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The purpose of this paper is to study the global stability properties of equilibria for age-dependent epidemiological models in presence of recurrence phenomenon. In these systems, the recurrence rate depends on asymptomatic–infection–age. The models are appropriate for human herpes virus (HSV-1 and HSV-2) and varicella-zoster virus. We derived explicit formulas for the basic reproductive number, which completely characterizes the global behaviour of solutions to the models: if the basic reproductive number is less than or equal to unity, the disease will die out; if the basic reproductive number is greater than unity, the disease will be persistent. Volterra-type Lyapunov functions are constructed to establish the global asymptotic stability of the infection-free and endemic steady states. Copyright © 2015 John Wiley & Sons, Ltd.

The treatment of human immunodeficiency virus (HIV) remains a major challenge, even if significant progress has been made in infection treatment by ‘drug cocktails’. Nowadays, research trend is to minimize the number of pills taken when treating infection. In this paper, an HIV-1 within host model where healthy cells follow a simple logistic growth is considered. Basic reproduction number of the model is calculated using next generation matrix method, steady states are derived; their local, as well as global stability, is discussed using the Routh–Hurwitz criteria, Lyapunov functions and the Lozinskii measure approach. The optimal control policy is formulated and solved as an optimal control problem. Numerical simulations are performed to compare several cases, representing a treatment by Interleukin2 alone, classical treatment by multitherapy drugs alone, then both treatments at the same time. Objective functionals aim to (i) minimize infected cells quantity; (ii) minimize free virus particles number; and (iii) maximize healthy cells density in blood. Copyright © 2015 John Wiley & Sons, Ltd.

The (G′/G,1/G)-expansion method and (1/G′)-expansion method are interesting approaches to find new and more general exact solutions to the nonlinear evolution equations. In this paper, these methods are applied to construct new exact travelling wave solutions of nonlinear Schrodinger equation. The travelling wave solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. It is shown that the proposed methods provide a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we apply the Jacobi collocation method for solving nonlinear fractional differential equations with integral boundary conditions. Due to existence of integral boundary conditions, after reformulation of this equation in the integral form, the method is proposed for solving the obtained integral equation. Also, the convergence and stability analysis of the proposed method are studied in two main theorems. Furthermore, the optimum degree of convergence in the L2 norm is obtained for this method. Furthermore, some numerical examples are presented in order to illustrate the performance of the presented method. Finally, an application of the model in control theory is introduced. Copyright © 2015 John Wiley & Sons, Ltd.

T. Qian As it will turn out in this paper, the recent hype about most of the Clifford–Fourier transforms is not thoroughly worth the pain. Almost everyone that has a real application is separable, and these transforms can be decomposed into a sum of real valued transforms with constant multivecor factors. This fact makes their interpretation, their analysis, and their implementation almost trivial. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a shifted fractional-order Jacobi orthogonal function (SFJF) based on the definition of the classical Jacobi polynomial. A new fractional integral operational matrix of the SFJF is presented and derived. We propose the spectral Tau method, in conjunction with the operational matrices of the Riemann–Liouville fractional integral for SFJF and derivative for Jacobi polynomial, to solve a class of time-fractional partial differential equations with variable coefficients. In this algorithm, the approximate solution is expanded by means of both SFJFs for temporal discretization and Jacobi polynomials for spatial discretization. The proposed tau scheme, both in temporal and spatial discretizations, successfully reduced such problem into a system of algebraic equations, which is far easier to be solved. Numerical results are provided to demonstrate the high accuracy and superiority of the proposed algorithm over existing ones. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we analyze the energy-conserved splitting finite-difference time-domain (FDTD) scheme for variable coefficient Maxwell's equations in two-dimensional disk domains. The approach is energy-conserved, unconditionally stable, and effective. We strictly prove that the EC-S-FDTD scheme for the variable coefficient Maxwell's equations in disk domains is of second order accuracy both in time and space. It is also strictly proved that the scheme is energy-conserved, and the discrete divergence-free is of second order convergence. Numerical experiments confirm the theoretical results, and practical test is simulated as well to demonstrate the efficiency of the proposed EC-S-FDTD scheme. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we investigate exact traveling wave solutions of the fourth-order nonlinear Schrodinger equation with dual-power law nonlinearity through Kudryashov method and (G'/G)-expansion method. We obtain miscellaneous traveling waves including kink, antikink, and breather solutions. These solutions may be useful in the explanation and understanding of physical behavior of the wave propagation in a highly dispersive optical medium. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a numerical method for solving Lane-Emden type equations, which are nonlinear ordinary differential equations on the semi-infinite domain, is presented. The method is based upon the modified rational Bernoulli functions; these functions are first introduced. Operational matrices of derivative and product of modified rational Bernoulli functions are then given and are utilized to reduce the solution of the Lane-Emden type equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, for a coupled system of one-dimensional wave equations with Dirichlet boundary controls, we show that the controllability of classical solutions implies the controllability of weak solutions. This conclusion can be applied in proving some results that are hardly obtained by a direct way in the framework of classical solutions. For instance, we strictly derive the necessary conditions for the exact boundary synchronization by two groups in the framework of classical solutions for the coupled system of wave equations. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we propose a discrete viral infection model with a general incidence rate. The discrete model is derived from a continuous case by using a 'mixed' Euler method, which is a mixture of both forward and backward Euler methods. We prove that the mixed Euler method preserves the qualitative properties of the corresponding continuous system, such as positivity, boundedness, and global behaviors of solutions. Furthermore, the model and mathematical results presented in another previous study are extended and generalized. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we prove the existence and uniqueness of the local mild solution to the Cauchy problem of the n-dimensional (n≥3) Wigner–Poisson–BGK equation in the space of some integrable functions whose inverse Fourier transform are integrable. The main difficulties in establishing mild solution are to derive the boundedness and locally Lipschitz properties of the appropriate nonlinear terms in the Wiener algebra. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhoff-type equations with Dirichlet boundary data as follows: −M∫Ω1p(x)|∇u|p(x)dxdiv(|∇u|p(x)−2∇u)=f(x,u)inΩ,u=0on∂Ω. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish some conditions on the existence of solutions. Copyright © 2015 John Wiley & Sons, Ltd.

This paper studies the Neimark–Sacker bifurcation of a diffusive food-limited model with a finite delay and Dirichlet boundary condition by the backward Euler difference scheme, Crank-Nicolson difference scheme, and nonstandard finite-difference scheme. The existence of Neimark-Sacker bifurcation at the equilibrium is obtained. Our results show that Crank-Nicolson and nonstandard finite-difference schemes are superior to the backward Euler difference scheme under the means of describing approximately the dynamics of the original system. Finally, numerical examples are provided to illustrate the analytical results. Copyright © 2015 John Wiley & Sons, Ltd.

G. R. Franssens In this paper, we present an explicit construction for the fundamental solution of the heat operator, the Schrodinger operator, and related first-order parabolic Dirac operators on a class of some conformally flat non-orientable orbifolds. More concretely, we treat a class of projective cylinders and tori where we can study parabolic monogenic sections with values in different pin bundles. We present integral representation formulas together with some elementary tools of harmonic analysis that enable us to solve boundary value problems on these orbifolds. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a new numerical method for solving the fractional Bagley-Torvik equation is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is introduced. This operator is then utilized to reduce the solution of the initial and boundary value problems for the fractional Bagley-Torvik differential equation to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2015 John Wiley & Sons, Ltd.

A fluid–particles system of the compressible Navier-Stokes equations and Vlasov-Fokker-Planck equation (including the case of Vlasov equation) in three-dimensional space is considered in this paper. The coupling arises from a drag force exerted by the fluid onto the particles. We study a Cauchy problem with large data, and establish the existence of global weak solutions through an approximation scheme, energy estimates, and weak convergence. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we consider the analytical solutions of fractional partial differential equations (PDEs) with Riesz space fractional derivatives on a finite domain. Here we considered two types of fractional PDEs with Riesz space fractional derivatives such as Riesz fractional diffusion equation (RFDE) and Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order α∈(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order β∈(0,1] and of order α∈(1,2] respectively. Here the analytic solutions of both the RFDE and RFADE are derived by using modified homotopy analysis method with Fourier transform. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method. Here the space fractional derivatives are defined as Riesz fractional derivatives. Copyright © 2015 John Wiley & Sons, Ltd.

In digital signal processing, it is a well know fact that a causal signal of finite energy is front loaded if and only if the corresponding analytic signal, or the physically realizable signal, is a minimum phase signal, or an outer function in the complex analysis terminology. Based on this fact, a series expansion method, called unwinding adaptive Fourier decomposition (AFD), to give rise to positive frequency representations with rapid convergence was proposed several years ago. It appears to be a promising positive frequency representation with great potential of applications. The corresponding algorithm, however, is complicated due to consecutive extractions of outer functions involving computation of Hilbert transforms. This paper is to propose a practical algorithm for unwinding AFD that does not depend on computation of Hilbert transform, but, instead, factorizes out the Blaschke product type of inner functions. The proposed method significantly improves applicability of unwinding AFD. As an application, we give the associated Dirac-type time-frequency distribution of physically realizable signals. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we prove the Saint-Venant compatibility conditions in Lp for p∈(1,+∞), in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in Lp to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where 1 < p < 2. This justifies the need to generalize and prove these rather classical results in the Hilbertian case (p = 2), to the full range p∈(1,+∞). Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a shifted Jacobi–Gauss collocation spectral algorithm is developed for solving numerically systems of high-order linear retarded and advanced differential–difference equations with variable coefficients subject to mixed initial conditions. The spatial collocation approximation is based upon the use of shifted Jacobi–Gauss interpolation nodes as collocation nodes. The system of differential–difference equations is reduced to a system of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The convergence is discussed graphically. The proposed method has an exponential convergence rate. The validity and effectiveness of the method are demonstrated by solving several numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a class of virus infection model with Beddington–DeAngelis infection function and cytotoxic T-lymphocyte immune response is investigated. Time delay in the immune response term is incorporated into the model. We show that the dynamics of the model are determined by the basic reproduction number and the immune response reproduction number . If , then the infection-free equilibrium is globally asymptotically stable. If , then the immune-free equilibrium is globally asymptotically stable. If , then the stability of the interior equilibrium is investigated. We conclude that Hopf bifurcation occurs as the time delay passes through a critical value. Numerical simulations are carried out to support our theoretical conclusion well. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we investigate the vacuum free boundary problem of a compressible Navier–Stokes–Poisson system with density-dependent viscosity. By introducing Eulerian and Lagrange energy, we obtain a local in time well-posedness of the strong solution to the Navier–Stokes–Poisson system in a spherically symmetric case. Copyright © 2015 John Wiley & Sons, Ltd.

The Hartley transform is an integral transformation that maps a real valued function into a real valued frequency function via the Hartley kernel, thereby avoiding complex arithmetic as opposed to the Fourier transform. Approximation of the Hartley integral by the trapezoidal quadrature results in the discrete Hartley transform, which has proven a contender to the discrete Fourier transform because of its involutory nature. In this paper, a discrete transform is proposed as a real transform with a convolution property and is an alternative to the discrete Hartley transform. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we study the nonlinear Schrodinger–Maxwell system where the potential V and the primitive of g are allowed to be sign-changing, and g is local superlinear. Under some simple assumptions on V,Q and g, we establish some existence criteria to guarantee that the aforementioned system has at least one nontrivial solution or infinitely many nontrivial solutions by using critical point theory. Recent results in the literature are generalized and significantly improved. Copyright © 2015 John Wiley & Sons, Ltd.

This paper deals with global dynamics of a class of delayed discrete susceptible-infected-recovered (SIR) compartmental epidemic models with general nonlinear incidence rate and disease-induced mortality, which are proposed from the Mickens nonstandard discretization of the corresponding delayed continuous epidemic models. By constructing discrete Lyapunov functions, the sufficient conditions for the global attractivity of the disease-free equilibrium and endemic equilibrium are established. Under some additional assumptions (see (H3) in Section 3 and (H4) in Section 4), it is shown that the disease-free equilibrium is globally attractive when basic reproduction number , and when , there is a unique endemic equilibrium, which is globally attractive. Furthermore, some special cases are discussed, and as corollaries, several idiographic results are established. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a delayed eco-epidemiological model with Holling type II functional response is investigated. By analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcations at the disease-free equilibrium, the susceptible predator-free equilibrium and the endemic-coexistence equilibrium are established, respectively. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are derived for the global stability of the endemic-coexistence equilibrium, the disease-free equilibrium, the susceptible predator-free equilibrium and the predator-extinction equilibrium of the system, respectively. Numerical simulations are carried out to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we devise a simple way to explicitly construct the Riemann theta function periodic wave solution of the nonlinear partial differential equation. The resulting theory is applied to the Hirota–Satsuma shallow water wave equation. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function. We obtain the one-periodic and two-periodic wave solutions of the equation. The relations between the periodic wave solutions and soliton solutions are rigorously established. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we construct some compactly supported orthogonal regular wavelet basis on Heisenberg group . Because of the regularity of wavelets, we could use such wavelets to characterize function spaces on , such as bounded mean oscillation space (BMO) space, Hardy space, Besov spaces and Besov–Morrey spaces. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper we obtain several extensions to the quaternionic setting of someresultsconcerningtheapproximation bypolynomials of functionscontinuous onacompact set and holomorphic in its interior. The results include approximationon compact starlike sets and compact axially symmetric sets. The cases of someconcrete particular sets are described in details, including quantitative estimatestoo. AMS 2010 Mathematics Subject Classification: Primary 30G35; Secondary 30E10,41A25.Keywords and phrases: Mergelyan’s theorem, quaternions, Riemann mapping, axiallysymmetric sets, approximation by polynomials, convolution operators, Cassini pseudo-metric, Cassini cell, order of approximation, slice regular functions. 1 Introduction It is well-known the fact that the Mergelyan’s approximation theorem is the ultimatedevelopment and generalization of the Weierstrass approximation theorem and Runge’stheorem in the complex plane. It can be stated as follows (see [13]):Theorem 1.1. Let K be a compact subset of the complex plane C such that C\ K isconnected. Then, every continuous function on K, f : K → C, which is holomorphic inthe interior of K, can be approximated uniformly on K by polynomials.Notice that all the known proofs of this result, based on the methods in complex analysisuse the Riemann mapping theorem.1

The purpose of this paper is to show existence of a solution of the Dirichlet problem for a nonlinear generalized Darcy–Forchheimer–Brinkman system in a bounded Lipschitz domain in , with small boundary datum in L2-based Sobolev spaces. A useful intermediary result is the well-posedness of the Poisson problem for a generalized Brinkman system in a bounded Lipschitz domain in , with Dirichlet boundary condition and data in L2-based Sobolev spaces. We obtain this well-posedness result by showing that the matrix type operator associated with the Poisson problem is an isomorphism. Then, we combine the well-posedness result from the linear case with a fixed point theorem in order to show the existence of a solution of the Dirichlet problem for the nonlinear generalized Darcy–Forchheimer–Brinkman system. Some applications are also included. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we study the global existence of solution for the quasilinear chemotaxis system with Dirichlet boundary conditions, and further we show that the blow up properties of the solution depend only on the first eigenvalue. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we consider a three dimensional quantum Navier-Stokes-Poisson equations. Existence of global weak solutions is obtained, and convergence toward the classical solution of the incompressible Navier-Stokes equation is rigorously proven for well prepared initial data. Furthermore, the associated convergence rates are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results. Copyright © 2014 John Wiley & Sons, Ltd.

Green's function technique serves as a powerful tool to find the particle displacements due to SH-wave propagation in layer of a shape different from the space between two parallel planes. Therefore, the present paper undertook to study the propagation of SH-wave in a transversely isotropic piezoelectric layer under the influence of a point source and overlying a heterogeneous substrate using Green's function technique. The coupled electromechanical field equations are solved with the aid of Green's function technique. Expression for displacements in both layer and substrate, scalar potential and finally the dispersion relation is obtained analytically for the case when wave propagates along the direction of layering. Numerical computations are carried out and demonstrated with the aid of graphs for six different piezoelectric materials namely PZT-5H ceramics, Barium titanate (BaTiO3) ceramics, Silicon dioxide (SiO2) glass, Borosilicate glass, Cobalt Iron Oxide (CoFe2O4), and Aluminum Nitride (AlN). The effects of heterogeneity, piezoelectric and dielectric constants on the dispersion curve are highlighted. Moreover, comparative study is carried out taking the phase velocity for different piezoelectric materials on one hand and isotropic case on the other. Dispersion relation is reduced to well-known classical Love wave equation with a view to illuminate the authenticity of problem. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we consider the shape inverse problem of a body immersed in the incompressible fluid governed by thermodynamic equations. By applying the domain derivative method, we obtain the explicit representation of the derivative of solution with respect to the boundary, which plays an important role in the inverse design framework. Moreover, according to the boundary parametrization technique, we present a regularized Gauss–Newton algorithm for the shape reconstruction problem. Finally, numerical examples indicate the proposed algorithm is feasible and effective for the low Reynolds numbers. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, a diffusive predator–prey system, in which the prey species exhibits herd behavior and the predator species with quadratic mortality, has been studied. The stability of positive constant equilibrium, Hopf bifurcations, and diffusion-driven Turing instability are investigated under the Neumann boundary condition. The explicit condition for the occurrence of the diffusion-driven Turing instability is derived, which is determined by the relationship of the diffusion rates of two species. The formulas determining the direction and the stability of Hopf bifurcations depending on the parameters of the system are derived. Finally, numerical simulations are carried out to verify and extend the theoretical results and show the existence of spatially homogeneous periodic solutions and nonconstant steady states. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, a collocation method is given to solve singularly perturbated two-point boundary value problems. By using the collocation points, matrix operations and the matrix relations of the Bessel functions of the first kind and their derivatives, the boundary value problem is converted to a system of the matrix equations. By solving this system, the approximate solution is obtained. Also, an error problem is constructed by the residual function, and it is solved by the presented method. Thus, the error function is estimated, and the approximate solutions are improved. Finally, numerical examples are given to show the applicability of the method, and also, our results are compared by existing results. Copyright © 2014 JohnWiley & Sons, Ltd.

The short-time Fourier transform has been shown to be a powerful tool for non-stationary signals and time-varying systems. This paper investigates the signal moments in the Hardy–Sobolev space that do not usually have classical derivatives. That is, signal moments become valid for non-smooth signals if we replace the classical derivatives by the Hardy–Sobolev derivatives. Our work is based on the extension of Cohen's contributions to the local and global behaviors of the signal. The relationship of the moments and spreads of the signal in the time, frequency and short-time Fourier domain are established in the Hardy–Sobolev space. Copyright © 2014 John Wiley & Sons, Ltd.

The concept of mono-component is widely used in nonstationary signal processing and time-frequency analysis. In this paper, we construct several classes of complete rational function systems in the Hardy space, whose boundary values are mono-components. Then, we propose a best approximation algorithm (BAA) based on optimal selections of two parameters in the orthonormal bases according to the approximation error. Effectiveness of BAA is evaluated by comparison experiments with the classical Fourier decomposition algorithm. It is also shown that BAA has promising results for filtering out noises and dealing with real-world signals. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, by incorporating latencies for both human beings and female mosquitoes to the mosquito-borne diseases model, we investigate a class of multi-group dengue disease model and study the impacts of heterogeneity and latencies on the spread of infectious disease. Dynamical properties of the multi-group model with distributed delays are established. The results showthat the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium depends only on the basic reproduction number. Our proofs for global stability of equilibria use the classical method of Lyapunov functions and the graph-theoretic approach for large-scale delay systems. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper we construct two distinct generalized holomorphic orthogonal function systems over infinite cylinders in . Explicit representation formulae and properties of the obtained basis functions are given. As an application, we present some plot simulations that illustrate the results of this work. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the Darboux transformation of the Kundu–nonlinear Schrodinger equation is derived and generalized to the matrix of n-fold Darboux transformation. From known solution Q, the determinant representation of n-th new solutions of Q[n] are obtained by the n-fold Darboux transformation. Then soliton solutions and positon solutions are generated from trivial seed solutions, breather solutions and rogue wave solutions that are obtained from periodic seed solutions. After that, the higher order rogue wave solutions of the Kundu–nonlinear Schrodinger equation are given. We show that free parameters in eigenfunctions can adjust the patterns of the higher order rogue waves. Meanwhile, the third-order rogue waves are given explicitly. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper we present a collection of a priori estimates of the electromagnetic field scattered by a general bounded domain. The constitutive relations of the scatterer are in general anisotropic. Surface averages are investigated and several results on the decay of these averages are presented. The norm of the exterior Calderon operator for a sphere is investigated and depicted as a function of the frequency.

In this paper, a SIR model with two delays and general nonlinear incidence rate is considered. The local and global asymptotical stabilities of the disease-free equilibrium are given. The local asymptotical stability and the existence of Hopf bifurcations at the endemic equilibrium are also established by analyzing the distribution of the characteristic values. Furthermore, the sufficient conditions for the permanence of the system are given. Some numerical simulations to support the analytical conclusions are carried out. At last, some conclusions are given. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we prove the -boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer with resolvent parameter , where , and our boundary conditions are nonhomogeneous Neumann on upper boundary and Dirichlet on lower boundary. We want to emphasize that we can choose 0 0 arbitrarily, although usual parabolic theorem tells us that we must choose a large γ0 > 0 for given 0

In this paper, the exponential synchronization problem of delayed coupled reaction-diffusion systems on networks (DCRDSNs) is investigated. Based on graph theory, a systematic method is designed to achieve exponential synchronization between two DCRDSNs by constructing a global Lyapunov function for error system. Two different kinds of sufficient synchronization criteria are derived in the form of Lyapunov functions and coefficients of drive-response systems, respectively. Finally, a numerical example is given to show the usefulness of the proposed criteria. Copyright © 2014 John Wiley & Sons, Ltd.

This paper describes well-posedness, spectral representations, and approximations of solutions of uniformly elliptic, second-order, divergence form elliptic boundary value problems on exterior regions U in when N ≥ 3. Inhomogeneous Dirichlet, Neumann, and Robin boundary conditions are treated. These problems are first shown to be well-posed in the space E1(U) of finite-energy functions on U using variational methods. Spectral representations of these solutions involving Steklov eigenfunctions and solutions subject to zero Dirichlet boundary conditions are described. Some approximation results for the A-harmonic components are obtained. Positivity and comparison results for these solutions are given. Copyright © 2014 John Wiley & Sons, Ltd.

The bound of a chaotic system is important for chaos control, chaos synchronization, and other applications. In the present paper, the bounds of the generalized Lorenz system are studied, based on the Lyapunov function theory and the Lagrange multiplier method. We obtain a precise bound for the generalized Lorenz system. The rate of the trajectories is also obtained. Furthermore, we perform the numerical simulations. Numerical simulations are presented to show the effectiveness of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we develop a continuation principle for general hyperbolic singular limit problems in more general Besov spaces, which covers the cases of usual Sobolev spaces with higher regularity in and the critical Besov space. As an application, we give a simple justification for the low Mach number limit of compressible magnetohydrodynamics equations. More precisely, for the Mach number sufficiently small, the smooth compressible flows exist on the (finite) time interval where the incompressible magnetohydrodynamics equations have smooth solutions, and the definite convergence orders are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.