi et al. All rights reserved. Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation Thu, 16 Jan 2014 09:30:21 +0000 By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: , where , and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions. M. R. S. Kulenović, Z. Nurkanović, and E. Pilav Copyright © 2014 M. R. S. Kulenović et al. All rights reserved. Interpolation by Hankel Translates of a Basis Function: Inversion Formulas and Polynomial Bounds Thu, 16 Jan 2014 09:11:05 +0000 For , the authors have developed elsewhere a scheme for interpolation by Hankel translates of a basis function in certain spaces of continuous functions () depending on a weight . The functions and are connected through the distributional identity , where denotes the generalized Hankel transform of order . In this paper, we use the projection operators associated with an appropriate direct sum decomposition of the Zemanian space in order to derive explicit representations of the derivatives and their Hankel transforms, the former ones being valid when is restricted to a suitable interval for which is continuous. Here, denotes the th iterate of the Bessel differential operator if , while is the identity operator. These formulas, which can be regarded as inverses of generalizations of the equation , will allow us to get some polynomial bounds for such derivatives. Corresponding results are obtained for the members of the interpolation space . Cristian Arteaga and Isabel Marrero Copyright © 2014 Cristian Arteaga and Isabel Marrero. All rights reserved. Generalizations on Some Hermite-Hadamard Type Inequalities for Differentiable Convex Functions with Applications to Weighted Means Thu, 16 Jan 2014 06:44:35 +0000 Some new Hermite-Hadamard type inequalities for differentiable convex functions were presented by Xi and Qi. In this paper, we present new generalizations on the Xi-Qi inequalities. Banyat Sroysang Copyright © 2014 Banyat Sroysang. All rights reserved. On Conformal Conic Mappings of Spherical Domains Tue, 14 Jan 2014 12:51:36 +0000 The problem of the generation of homogeneous grids for spherical domains is considered in the class of conformal conic mappings. The equivalence between secant and tangent projections is shown and splitting the set of conformal conic mappings into equivalence classes is presented. The problem of minimization of the mapping factor variation is solved in the class of conformal conic mappings. Obtained results can be used in applied sciences, such as geophysical fluid dynamics and cartography, where the flattening of the Earth surface is required. Andrei Bourchtein and Ludmila Bourchtein Copyright © 2014 Andrei Bourchtein and Ludmila Bourchtein. All rights reserved. Infinitely Many Weak Solutions of the -Laplacian Equation with Nonlinear Boundary Conditions Tue, 14 Jan 2014 06:31:41 +0000 We study the following -Laplacian equation with nonlinear boundary conditions: and where is a bounded domain in with smooth boundary . We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and do not need to satisfy the or condition. Feng-Yun Lu and Gui-Qian Deng Copyright © 2014 Feng-Yun Lu and Gui-Qian Deng. All rights reserved. Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument Sun, 12 Jan 2014 13:10:32 +0000 We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green’s function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results. Kuo-Shou Chiu Copyright © 2014 Kuo-Shou Chiu. All rights reserved. Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators Sun, 12 Jan 2014 07:13:55 +0000 The nonlocal boundary value problem for the parabolic differential equation in an arbitrary Banach space with the dependent linear positive operator is investigated. The well-posedness of this problem is established in Banach spaces of all -valued continuous functions on satisfying a Hölder condition with a weight . New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established. Allaberen Ashyralyev and Asker Hanalyev Copyright © 2014 Allaberen Ashyralyev and Asker Hanalyev. All rights reserved. On the Fourth Power Mean of the Two-Term Exponential Sums Sun, 12 Jan 2014 06:42:55 +0000 The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of two-term exponential sums and give an interesting identity and asymptotic formula for it. Han Zhang and Wenpeng Zhang Copyright © 2014 Han Zhang and Wenpeng Zhang. All rights reserved. The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear Volterra-Fredholm Integrodifferential Equations Sun, 12 Jan 2014 00:00:00 +0000 We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations. Behzad Ghanbari Copyright © 2014 Behzad Ghanbari. All rights reserved. Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials Sun, 12 Jan 2014 00:00:00 +0000 A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. S. Mashayekhi, M. Razzaghi, and O. Tripak Copyright © 2014 S. Mashayekhi et al. All rights reserved. Analysis of Rattleback Chaotic Oscillations Wed, 08 Jan 2014 12:03:05 +0000 Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback’s chaotic dynamics are studied by applying Kane’s model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors’ invariant parameters. Michael Hanias, Stavros G. Stavrinides, and Santo Banerjee Copyright © 2014 Michael Hanias et al. All rights reserved. Equivalent Conditions of Generalized Convex Fuzzy Mappings Wed, 08 Jan 2014 09:52:16 +0000 We obtain some equivalent conditions of (strictly) pseudoconvex and quasiconvex fuzzy mappings. These results will be useful to present some characterizations of solutions for fuzzy mathematical programming. Xue Wen Liu and Dou He Copyright © 2014 Xue Wen Liu and Dou He. All rights reserved. Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations Sun, 05 Jan 2014 13:37:31 +0000 We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. Fukang Yin, Junqiang Song, Hongze Leng, and Fengshun Lu Copyright © 2014 Fukang Yin et al. All rights reserved. Weighted Multilinear Hardy Operators on Herz Type Spaces Sun, 05 Jan 2014 08:16:48 +0000 This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained results to the product Morrey-Herz spaces. Shuli Gong, Zunwei Fu, and Bolin Ma Copyright © 2014 Shuli Gong et al. All rights reserved. The S-Transform of Distributions Thu, 02 Jan 2014 16:14:44 +0000 Parseval’s formula and inversion formula for the S-transform are given. A relation between the S-transform and pseudodifferential operators is obtained. The S-transform is studied on the spaces and . Sunil Kumar Singh Copyright © 2014 Sunil Kumar Singh. All rights reserved. Stability Analysis of Distributed Order Fractional Chen System Sun, 29 Dec 2013 18:16:39 +0000 We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. H. Aminikhah, A. Refahi Sheikhani, and H. Rezazadeh Copyright © 2013 H. Aminikhah et al. All rights reserved. Coefficient Estimates for Initial Taylor-Maclaurin Coefficients for a Subclass of Analytic and Bi-Univalent Functions Defined by Al-Oboudi Differential Operator Sun, 29 Dec 2013 11:54:09 +0000 We introduce and investigate an interesting subclass of analytic and bi-univalent functions in the open unit disk . For functions belonging to the class , we obtain estimates on the first two Taylor-Maclaurin coefficients and . Serap Bulut Copyright © 2013 Serap Bulut. All rights reserved. An Interval-Valued Intuitionistic Fuzzy TOPSIS Method Based on an Improved Score Function Wed, 25 Dec 2013 15:11:29 +0000 This paper proposes an improved score function for the effective ranking order of interval-valued intuitionistic fuzzy sets (IVIFSs) and an interval-valued intuitionistic fuzzy TOPSIS method based on the score function to solve multicriteria decision-making problems in which all the preference information provided by decision-makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by IVIFS value and the information about criterion weights is known. We apply the proposed score function to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s) can be selected in the decision-making process. Finally, two illustrative examples for multicriteria fuzzy decision-making problems of alternatives are used as a demonstration of the applications and the effectiveness of the proposed decision-making method. Zhi-yong Bai Copyright © 2013 Zhi-yong Bai. All rights reserved. Cotton-Type and Joint Invariants for Linear Elliptic Systems Wed, 25 Dec 2013 08:32:29 +0000 Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results. A. Aslam and F. M. Mahomed Copyright © 2013 A. Aslam and F. M. Mahomed. All rights reserved. Explicit Solutions of a Gravity-Induced Film Flow along a Convectively Heated Vertical Wall Wed, 25 Dec 2013 07:55:33 +0000 The gravity-driven film flow has been analyzed along a vertical wall subjected to a convective boundary condition. The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly by using homotopy analysis method (HAM). The resulting solutions are investigated for heat transfer effects on velocity and temperature profiles. Ammarah Raees and Hang Xu Copyright © 2013 Ammarah Raees and Hang Xu. All rights reserved. Multiple Solutions for Nonhomogeneous Neumann Differential Inclusion Problems by the -Laplacian Tue, 24 Dec 2013 15:56:35 +0000 A class of nonlinear Neumann problems driven by -Laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper is the variational method for locally Lipschitz functions. More precisely, Weierstrass theorem and Mountain Pass theorem are used to prove the existence of at least two nontrivial solutions. Qing-Mei Zhou Copyright © 2013 Qing-Mei Zhou. All rights reserved. An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations Sun, 22 Dec 2013 18:35:13 +0000 We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior. Fazlollah Soleymani, Stanford Shateyi, and Gülcan Özkum Copyright © 2013 Fazlollah Soleymani et al. All rights reserved. The Oscillation on Solutions of Some Classes of Linear Differential Equations with Meromorphic Coefficients of Finite -Order Mon, 16 Dec 2013 09:07:23 +0000 This paper considers the oscillation on meromorphic solutions of the second-order linear differential equations with the form where is a meromorphic function with -order. We obtain some theorems which are the improvement and generalization of the results given by Bank and Laine, Cao and Li, Kinnunen, and others. Hong-Yan Xu, Jin Tu, and Zu-Xing Xuan Copyright © 2013 Hong-Yan Xu et al. All rights reserved. Sufficient Condition on the Fractional Integral for the Convergence of a Function Sun, 15 Dec 2013 16:17:45 +0000 A sufficient condition on the fractional integral of the absolute value of a function is given in this paper, which allows to assure the convergence of the function to zero. This result can be useful to assure the convergence of a function when it is hard to know its exact evolution, but conditions on its fractional integral can be stated. Manuel A. Duarte-Mermoud, Norelys Aguila-Camacho, and Javier A. Gallegos Copyright © 2013 Manuel A. Duarte-Mermoud et al. All rights reserved. Analysis of a Fractional-Order Couple Model with Acceleration in Feelings Thu, 12 Dec 2013 16:56:23 +0000 A fractional-order nonlinear dynamical model of couple has been introduced. Upper bounds are obtained for a fractional-order nonlinear dynamical model. Also different from other models, a model with the order 2α is discussed. We are expecting an acceleration in feelings; that is why we increase the order of the derivative between . Stability analysis of the fractional-order nonlinear dynamical model of involving two persons is studied using the fractional Routh-Hurwitz criteria. By using stability analysis on fractional-order system, we obtain sufficient condition on the parameters for the locally asymptotic stability of equilibrium points. Finally, numerical simulations are presented to verify the obtained results. Ilknur Koca and Nuri Ozalp Copyright © 2013 Ilknur Koca and Nuri Ozalp. All rights reserved. New Result of Analytic Functions Related to Hurwitz Zeta Function Thu, 12 Dec 2013 16:55:45 +0000 By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed. F. Ghanim and M. Darus Copyright © 2013 F. Ghanim and M. Darus. All rights reserved. Numerical Solution of Some Types of Fractional Optimal Control Problems Mon, 09 Dec 2013 09:24:32 +0000 We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches. Nasser Hassan Sweilam, Tamer Mostafa Al-Ajami, and Ronald H. W. Hoppe Copyright © 2013 Nasser Hassan Sweilam et al. All rights reserved. Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces Sun, 08 Dec 2013 14:16:10 +0000 In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, a.e. on , , , , (*), where is a closed subset in a Banach space , , , , is an upper semicontinuous set-valued mapping with convex values satisfying , , where , with , and . The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces. Messaoud Bounkhel Copyright © 2013 Messaoud Bounkhel. All rights reserved. Active Joint Mechanism Driven by Multiple Actuators Made of Flexible Bags: A Proposal of Dual Structural Actuator Thu, 05 Dec 2013 15:56:18 +0000 An actuator is required to change its speed and force depending on the situation. Using multiple actuators for one driving axis is one of the possible solutions; however, there is an associated problem of output power matching. This study proposes a new active joint mechanism using multiple actuators. Because the actuator is made of a flexible bag, it does not interfere with other actuators when it is depressurized. The proposed joint achieved coordinated motion of multiple actuators. This report also discusses a new actuator which has dual cylindrical structure. The cylinders are composed of flexible bags with different diameters. The joint torque is estimated based on the following factors: empirical formula for the flexible actuator torque, geometric relationship between the joint and the actuator, and the principle of virtual work. The prototype joint mechanism achieves coordinated motion of multiple actuators for one axis. With this motion, small inner actuator contributes high speed motion, whereas large outer actuator generates high torque. The performance of the prototype joint is examined by speed and torque measurements. The joint showed about 30% efficiency at 2.0 Nm load torque under 0.15 MPa air input. Hitoshi Kimura, Takuya Matsuzaki, Mokutaro Kataoka, and Norio Inou Copyright © 2013 Hitoshi Kimura et al. All rights reserved. A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo Thu, 05 Dec 2013 15:35:20 +0000 A mathematical model for the relationship between the populations of giant pandas and two kinds of bamboo is established. We use the impulsive perturbations to take into account the effect of a sudden collapse of bamboo as a food source. We show that this system is uniformly bounded. Using the Floquet theory and comparison techniques of impulsive equations, we find conditions for the local and global stabilities of the giant panda-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent. The results provide a theoretical basis for giant panda habitat protection. Xiang-yun Shi and Guo-hua Song Copyright © 2013 Xiang-yun Shi and Guo-hua Song. All rights reserved. Asymptotic Bounds for the Time-Periodic Solutions to the Singularly Perturbed Ordinary Differential Equations Wed, 04 Dec 2013 17:12:36 +0000 The periodical in time problem for singularly perturbed second order linear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented. Gabil M. Amiraliyev and Aysenur Ucar Copyright © 2013 Gabil M. Amiraliyev and Aysenur Ucar. All rights reserved. Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation Wed, 04 Dec 2013 12:06:13 +0000 We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form where the parameters ,, and are positive numbers and the initial conditions and are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable. M. Garić-Demirović, M. R. S. Kulenović, and M. Nurkanović Copyright © 2013 M. Garić-Demirović et al. All rights reserved. Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions Thu, 28 Nov 2013 18:17:47 +0000 We apply generalized operators of fractional integration involving Appell’s function due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions. D. Baleanu, P. Agarwal, and S. D. Purohit Copyright © 2013 D. Baleanu et al. All rights reserved. On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series Tue, 26 Nov 2013 11:29:34 +0000 Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler’s mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler’s means of conjugate of functions belonging to class has been obtained. and classes are the particular cases of class. The main result of this paper generalizes some well-known results in this direction. Jitendra Kumar Kushwaha Copyright © 2013 Jitendra Kumar Kushwaha. All rights reserved. Davey-Stewartson Equation with Fractional Coordinate Derivatives Mon, 25 Nov 2013 17:05:18 +0000 We have used the homotopy analysis method (HAM) to obtain solution of Davey-Stewartson equations of fractional order. The fractional derivative is described in the Caputo sense. The results obtained by this method have been compared with the exact solutions. Stability and convergence of the proposed approach is investigated. The effects of fractional derivatives for the systems under consideration are discussed. Furthermore, comparisons indicate that there is a very good agreement between the solutions of homotopy analysis method and the exact solutions in terms of accuracy. H. Jafari, K. Sayevand, Yasir Khan, and M. Nazari Copyright © 2013 H. Jafari et al. All rights reserved. The Exact Distribution of the Condition Number of Complex Random Matrices Mon, 25 Nov 2013 11:47:20 +0000 Let be a complex random matrix and which is the complex Wishart matrix. Let and denote the eigenvalues of the W and singular values of , respectively. The 2-norm condition number of is . In this paper, the exact distribution of the condition number of the complex Wishart matrices is derived. The distribution is expressed in terms of complex zonal polynomials. Lin Shi, Taibin Gan, Hong Zhu, and Xianming Gu Copyright © 2013 Lin Shi et al. All rights reserved. Drawing Dynamical and Parameters Planes of Iterative Families and Methods Sun, 24 Nov 2013 13:42:40 +0000 The complex dynamical analysis of the parametric fourth-order Kim’s iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us the excellent schemes (or dreadful ones). Francisco I. Chicharro, Alicia Cordero, and Juan R. Torregrosa Copyright © 2013 Francisco I. Chicharro et al. All rights reserved. Strong Convergence of a Monotone Projection Algorithm in a Banach Space Thu, 21 Nov 2013 11:32:50 +0000 In this paper, a common solution problem is investigated based on a Bregman projection. Strong convergence of the monotone projection algorithm for monotone operators and bifunctions is obtained in a reflexive Banach space. Songtao Lv Copyright © 2013 Songtao Lv. All rights reserved. Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment Thu, 21 Nov 2013 11:00:19 +0000 This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results. Junhong Li and Ning Cui Copyright © 2013 Junhong Li and Ning Cui. All rights reserved. Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces and Thu, 14 Nov 2013 18:56:02 +0000 We introduce the sequence space of none absolute type which is a -normed space and space in the cases and , respectively, and prove that and are linearly isomorphic for . Furthermore, we give some inclusion relations concerning the space and we construct the basis for the space , where . Furthermore, we determine the alpha-, beta- and gamma-duals of the space for . Finally, we investigate some geometric properties concerning Banach-Saks type and give Gurarii's modulus of convexity for the normed space . Feyzi Başar and Ali Karaisa Copyright © 2013 Feyzi Başar and Ali Karaisa. All rights reserved. Positive Periodic Solutions of an Epidemic Model with Seasonality Sun, 10 Nov 2013 14:35:43 +0000 An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number is obtained. Moreover, only the basic reproduction number cannot ensure the existence of the positive equilibrium, which needs additional condition . For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number. Gui-Quan Sun, Zhenguo Bai, Zi-Ke Zhang, Tao Zhou, and Zhen Jin Copyright © 2013 Gui-Quan Sun et al. All rights reserved. An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order Sun, 10 Nov 2013 09:44:31 +0000 We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type. Ricardo Almeida and Delfim F. M. Torres Copyright © 2013 Ricardo Almeida and Delfim F. M. Torres. All rights reserved. Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems Wed, 06 Nov 2013 17:28:12 +0000 This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem , , , where is a real number, is the Caputo fractional derivative, and is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii’s fixed point theorem and Leggett-Williams fixed point theorem, some new existence criteria for fractional boundary value problem are established; secondly, by applying a new extension of Krasnoselskii’s fixed point theorem, a sufficient condition is obtained for the existence of multiple positive solutions to the considered boundary value problem from its auxiliary problem. Finally, as applications, some illustrative examples are presented to support the main results. Daliang Zhao and Yansheng Liu Copyright © 2013 Daliang Zhao and Yansheng Liu. All rights reserved. Nonuniform Exponential Dichotomies in Terms of Lyapunov Functions for Noninvertible Linear Discrete-Time Systems Wed, 06 Nov 2013 15:10:47 +0000 The aim of this paper is to give characterizations in terms of Lyapunov functions for nonuniform exponential dichotomies of nonautonomous and noninvertible discrete-time systems. Ioan-Lucian Popa, Mihail Megan, and Traian Ceauşu Copyright © 2013 Ioan-Lucian Popa et al. All rights reserved. Locally Expansive Solutions for a Class of Iterative Equations Tue, 05 Nov 2013 17:17:50 +0000 Iterative equations which can be expressed by the following form , where , are investigated. Conditions for the existence of locally expansive solutions for such equations are given. Wei Song and Sheng Chen Copyright © 2013 Wei Song and Sheng Chen. All rights reserved. Korovkin-Type Theorems in Weighted -Spaces via Summation Process Tue, 05 Nov 2013 15:28:06 +0000 Korovkin-type theorem which is one of the fundamental methods in approximation theory to describe uniform convergence of any sequence of positive linear operators is discussed on weighted spaces, for univariate and multivariate functions, respectively. Furthermore, we obtain these types of approximation theorems by means of -summability which is a stronger convergence method than ordinary convergence. Tuncer Acar and Fadime Dirik Copyright © 2013 Tuncer Acar and Fadime Dirik. All rights reserved. Some Endpoint Results for β-Generalized Weak Contractive Multifunctions Mon, 04 Nov 2013 08:42:22 +0000 We introduce β-generalized weak contractive multifunctions and give some results about endpoints of the multifunctions. Also, we give some results about role of a point in the existence of endpoints. H. Alikhani, D. Gopal, M. A. Miandaragh, Sh. Rezapour, and N. Shahzad Copyright © 2013 H. Alikhani et al. All rights reserved. Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the ()-Laplacian Operator Sun, 03 Nov 2013 13:19:22 +0000 Existence results of three weak solutions for a Dirichlet double eigenvalue quasilinear elliptic system involving the ()-Laplacian operator, under suitable assumptions, are established. Our main tool is based on a recent three-critical-point theorem obtained by Ricceri. We also give some examples to illustrate the obtained results. Armin Hadjian and Saleh Shakeri Copyright © 2013 Armin Hadjian and Saleh Shakeri. All rights reserved. Some New Inequalities of Jordan Type for Sine Thu, 31 Oct 2013 12:00:14 +0000 The authors find some new inequalities of Jordan type for the sine function. These newly established inequalities are of new form and are applied to deduce some known results. Shan-Peng Zeng and Yue-Sheng Wu Copyright © 2013 Shan-Peng Zeng and Yue-Sheng Wu. All rights reserved. Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions Thu, 31 Oct 2013 11:20:48 +0000 The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples are provided to illustrate the applications of our results. Xian-Feng Zhou, Song Liu, Zhixin Zhang, and Wei Jiang Copyright © 2013 Xian-Feng Zhou et al. All rights reserved. On Harmonic Meromorphic Functions Associated with Basic Hypergeometric Functions Thu, 31 Oct 2013 09:34:28 +0000 By making use of basic hypergeometric functions, a class of complex harmonic meromorphic functions with positive coefficients is introduced. We obtain some properties such as coefficient inequality, growth theorems, and extreme points. Huda Al dweby and Maslina Darus Copyright © 2013 Huda Al dweby and Maslina Darus. All rights reserved. Certain Subclasses of Analytic Functions with Complex Order Tue, 29 Oct 2013 10:20:29 +0000 Two new subclasses of analytic functions of complex order are introduced. Apart from establishing coefficient bounds for these classes, we establish inclusion relationships involving () neighborhoods of analytic functions with negative coefficients belonging to these subclasses. A. Selvam, P. Sooriya Kala, and N. Marikkannan Copyright © 2013 A. Selvam et al. All rights reserved. Viscosity-Projection Method for a Family of General Equilibrium Problems and Asymptotically Strict Pseudocontractions in the Intermediate Sense Mon, 28 Oct 2013 14:10:25 +0000 In this paper, a Meir-Keeler contraction is introduced to propose a viscosity-projection approximation method for finding a common element of the set of solutions of a family of general equilibrium problems and the set of fixed points of asymptotically strict pseudocontractions in the intermediate sense. Strong convergence of the viscosity iterative sequences is obtained under some suitable conditions. Results presented in this paper extend and unify the previously known results announced by many other authors. Dao-Jun Wen Copyright © 2013 Dao-Jun Wen. All rights reserved. On the Stability of One-Dimensional Wave Equation Sun, 27 Oct 2013 16:14:03 +0000 We prove the generalized Hyers-Ulam stability of the one-dimensional wave equation, , in a class of twice continuously differentiable functions. Soon-Mo Jung Copyright © 2013 Soon-Mo Jung. All rights reserved. Multiple Solutions for a Singular Quasilinear Elliptic System Thu, 24 Oct 2013 14:07:34 +0000 We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system , , , , , where , , , , , . The functions , , , , , , and satisfy some suitable conditions. We will prove that the problem has at least two nontrivial solutions by using Mountain Pass Theorem and Ekeland's variational principle. Lin Chen, Caisheng Chen, and Zonghu Xiu Copyright © 2013 Lin Chen et al. All rights reserved. Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations Tue, 22 Oct 2013 15:59:08 +0000 An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. Ning-Bo Tan, Ting-Zhu Huang, and Ze-Jun Hu Copyright © 2013 Ning-Bo Tan et al. All rights reserved. Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean Tue, 22 Oct 2013 15:17:14 +0000 The authors find the greatest value and the least value , such that the double inequality holds for all and with , where , , and denote, respectively, the centroidal, arithmetic, and Toader means of the two positive numbers and . Wei-Dong Jiang Copyright © 2013 Wei-Dong Jiang. All rights reserved. An Efficient Method for Systems of Variable Coefficient Coupled Burgers’ Equation with Time-Fractional Derivative Thu, 10 Oct 2013 18:48:31 +0000 A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered as a power series expansion that converges rapidly to the nonlinear problem. The new approximate analytical procedure depends on two iteratives. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractional-order partial differential equations. Hossein Aminikhah and Nasrin Malekzadeh Copyright © 2013 Hossein Aminikhah and Nasrin Malekzadeh. All rights reserved. Inclusions in a Single Variable in Ultrametric Spaces and Hyers-Ulam Stability Tue, 01 Oct 2013 15:45:35 +0000 We present some properties of set-valued inclusions in a single variable in ultrametric spaces. As a consequence, we obtain stability results for the corresponding functional equations. Magdalena Piszczek Copyright © 2013 Magdalena Piszczek. All rights reserved. A Higher Order Iterative Method for Computing the Drazin Inverse Mon, 30 Sep 2013 15:33:46 +0000 A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. F. Soleymani and Predrag S. Stanimirović Copyright © 2013 F. Soleymani and Predrag S. Stanimirović. All rights reserved. Trichotomy for Dynamical Systems in Banach Spaces Sun, 29 Sep 2013 14:55:53 +0000 We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skew-evolution semiflows. Therefore, we introduce the concept of -trichotomy. Characterizations in a uniform setting are proved, using techniques from the domain of nonautonomous evolution equations with unbounded coefficients, and connections with the classic notion of trichotomy are given. The statements are sustained by several examples. Codruţa Stoica Copyright © 2013 Codruţa Stoica. All rights reserved. Controllability in Hybrid Kinetic Equations Modeling Nonequilibrium Multicellular Systems Thu, 26 Sep 2013 15:30:03 +0000 This paper is concerned with the derivation of hybrid kinetic partial integrodifferential equations that can be proposed for the mathematical modeling of multicellular systems subjected to external force fields and characterized by nonconservative interactions. In order to prevent an uncontrolled time evolution of the moments of the solution, a control operator is introduced which is based on the Gaussian thermostat. Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation. Carlo Bianca Copyright © 2013 Carlo Bianca. All rights reserved. New Criteria for Functions to Be in a Class of -Valent Alpha Convex Functions Thu, 26 Sep 2013 09:03:10 +0000 We obtain certain simple sufficiency criteria for a class of -valent alpha convex functions. Many known results appear as special consequences of our work. Some applications of our work to the generalized integral operator are also given. Muhammad Arif, Muhammad Ayaz, and Mohamed Kamal Aouf Copyright © 2013 Muhammad Arif et al. All rights reserved. Taylor’s Expansion for Composite Functions Wed, 25 Sep 2013 14:26:12 +0000 We build a Taylor’s expansion for composite functions. Some applications are introduced, where the proposed technique allows the authors to obtain an asymptotic expansion of high order in many small parameters of solutions. Le Thi Phuong Ngoc and Nguyen Anh Triet Copyright © 2013 Le Thi Phuong Ngoc and Nguyen Anh Triet. All rights reserved. Existence and Uniqueness of Solution for a Class of Stochastic Differential Equations Thu, 19 Sep 2013 17:13:17 +0000 A class of stochastic differential equations given by ,  ,  , are investigated. Upon making some suitable assumptions, the existence and uniqueness of solution for the equations are obtained. Moreover, the existence and uniqueness of solution for stochastic Lorenz system, which is illustrated by example, are in good agreement with the theoretical analysis. Junfei Cao, Zaitang Huang, and Caibin Zeng Copyright © 2013 Junfei Cao et al. All rights reserved. Dual Synchronization of Fractional-Order Chaotic Systems via a Linear Controller Sat, 14 Sep 2013 08:39:56 +0000 The problem of the dual synchronization of two different fractional-order chaotic systems is studied. By a linear controller, we realize the dual synchronization of fractional-order chaotic systems. Finally, the proposed method is applied for dual synchronization of Van der Pol-Willis systems and Van der Pol-Duffing systems. The numerical simulation shows the accuracy of the theory. Jian Xiao, Zhen-zhen Ma, and Ye-hong Yang Copyright © 2013 Jian Xiao et al. All rights reserved. Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle Wed, 04 Sep 2013 10:37:09 +0000 We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh’s extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. M. Z. Ahmad, M. K. Hasan, and S. Abbasbandy Copyright © 2013 M. Z. Ahmad et al. All rights reserved. Positive Solutions of Advanced Differential Systems Sat, 31 Aug 2013 15:15:44 +0000 We study asymptotic behavior of solutions of general advanced differential systems , where is a continuous quasi-bounded functional which satisfies a local Lipschitz condition with respect to the second argument and is a subset in , , , and , . A monotone iterative method is proposed to prove the existence of a solution defined for with the graph coordinates lying between graph coordinates of two (lower and upper) auxiliary vector functions. This result is applied to scalar advanced linear differential equations. Criteria of existence of positive solutions are given and their asymptotic behavior is discussed. Josef Diblík and Mária Kúdelčíková Copyright © 2013 Josef Diblík and Mária Kúdelčíková. All rights reserved. On the Normed Space of Equivalence Classes of Fuzzy Numbers Thu, 29 Aug 2013 11:40:42 +0000 We study the norm induced by the supremum metric on the space of fuzzy numbers. And then we propose a method for constructing a norm on the quotient space of fuzzy numbers. This norm is very natural and works well with the induced metric on the quotient space. Dong Qiu, Chongxia Lu, and Wei Zhang Copyright © 2013 Dong Qiu et al. All rights reserved. Fixed Point Results of Locally Contractive Mappings in Ordered Quasi-Partial Metric Spaces Sun, 25 Aug 2013 10:59:30 +0000 Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how this result can be used when the corresponding results cannot. Our results generalize, extend, and improve several well-known conventional results. Abdullah Shoaib, Muhammad Arshad, and Jamshaid Ahmad Copyright © 2013 Abdullah Shoaib et al. All rights reserved. Oscillation of a Class of Fractional Differential Equations with Damping Term Wed, 21 Aug 2013 10:34:50 +0000 We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with respect to the new variable. Then, using Riccati transformation, inequality, and integration average technique, some new oscillatory criteria for the equations are established. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results. Huizeng Qin and Bin Zheng Copyright © 2013 Huizeng Qin and Bin Zheng. All rights reserved. On Generalized Carleson Operators of Periodic Wavelet Packet Expansions Tue, 20 Aug 2013 13:07:26 +0000 Three new theorems based on the generalized Carleson operators for the periodic Walsh-type wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied. Shyam Lal and Manoj Kumar Copyright © 2013 Shyam Lal and Manoj Kumar. All rights reserved. Fractional Solutions of Bessel Equation with -Method Mon, 19 Aug 2013 09:40:01 +0000 This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the -fractional calculus operator method, we derive the fractional solutions of the equation. Erdal Bas, Resat Yilmazer, and Etibar Panakhov Copyright © 2013 Erdal Bas et al. All rights reserved. Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions Sun, 18 Aug 2013 12:00:21 +0000 We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and grid-independent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confirming the ability of these types of solvers to approximate the solutions of hyperbolic equations efficiently and accurately. Andrew N. Guarendi and Abhilash J. Chandy Copyright © 2013 Andrew N. Guarendi and Abhilash J. Chandy. All rights reserved. Exceptional Values of Meromorphic Function on Annulus Mon, 05 Aug 2013 10:19:41 +0000 The main purpose of this paper is to study the exceptional values of meromorphic function and its derivative on annulus. We also give some theorems and corollaries about exceptional values of meromorphic function on the annulus, which are the improvement of the previous results given by Chen and Wu. Hong-Yan Xu Copyright © 2013 Hong-Yan Xu. All rights reserved. On the Connection Coefficients of the Chebyshev-Boubaker Polynomials Sun, 04 Aug 2013 11:49:02 +0000 The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection coefficients as well as recurrence relations that define them. Paul Barry Copyright © 2013 Paul Barry. All rights reserved. Existence of Multiple Solutions for a -Kirchhoff Problem with Nonlinear Boundary Conditions Thu, 25 Jul 2013 14:17:19 +0000 The paper considers the existence of multiple solutions of the singular nonlocal elliptic problem , ,   = , on , where , . By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied. Zonghu Xiu and Caisheng Chen Copyright © 2013 Zonghu Xiu and Caisheng Chen. All rights reserved. On Weak Exponential Expansiveness of Evolution Families in Banach Spaces Thu, 25 Jul 2013 14:06:35 +0000 The aim of this paper is to give several characterizations for the property of weak exponential expansiveness for evolution families in Banach spaces. Variants for weak exponential expansiveness of some well-known results in stability theory (Datko (1973), Rolewicz (1986), Ichikawa (1984), and Megan et al. (2003)) are obtained. Tian Yue, Xiao-qiu Song, and Dong-qing Li Copyright © 2013 Tian Yue et al. All rights reserved. On th-Order Slant Weighted Toeplitz Operator Wed, 17 Jul 2013 08:34:42 +0000 Let be a sequence of positive numbers with , when and when . A th-order slant weighted Toeplitz operator on is given by , where is the multiplication on and is an operator on given by , being the orthonormal basis for . In this paper, we define a th-order slant weighted Toeplitz matrix and characterise in terms of this matrix. We further prove some properties of using this characterisation. S. C. Arora and Ritu Kathuria Copyright © 2013 S. C. Arora and Ritu Kathuria. All rights reserved. On Satnoianu-Wu’s Inequality Tue, 16 Jul 2013 14:27:20 +0000 By applying techniques in the theory of convex functions and Schur-geometrically convex functions, the author investigates a conjecture of Satnoianu on an algebraic inequality and generalizes some known results in recent years. Bo-Yan Xi Copyright © 2013 Bo-Yan Xi. All rights reserved. On a Family of Multivariate Modified Humbert Polynomials Sun, 14 Jul 2013 12:24:30 +0000 This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials. Rabia Aktaş and Esra Erkuş-Duman Copyright © 2013 Rabia Aktaş and Esra Erkuş-Duman. All rights reserved.