In this paper, we consider the Timoshenko systems with frictional dissipation working only on the vertical displacement. We prove that the system is exponentially stable if and only if the wave speeds are the same. On the contrary, we show that the Timoshenko systems is polynomially stable giving the optimal decay rate. Copyright © 2013 John Wiley & Sons, Ltd.

We provide a short proof on the infinite dimensionality of global attractors for a class of porous media equations. The proof is mainly based on the Z₂ index theory and proper use of energy functions and is completely different from the approaches in the existing literatures (M. Efendiev and S. Zelik, Finite and infinite dimensional attractors for porous media equations, Proc. London Math. Soc. 2008, 96:51–77; M. Efendiev, Infinite dimensional attractors for porous medium equations in heterogeneous medium, Math. Meth. Appl. Sci. 2012, DOI: 10.1002/mma.2619). Copyright © 2013 John Wiley & Sons, Ltd.

This paper is concerned with the existence, nonexistence, uniqueness, and non-uniqueness of solutions for a singular parabolic equation in one dimension case. For different cases of some constant m of the equation, we study the uniqueness of solutions for m > − 1, the nonexistence of solutions for m ≤ − p, and the existence and non-uniqueness of solutions for − p < m ≤ − 1. The novelty of this paper lies in the study of nonexistence. Moreover, the other results of this paper extend some recent works. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we introduce the definition of complex complete synchronization (CCS) of hyperchaotic complex nonlinear systems that have not been introduced recently in the literature. This type of synchronization can study only for complex nonlinear systems. On the basis of Lyapunov function, a scheme is designed to achieve the CCS of two nonidentical hyperchaotic attractors of these systems. The effectiveness of the obtained results is illustrated by a simulation example. Numerical results are plotted to show state variables, modules errors, and phases errors of these hyperchaotic attractors after synchronization to prove that CCS is achieved. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, a coupled Burgers’ equation has been numerically solved by a Galerkin quadratic B-spline FEM. The performance of the method has been examined on three test problems. Results obtained by the method have been compared with known exact solution and other numerical results in the literature. A Fourier stability analysis of the method is also investigated. Copyright © 2013 John Wiley & Sons, Ltd.

Our goal is to establish existence with suitable initial data of solutions to general parabolic equation in one dimension, u_t = L(u_x)_x, where L is merely a monotone function. We also expose the basic properties of solutions, concentrating on maximal possible regularity. Analysis of solutions with convex initial data explains why we may call them almost classical. Some qualitative aspects of solutions, such as facets (flat regions of solutions), are studied too. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we propose a new linear matrix inequality criterion for suppression of limit cycles in state–space direct form digital filters with saturation arithmetic and external interference via a passivity approach. The passive approach is employed to reduce the effect of external interference on the digital filter. The criterion guarantees not only asymptotic stability but also passivity from the external interference to the output vector. This criterion is in the form of linear matrix inequality; hence, it is computationally tractable. An example shows the effectiveness of the proposed criterion. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we study the following semilinear elliptic system

where N > 2, f(x,t) and g(x,t) are continuous functions and satisfy additional conditions. By using critical point theory of strongly indefinite functionals, we obtain a positive ground state solution and infinitely many geometrically distinct solutions when f(x,t) and g(x,t) are periodic in X and odd in t. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we construct a space of boundary values of the minimal symmetric discrete Hamiltonian operator with defect index (2,2), which is known as Weyl's limit-circle cases at ± ∞ , acting in the Hilbert space , where . With the help of the space of the boundary values, we describe all maximal dissipative (accretive), self-adjoint, and other extensions of such a symmetric operator. In these descriptions, we investigate maximal dissipative operators with general boundary conditions. For maximal dissipative operator, a self-adjoint dilation is constructed. Further, following the scattering theory, its incoming and outgoing spectral representations are set. These representations allow us to determine the scattering matrix of the dilation. Moreover, we construct a functional model of the maximal dissipative operator, and we define its characteristic function in terms of the scattering matrix of the dilation. Finally, we prove a completeness theorem about the system of root vectors of the maximal dissipative operator. Copyright © 2013 John Wiley & Sons, Ltd.

This paper concerns solutions for the Hamiltonian system: , where H(t,u) = 1 ∕ 2Lu ⋅ u + W(t,u), L is a 2N × 2N symmetric matrix, and . We consider the case that 0 ∉ σ_c( − (Jd ∕ dt + L)) and W satisfies some new generalized super quadratic condition different from the type of Ambrosetti–Rabinowitz. The method is variational: By virtue of some auxiliary system related to the ‘limit equation’ of the Hamiltonian system, we first establish that (C)_c-condition holds true for all c less than the least energy of the limit equation. Then, using some weak linking theorem recently developed, we obtain one least energy solution of the Hamiltonian system. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we establish the local well-posedness for the two-component b-family system in a range of the Besov space. We also derive the blow-up scenario for strong solutions of the system. In addition, we determine the wave-breaking mechanism to the two-component Dullin–Gottwald–Holm system. Copyright © 2013 John Wiley & Sons, Ltd.

Two-level penalty finite volume method for the stationary Navier–Stokes equations based on the P₁ − P₀ element is considered in this paper. The method involves solving one small penalty Navier–Stokes problem on a coarse mesh with mesh size H = ϵ^1 / 4h^1 / 2, a large penalty Stokes problem on a fine mesh with mesh size h, where 0 < ϵ < 1 is a penalty parameter. The method we study provides an approximate solution with the convergence rate of same order as the penalty finite volume solution (u_ϵh,p_ϵh), which involves solving one large penalty Navier–Stokes problem on a fine mesh with the same mesh size h. However, our method can save a large amount of computational time. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we study one-dimensional compressible isentropic Navier–Stokes equations with density-dependent viscosity. We can obtain the asymptotic stability of rarefaction waves for the compressible isentropic Navier–Stokes equations when the power of viscosity coefficient , which enlarge the range of α in the article [Jiu Q, Wang Y, Xin ZP, Communication in Partial Differential Equations 2011; 36: 602-634]. Copyright © 2013 John Wiley & Sons, Ltd.

This paper analyzes the existence and the uniqueness problem for an n-dimensional nonlinear inverse reaction-diffusion problem with a nonlinear source. A transformation is used to obtain a new inverse coefficient problem. Then, a parabolic differential operator L_λ is defined to establish the relation between the solution of L_λ = 0 and the new inverse problem. Following this, it is shown that the inverse problem has at least one solution in the class of admissible coefficients. Furthermore, it is proved that this solution is the unique solution of the undertaken inverse problem. A numerical example is given to illustrate ill-posedness of the inverse problem. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we study the existence of solutions for damped nonlinear impulsive differential equations with Dirichlet boundary conditions. By using critical point theory and variational methods, we give some new criteria to guarantee that the impulsive problems have at least one solution. Some recent results are extended and significantly improved. Finally, some examples are presented to illustrate our main results. Copyright © 2013 John Wiley & Sons, Ltd.

A Legendre–Gauss–Lobatto spectral collocation method is introduced for the numerical solutions of a class of nonlinear delay differential equations. An efficient algorithm is designed for the single-step scheme and applied to the multiple-domain case. As a theoretical result, we obtain a general convergence theorem for the single-step case. Numerical results show that the suggested algorithm enjoys high-order accuracy both in time and in the delayed argument and can be implemented in a robust and efficient manner. Copyright © 2013 John Wiley & Sons, Ltd.

In this article, we consider a three-dimensional Navier–Stokes–Voight model with memory where relaxation effects are described through a distributed delay. We prove the existence of uniform global attractors , where ϵ ∈ (0,1) is the scaling parameter in the memory kernel. Furthermore, we prove that the model converges to the classical three-dimensional Navier–Stokes–Voight system in an appropriate sense as ϵ → 0. In particular, we construct a family of exponential attractors Ξ_ϵ that is robust as ϵ → 0. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we describe a layer potential analysis in order to show an existence result for an interface boundary value problem of Robin-transmission type for the Stokes and Brinkman systems on Lipschitz domains in Euclidean setting, when the given boundary data belong to some L^p or Sobolev spaces associated to such domains. Applications related to an exterior three-dimensional Stokes flow past two concentric porous spheres with stress jump conditions on the fluid-porous interface are also considered. Copyright © 2013 John Wiley & Sons, Ltd.

Results on the existence of solutions of a periodic-type boundary value problem of singular multi-term fractional differential equations with the nonlinearity depending on are established and being singular at t = 0 and t = 1. The analysis relies on the well-known fixed-point theorems. An example is given to illustrate the efficiency of the main theorems. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, a class of impulsive damped vibration problems are considered. Existence results are obtained by using variational method and critical point theorem. The obtained results are also valid and new even if the impulsive damped vibration problem is reduced to impulsive Hamiltonian system and Hamiltonian system. Examples are presented to illustrate the feasibility and effectiveness of the results. Copyright © 2013 John Wiley & Sons, Ltd.

A gradient flow-based explicit finite element method (L2GF) for reconstructing the 3D density function from a set of 2D electron micrographs has been proposed in recently published papers. The experimental results showed that the proposed method was superior to the other classical algorithms, especially for the highly noisy data. However, convergence analysis of the L2GF method has not been conducted. In this paper, we present a complete analysis on the convergence of L2GF method for the case of using a more general form regularization term, which includes the Tikhonov-type regularizer and modified or smoothed total variation regularizer as two special cases. We further prove that the L²-gradient flow method is stable and robust. These results demonstrate that the iterative variational reconstruction method derived from the L²-gradient flow approach is mathematically sound and effective and has desirable properties. Copyright © 2013 John Wiley & Sons, Ltd.

This work focuses on a class of linear positive operators of discrete type. We present the relationship between the local smoothness of functions and the local approximation. Also, the degree of approximation in terms of the moduli of smoothness is established, and the statistical convergence of the sequence is studied. Copyright © 2013 John Wiley & Sons, Ltd.

A set of linear time-variant dynamic models for the interactive respiratory/cardiovascular mechanism is constructed and analyzed in this work. By using equivalent electric circuits for heart/blood and lung/air subsystems, the dynamics of cardiovascular subsystem and respiration cycle are established. In order to verify the validity of the dynamic models, numerical simulations and analysis on heart–lung interactions, including the valvular closure incompetence and pulmonary obstruction, are presented and compared with the empirical reports in literature. The derived dynamics of heart–lung interactions can be realized and examined in the biomechanical and medical engineering fields. In addition, the dynamic models can also be used for the model-based controller synthesis in medical instrumentations, for example, the extracorporeal membrane oxygenation, to retain the function of blood circulation and/or respiration by artificial intelligence. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is concerned with the sparse representation of analytic signal in Hardy space , where is the open unit disk in the complex plane. In recent years, adaptive Fourier decomposition has attracted considerable attention in the area of signal analysis in . As a continuation of adaptive Fourier decomposition-related studies, this paper proves rapid decay properties of singular values of the dictionary. The rapid decay properties lay a foundation for applications of compressed sensing based on this dictionary. Through Hardy space decomposition, this program contributes to sparse representations of signals in the most commonly used function spaces, namely, the spaces of square integrable functions in various contexts. Numerical examples are given in which both compressed sensing and ℓ₁-minimization are used. Copyright © 2013 John Wiley & Sons, Ltd.

On the basis of bifurcation theory, we use Newton's method to compute and visualize the multiple solutions to a series of typical semilinear elliptic boundary value problems with a homogeneous Dirichlet boundary condition in . We present three algorithms on the basis of the bifurcation method to solving these multiple solutions. We will compute and visualize the profiles of such multiple solutions, thereby exhibiting the geometrical effects of the domains on the multiplicity. The domains include the square, disk, symmetric or nonsymmetric annuli and dumbbell. The nonlinear partial differential equations include the Lane–Emden equation, concave–convex nonlinearities, Henon equation, and generalized Lane–Emden system. Copyright © 2013 John Wiley & Sons, Ltd.

We study the Robin problem for the scalar Oseen equation in an open n-dimensional set with compact Ljapunov boundary. We prescribe two types of Robin boundary conditions, and prove the unique solvability of these problems as well as a representation formula for the solution in form of a scalar Oseen single layer potential. Moreover, we prove the maximum principle for the solution to the Robin problem of the scalar Oseen equation. Copyright © 2013 John Wiley & Sons, Ltd.

We propose an image restoration method. The method generalizes image restoration algorithms that are based on the Moore–Penrose solution of certain matrix equations that define the linear motion blur. Our approach is based on the usage of least squares solutions of these matrix equations, wherein an arbitrary matrix of appropriate dimensions is included besides the Moore–Penrose inverse. In addition, the method is a useful tool for improving results obtained by other image restoration methods. Toward that direction, we investigate the case where the arbitrary matrix is replaced by the matrix obtained by the Haar basis reconstructed image. The method has been tested by reconstructing an image after the removal of blur caused by the uniform linear motion and filtering the noise that is corrupted with the image pixels. The quality of the restoration is observable by a human eye. Benefits of using the method are illustrated by the values of the improvement in signal-to-noise ratio and in the values of peak signal-to-noise ratio. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we derive time reversal imaging functionals for two strongly causal acoustic attenuation models, which have been proposed recently. The time reversal techniques are based on recently proposed ideas of Ammari et al. for the thermo-viscous wave equation. Here and there, an asymptotic analysis provides reconstruction functionals from first order corrections for the attenuating effect. In addition, we present a novel approach for higher order corrections. Copyright © 2013 John Wiley & Sons, Ltd.

We study precisely the solution of a semi-discrete von Mises problem with known pressure to generalize a method for an inverse problem: the problem with known displacement. We prove the boundedness of the diffusive term, the uniqueness and the continuity of the solution with respect to the pressure and a coercivity property. However, the estimate of the diffusive term is not sharp enough for the inverse problem. We highlight a special behaviour of this term due to the combination of the nonlinearity with the degeneracy of the diffusion coefficient. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we obtain the existence of at least two nontrivial solutions for a Robin-type differential inclusion problem involving p(x)-Laplacian type operator and nonsmooth potentials. Our approach is variational, and it is based on the nonsmooth critical point theory for locally Lipschitz functions. Copyright © 2013 John Wiley & Sons, Ltd.

The method of asymptotic partial domain decomposition has been proposed for partial differential equations set in rod structures, depending on a small parameter. It reduces the dimension of the problem (or simplifies it in another way) in the main part of the domain keeping the initial formulation in the remaining part and prescribing the asymptotically precise conditions on the interface. This paper is devoted to the finite volume implementation of the method of asymptotic partial domain decomposition. We consider a model problem in a thin domain (its thickness is a small parameter). We obtain an error estimate, expressed in terms of the small parameter and the step of the mesh. Copyright © 2013 John Wiley & Sons, Ltd.

We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof, which is essentially based on an elliptic Carleman inequality. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we give some sufficient conditions to guarantee global asymptotic stability of the zero solution of the third-order nonlinear differential equation: x ′ ′ ′ + g(x,x ′ ,x ′ ′ ) + f(x,x ′ )x ′ + h(x) = 0. Two examples are also given to illustrate our results. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is concerned with the large time behavior of solutions of the Cauchy problem to the one-dimensional compressible fluid models of Korteweg type, which governs the motions of the compressible fluids with internal capillarity. When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, it is shown that the viscous contact wave corresponding to the contact discontinuity is asymptotically stable provided that the strength of contact discontinuity and the initial perturbation are suitably small. The analysis is based on the elementary L²-energy method together with continuation argument. Copyright © 2013 John Wiley & Sons, Ltd.

We consider the problem of the rigorous description of nonequilibrium quantum correlations. Within the framework of an alternative approach to the description of the evolution of states of finitely many particles in terms of correlation operators governed by the von Neumann hierarchy, we derive the nonlinear quantum Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy for marginal correlation operators that is adopted to the description of quantum infinite-particle systems as well. A nonperturbative solution of the Cauchy problem of the nonlinear quantum BBGKY hierarchy for marginal correlation operators is constructed. Copyright © 2013 John Wiley & Sons, Ltd.

This paper deals with a nonlocal free boundary problem arising in the study of the dynamics of the confinement of a plasma in a Stellarator device. The free boundary represents the separation between the plasma and vacuum regions, and the nonlocal term involves the notions of relative rearrangement and monotone rearrangement. We establish some new properties on the decreasing rearrangement that can be used to prove the convergence of the approximate problem, and then prove the existence of solutions by Galerkin method. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider a hyperbolic differential inclusion with viscoelastic boundary conditions localized on a part of the boundary. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider a nonhomogeneous space-time fractional telegraph equation defined in a bounded space domain, which is obtained from the standard telegraph equation by replacing the first-order or second-order time derivative by the Caputo fractional derivative , α > 0 and the Laplacian operator by the fractional Laplacian ( − Δ)^β ∕ 2, β ∈ (0,2]. We discuss and derive the analytical solutions under nonhomogeneous Dirichlet and Neumann boundary conditions by using the method of separation of variables. The obtained solutions are expressed through multivariate Mittag-Leffler type functions. Special cases of solutions are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.

By using the smoothing functions and the least square reformulation, in this paper, we present a smoothing least square method for the nonlinear complementarity problem. The method can overcome the difficulty of the non-smooth method and a major drawback of some existed equation-based methods. Under the standard assumptions, we obtain the global convergence of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider the existence and multiplicity for second-order nonlinear impulsive differential equations with Dirichlet boundary condition and a parameter. By using critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution or infinitely many solutions, assuming that the impulsive functions satisfy the superlinear growth condition and the parameter inequality is reverse. Our results extend and improve some recent results. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we study the asymptotic stability of a composite wave consisting of two traveling waves to a hyperbolic–parabolic system modeling repulsive chemotaxis. On the basis of elementary energy estimates, we show that the composite wave is asymptotically stable under general initial perturbations, which are not necessarily zero integral. As an application, we obtain a similar result for this system in the presence of a boundary. Copyright © 2013 John Wiley & Sons, Ltd.

A method for studying the one-dimensional heat transfer process within an inhomogeneous spatially bounded medium in the presence of an external heat source is presented. It is based on a recently introduced technique for solving problems related to Sturm–Liouville equations that consists in the representation of solutions in the form of a spectral parameter power series. We consider a heat transfer model linked to photoacoustic and show that the introduced method, besides its relative simplicity and analytical nature, offers an efficient numerical algorithm as well as a convenient way to work separately with different physically meaningful components of the temperature distribution function. Detailed explanations and numerical examples are given. Copyright © 2013 John Wiley & Sons, Ltd.

We derive a new ( 2 + 1)-dimensional Korteweg–de Vries 4 (KdV4) equation by using the recursion operator of the KdV equation. This study shows that the new KdV4 equation possess multiple soliton solutions the same as the multiple soliton solutions of the KdV hierarchy, but differ only in the dispersion relations. We also derive other traveling wave solutions. Copyright © 2013 John Wiley & Sons, Ltd.

We present numerical schemes for the P1-moment and M1-moment approximations of a non-classical transport equation modeling radiative transfer in atmospheric clouds. In contrast to classical radiative transfer, the photon path-length is introduced as an additional variable and serves as pseudo-time in this model. Because clouds may have optically thick regions, we introduce a diffusive scaling and show that the diffusion limits of the moment models and the original equations agree. Furthermore, we show that the numerical schemes also preserve the diffusion asymptotics as well as the set of admissible and realizable states, both for the explicit and the implicit discretization of the pseudo-time variable. A source iteration-like method is proposed, and we observe that it converges slowly in the optical thick case, but a suitable initialization can help to overcome this problem. We validate our method in 1D and present simulation results in the 2D-case for real cloud data. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we employ the complex method to obtain first all meromorphic solutions of an auxiliary ordinary differential equation and then find all meromorphic exact solutions of the classical Korteweg–de Vries equation, Boussinesq equation, ( 3 + 1)-dimensional Jimbo–Miwa equation, and Benjamin–Bona–Mahony equation. Our results show that the method is more simple than other methods. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we study the heat transfer in a one-dimensional fully developed flow of granular materials down a heated inclined plane. For the heat flux vector, we use a recently derived constitutive equation that reflects the dependence of the heat flux vector on the temperature gradient, the density gradient, and the velocity gradient in an appropriate frame invariant formulation. We use two different boundary conditions at the inclined surface: a constant temperature boundary condition and an adiabatic condition. A parametric study is performed to examine the effects of the material dimensionless parameters. The derived governing equations are coupled nonlinear second-order ordinary differential equations, which are solved numerically, and the results are shown for the temperature, volume fraction, and velocity profiles. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is concerned with the existence, uniqueness, and asymptotic behavior of solutions for the quasilinear parabolic systems with mixed quasimonotone reaction functions, the elliptic operators in which are allowed to be degenerate. By the method of the coupled upper and lower solutions, and its monotone iterations, it shows that a pair of coupled upper and lower solutions ensures that the unique positive solution exists and globally stable if the quasisolutions are equal. Moreover, we study the asymptotic behavior of solutions to the Lotka–Volterra model with the density-dependent diffusion. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider the global existence of weak solutions for a two-component μ-Camassa–Holm system in the periodic setting. Global existence for strong solutions to the system with smooth approximate initial value is derived. Then, we show that the limit of approximate solutions is a global-in-time weak solution of the two-component μ-Camassa–Holm system. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider the following elliptic systems with critical Sobolev growth and Hardy potentials:

where N ≥ 3, η > 0, λ₁,λ₂ ∈ [0,Λ_N), and is the best Hardy constant. is the critical Sobolev exponent. a₁, a₂, b₁, and b₂ are positive parameters, and α,β > 1 satisfy 2 < α + β < 2*. h(x) ≢ 0, h(x) ≥ 0, , , and with . By means of the concentration–compactness principle and R. Kajikiya's new version of symmetric mountain pass lemma, we obtain infinitely many solutions that tend to zero. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider the scattering theory of a nonlinear Klein–Gordon system, which describes the interaction of two scalar fields. The analysis in this paper is an adaptation of the technique used by Nakanishi, which is originally due to Bourgain. The new technical point appears in the localization argument of proving a concentration phenomenon. Copyright © 2013 John Wiley & Sons, Ltd.

This work presents a study of Mandarin speech focusing on consistency analysis of the spectrum and prosody within syllables. Identified as a result of inspection of the human pronunciation process, this consistency can be interpreted as a high correlation between the warping curves of the spectrum and the prosody intra a syllable. The consistency analysis consisted of three steps. First, the hidden Markov model algorithm was used to decode the hidden Markov model-state sequences within a syllable, while at the same time dividing them into three segments. Second, based on a designated syllable, the vector quantization (VQ) with the Linde–Buzo–Gray algorithm was employed to train the VQ codebooks of the prosodic vector of each segment. Third, the prosodic vector of each segment was encoded as an index using the VQ codebooks, and then, to analyze the consistency, the probability of each possible path was evaluated as a prerequisite. Finally, two syllables were used as examples to verify the consistency property found in the experiments. It is demonstrated experimentally that there is definitely consistency in the case where the syllable is located in exactly the same word. These results offer a research direction in that the warping process between the spectrum and the prosody intra a syllable must be considered in text-to-speech systems to improve the synthesized speech quality. Copyright © 2013 John Wiley & Sons, Ltd.

Four numerical techniques based on the linear B-spline functions are presented for the numerical solution of the Lane–Emden equation. Some properties of the B-spline functions are presented and are utilized to reduce the solution of the Lane–Emden equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new techniques. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we prove a stability result about the asymptotic dynamics of a perturbed nonautonomous evolution equation in governed by a maximal monotone operator. Copyright © 2013 John Wiley & Sons, Ltd.

Multidimensional persistence mostly studies topological features of shapes by analyzing the lower level sets of vector-valued functions, called filtering functions. As is well known, in the case of scalar-valued filtering functions, persistent homology groups can be studied through their persistent Betti numbers, that is, the dimensions of the images of the homomorphisms induced by the inclusions of lower level sets into each other. Whenever such inclusions exist for lower level sets of vector-valued filtering functions, we can consider the multidimensional analog of persistent Betti numbers. Varying the lower level sets, we obtain that persistent Betti numbers can be seen as functions taking pairs of vectors to the set of non-negative integers. In this paper, we prove stability of multidimensional persistent Betti numbers. More precisely, we prove that small changes of the vector-valued filtering functions imply only small changes of persistent Betti numbers functions. This result can be obtained by assuming the filtering functions to be just continuous. Multidimensional stability opens the way to a stable shape comparison methodology based on multidimensional persistence. In order to obtain our stability theorem, some other new results are proved for continuous filtering functions. They concern the finiteness of persistent Betti numbers for vector-valued filtering functions and the representation via persistence diagrams of persistent Betti numbers, as well as their stability, in the case of scalar-valued filtering functions. Finally, from the stability of multidimensional persistent Betti numbers, we obtain a lower bound for the natural pseudo-distance. Copyright © 2012 John Wiley & Sons, Ltd.

In continuation of recent studies, we discuss two constructive approaches for the generation of harmonic conjugates to find null solutions to the Riesz system in . This class of solutions coincides with the subclass of monogenic functions with values in the reduced quaternions. Our first algorithm for harmonic conjugates is based on special systems of homogeneous harmonic and monogenic polynomials, whereas the second one is presented by means of an integral representation. Some examples of function spaces illustrating the techniques involved are given. More specifically, we discuss the (monogenic) Hardy and weighted Bergman spaces on the unit ball in consisting of functions with values in the reduced quaternions. We end up proving the boundedness of the underlying harmonic conjugation operators in certain weighted spaces. Copyright © 2012 John Wiley & Sons, Ltd.

The thermostatted kinetic framework has been recently proposed in [C. Bianca, Nonlinear Analysis: Real World Applications 13 (2012) 2593-2608] for the modeling of complex systems in the applied sciences under the action of an external force field that moves out of equilibrium the system. The framework consists in an integro-differential equation with quadratic nonlinearity coupled with the Gaussian isokinetic thermostat. This paper is concerned with the existence of stationary solutions proof. The main result is gained by fixed point and measure theory arguments. Copyright © 2013 John Wiley & Sons, Ltd.

We consider a boundary value problem for the Sturm–Liouville equation with piecewise-constant leading coefficient. We prove that some integral representations for the solutions of the considered equation can be obtained by using classical transformation operators for the Sturm–Liouville operator at the end points of a finite interval. We also investigate the spectral characteristics of the boundary value problem, prove the completeness and expansion theorem. Copyright © 2012 John Wiley & Sons, Ltd.

The pseudo-spectral Legendre–Galerkin method (PS-LGM) is applied to solve a nonlinear partial integro-differential equation arising in population dynamics. This equation is a competition model in which similar individuals are competing for the same resources. It is a kind of reaction–diffusion equation with integral term corresponding to nonlocal consumption of resources. The proposed method is based on the Legendre–Galerkin formulation for the linear terms and interpolation operator at the Chebyshev–Gauss–Lobatto (CGL) points for the nonlinear terms. Also, the integral term, which is a kind of convolution, is directly computed by a fast and accurate method based on CGL interpolation operator, and thus, the use of any quadrature formula in its computation is avoided. The main difference of the PS-LGM presented in the current paper with the classic LGM is in treating the nonlinear terms and imposing boundary conditions. Indeed, in the PS-LGM, the nonlinear terms are efficiently handled using the CGL points, and also the boundary conditions are imposed strongly as collocation methods. Combination of the PS-LGM with a semi-implicit time integration method such as second-order backward differentiation formula and Adams-Bashforth method leads to reducing the complexity of computations and obtaining a linear algebraic system of equations with banded coefficient matrix. The desired equation is considered on one and two-dimensional spatial domains. Efficiency, accuracy, and convergence of the proposed method are demonstrated numerically in both cases. Copyright © 2012 John Wiley & Sons, Ltd.

The purpose of this paper is to construct a family of fundamental solutions for elliptic partial differential operators with quaternion constant coefficients. The elements of such family are expressed by means of functions, which depend jointly real analytically on the coefficients of the operators and on the spatial variable. We show some regularity properties in the frame of Schauder spaces for the corresponding single layer potentials. Ultimately, we exploit our construction by showing a real analyticity result for perturbations of the layer potentials corresponding to complex elliptic partial differential operators of order two. Copyright © 2012 John Wiley & Sons, Ltd.

Alzheimer's disease (AD) is a severe neurodegenerative disorder characterised by cognitive impairment and dementia. In the AD-affected brain, microglia cells are up-regulated and accumulate at senile plaques, the most prominent pathological feature of AD. In order to further study and predict the movement of activated microglia, we utilised their chemotactic properties. Specifically, we formulated the string gradient weighted moving finite element method for a system of partial differential equations in two dimensions, which includes nonlinear diffusion of a different variable found in chemotaxis models. The method was applied successfully to solve highly nonlinear chemorepulsion–chemorepellent models in two dimensions, and the results were compared with one-dimensional results found previously in the literature. We conclude that the string gradient weighted moving finite element method is easily applied to chemotaxis models, in particular movement and aggregation of microglia, resulting in the ability to study the models extended in two dimensions efficiently. Our study highlights the feasibility and power of mathematical modelling to advance our understanding of pathophysiological processes in neurodegenerative diseases, including AD. Copyright © 2012 John Wiley & Sons, Ltd.

Conditions for the existence of polynomial solutions of certain second-order differential equations have recently been investigated by several authors. In this paper, a new algorithmic procedure is given to determine necessary and sufficient conditions for a differential equation with polynomial coefficients containing parameters to admit polynomial solutions and to compute these solutions. The effectiveness of this approach is illustrated by applying it to determine new solutions of several differential equations of current interest. A comparative analysis is given to demonstrate the advantage of this algorithmic procedure over existing software. Copyright © 2012 John Wiley & Sons, Ltd.

We consider a coupled model for steady flows of viscous incompressible heat-conducting fluids with dissipative and adiabatic heating and temperature-dependent material coefficients in a plane bounded domain. The existence of a strong solution is proven by a fixed-point technique based on Schauder theorem for sufficiently small external forces. Copyright © 2012 John Wiley & Sons, Ltd.

A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet–Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing momentum relaxation limit. It consists of a drift-diffusion-type equation for the electron density, involving temperature gradients, a nonlinear heat equation for the electron temperature, and the Poisson equation for the electric potential. The global-in-time existence of bounded weak solutions is proved. The proof is based on the Stampacchia truncation method and a careful use of the temperature equation. Under some regularity assumptions on the gradients of the variables, the uniqueness of solutions is shown. Finally, numerical simulations for a ballistic diode in one space dimension illustrate the behavior of the solutions. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we propose a Tau method for solving the singular Lane–Emden equation—a nonlinear ordinary differential equation on a semi-infinite interval. We applied collocation, Galerkin, and Tau methods for solving this problem, and according to the results, the solution of Tau method is the most accurate. The operational derivative and product matrices of the modified generalized Laguerre functions are presented. These matrices, in conjunction with the Tau method, are then utilized to reduce the solution of the Lane–Emden equation to that of a system of algebraic equations. We also present a comparison of this work with some well-known results and show that the present solution is highly accurate. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the problem of μ-stability of impulsive differential systems with unbounded time-varying delays and nonlinear perturbations. Some μ-stability criteria, which depend on the range of distributed delay and the decay rate of discrete delay (not the range), are derived by using Lyapunov–Krasovski functional method. Those criteria are expressed in the form of linear matrix inequalities and they can easily be checked. Two numerical examples are provided to demonstrate the effectiveness of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.

A kind of partially dissipative quasilinear hyperbolic systems in which a part of equations possesses the strict dissipation and the others are weakly linearly degenerate are discussed. Under some weaker hypotheses on the interactions between two parts of equations, it is proved that for any given initial data with small W^1,1 and C¹ norms, the corresponding Cauchy problem admits a unique C¹ global classical solution. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we obtain a multiplicity result for a class of asymptotically linear noncooperative elliptic systems by using saddle point reduction technique and two abstract critical point theorems. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, instead of energy methods, we apply the supersolution and subsolution methods to investigate the critical extinction exponents for a polytropic filtration equation with absorption and source, and improve the results of Mu et al. (J. Math. Anal. Appl. 2012; 391:429–440). Copyright © 2012 John Wiley & Sons, Ltd.

In this work, a discontinuous boundary-value problem with retarded argument that contains a spectral parameter in the transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. Copyright © 2012 John Wiley & Sons, Ltd.

Sufficient conditions for the existence of at least one periodic solution of two classes of nonlinear higher order periodic difference equations are established, respectively. The results show us that sufficient conditions for the existence of T − periodic solutions of difference equation are different from those ones for the existence of T − periodic solutions of differential equation. Copyright © 2012 John Wiley & Sons, Ltd.

We considered the inverse problem of scattering theory for a boundary value problem on the half line generated by Klein–Gordon differential equation with a nonlinear spectral parameter-dependent boundary condition. We defined the scattering data, and we proved the continuity of the scattering function S(λ); in a special case, the relation for the difference of the logarithm of the scattering function, which is called the Levinson-type formula, was obtained. Copyright © 2012 John Wiley & Sons, Ltd.

We propose a novel numerical method based on a generalized eigenvalue decomposition for solving the diffusion equation governing the correlation diffusion of photons in turbid media. Medical imaging modalities such as diffuse correlation tomography and ultrasound-modulated optical tomography have the (elliptic) diffusion equation parameterized by a time variable as the forward model. Hitherto, for the computation of the correlation function, the diffusion equation is solved repeatedly over the time parameter. We show that the use of a certain time-independent generalized eigenfunction basis results in the decoupling of the spatial and time dependence of the correlation function, thus allowing greater computational efficiency in arriving at the forward solution. Besides presenting the mathematical analysis of the generalized eigenvalue problem on the basis of spectral theory, we put forth the numerical results that compare the proposed numerical method with the standard technique for solving the diffusion equation. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we study some new special functions that arise naturally within the framework of Hermitian Clifford analysis, which concerns the study of Dirac-like systems in several complex variables. In particular, we focus on Hermite polynomials, Bessel functions, and generalized powers. We also derive a Vekua system for solutions of Hermitian systems in axially symmetric domains. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents an accurate numerical method for solving a class of fractional variational problems (FVPs). The fractional derivative in these problems is in the Caputo sense. The proposed method is called fractional Chebyshev finite difference method. In this technique, we approximate FVPs and end up with a finite-dimensional problem. The method is based on the combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The Caputo fractional derivative is replaced by a difference quotient and the integral by a finite sum. The fractional derivative approximation using Clenshaw and Curtis formula introduced here, along with Clenshaw and Curtis procedure for the numerical integration of a non-singular functions and the Rayleigh–Ritz method for the constrained extremum, is considered. By this method, the given problem is reduced to the problem for solving a system of algebraic equations, and by solving this system, we obtain the solution of FVPs. Special attention is given to study the convergence analysis and evaluate an error upper bound of the obtained approximate formula. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique. A comparison with another method is given. Copyright © 2012 John Wiley & Sons, Ltd.

A weighted blending interpolator, a kind of smooth rational spline based only on function values, is constructed using a rational cubic spline and a polynomial spline. In order to meet the needs of practical design, a new control method is employed to control the shape of curves. The advantage of the method is that it can be applied to modify the local shape of an interpolating curve by selecting suitable parameters and weight coefficients simply. Also, when the weight coefficient is in [0,1], the error estimation formula of this interpolator is obtained. Copyright © 2012 John Wiley & Sons, Ltd.

An analytical approach based on the parametric representation of the wave propagation in non-uniform media was considered. In addition to the previously developed theory of parametric antiresonance describing the field attenuation in stop bands, in the present paper, the behaviour of the Bloch wave in a transmission band was investigated. A wide class of exact solutions was found, and the correspondence to the quasi-periodic Floquet solutions was shown. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with a compressible viscoelastic fluids of Oldroyd-B type. We prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition. Moreover, we establish a blow-up criterion for the strong solution in terms of the norm of the density tensor ρ and the norm of the symmetric tensor of constraints τ. All the results hold for the initial density vanishing from below. Copyright © 2012 John Wiley & Sons, Ltd.

The article aims to study the basic dynamical features of a modified Holling–Tanner prey–predator model with ratio-dependent functional response. We have proved the global existence of the solution for the deterministic model. The parametric restriction for persistence of both species is also obtained along with the proof of local asymptotic stability of the interior equilibrium point(s). Conditions for local bifurcations of interior equilibrium points are provided. The global dynamic behavior is examined thoroughly with supportive numerical simulation results. Next, we have formulated the stochastic model by perturbing the intrinsic growth rates of prey and predator populations with white noise terms. The existence uniqueness of solutions for stochastic model is established. Further, we have derived the parametric restrictions required for the persistence of the stochastic model. Finally, we have discussed the stochastic stability results in terms of the first and second order moments. Numerical simulation results are provided to support the analytical findings. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we investigate a problem of the identification of an unknown source on Poisson equation from some fixed location. A conditional stability estimate for an inverse heat source problem is proved. We show that such a problem is mildly ill-posed and further present two Tikhonov-type regularization methods (a generalized Tikhonov regularization method and a simplified generalized Tikhonov regularization method) to deal with this problem. Convergence estimates are presented under the a priori choice of the regularization parameter. Numerical results are presented to illustrate the accuracy and efficiency of our methods. Copyright © 2012 John Wiley & Sons, Ltd.

The purpose of the paper is to study the asymptotic behavior at infinity of solutions of a perturbed Dirac equation in called k-monogenic. Every such solution is a solution of the Helmholtz equation with values in a complex Clifford algebra. The main goal is to use the far-field pattern to characterize the radiating (outgoing) k-monogenic functions among the radiating solutions of the Helmholtz equation. It will be shown that an algebraic condition characterizes these far-field patterns. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with a simplified system, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. We establish a blowup criterion for three-dimensional compressible nematic liquid crystal flows, which is analogous to the well-known Serrin's blowup criterion for three-dimensional incompressible viscous flows. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we consider a mathematical model describing the two-phase interaction between water and mud in a water canal when the width of the canal is small compared with its depth. The mud is treated as a non-Newtonian fluid, and the interface between the mud and fluid is allowed to move under the influence of gravity and surface tension. We reduce the mathematical formulation, for small boundary and initial data, to a fully nonlocal and nonlinear problem and prove its local well-posedness by using abstract parabolic theory. Copyright © 2012 John Wiley & Sons, Ltd.

We propose a model for nonisothermal ferromagnetic phase transition based on a phase field approach, in which the phase parameter is related but not identified with the magnetization. The magnetization is split in a paramagnetic and in a ferromagnetic contribution, dependent on a scalar phase parameter and identically null above the Curie temperature. The dynamics of the magnetization below the Curie temperature is governed by the order parameter evolution equation and by a Landau–Lifshitz type equation for the magnetization vector. In the simple situation of a uniaxial magnet, it is shown how the order parameter dynamics reproduces the hysteresis effect of the magnetization. Copyright © 2012 John Wiley & Sons, Ltd.

The existence of global solutions is established for compressible Navier–Stokes equations by taking into account the radiative and reactive processes, when the heat conductivity κ (κ₁(1 + θ^q) ≤ κ ≤ κ₂(1 + θ^q),q ≥ 0), where θ is the temperature. This improves the previous results by enlarging the scope of q including the constant heat conductivity. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the initial value problem for the fourth-order nonlinear Schrödinger type equation related to the theory of vortex filament. By deriving a fundamental estimate on dyadic blocks for the fourth-order Schrödinger through the [k,Z]-multiplier norm method. we establish multilinear estimates for this nonlinear fourth-order Schrödinger type equation. The local well-posedness for initial data in with s > 1 ∕ 2 is implied by the multilinear estimates. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we consider a three-dimensional viral model with delay. We first investigate the linear stability and the existence of a Hopf bifurcation. It is shown that Hopf bifurcations occur as the delay τ passes through a sequence of critical values. Then, using the normal form theory and center manifold reduction, we derive the explicit formulaes that determine the stability, the direction, and the period of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the validity of the main results. Finally, some brief conclusions are given. Copyright © 2012 John Wiley & Sons, Ltd.

An a priori error estimate using a so called α,β- periodic transformation to study electromagnetic waves in a periodic diffraction grating is derived. It has been reported for single scattering that there is an instability in numerical methods for high wavenumbers. To address this problem, the analytical solution of the scattering problem when the domain is scatterer free and an unknown function called the α,β-quasi periodic solution are used to transform the associated Helmholtz problem. The well-posedness of the resulting continuous problem is analysed before approximating its solution using a finite element discretization. To guarantee the uniqueness of this approximate solution, an a priori error estimate is derived. Finally, numerical results are presented that suggest that the α,β-quasi periodic method converges at a far lower number of degrees of freedom than the α,0-quasi periodic method reported previously; especially for high wavenumbers. This is particularly true when the incident wave only undergoes a small perturbation because of the presence of the scatterer. Copyright © 2012 John Wiley & Sons, Ltd.

A system of particles, in general d-dimensional space, that interact by means of pair potentials and adjust their positions according to the gradient flow dynamics induced by the total energy of the system is studied. The case when the range of the interaction is of the same order as the mean interparticle distance is considered. It is also assumed that particles, locally, are located close to some crystallographic lattice. An appropriate system of equations that describes the evolution of macroscopic deformation of the crystallographic lattice, as well as the system that describes the evolution of the main crystallographic directions is derived. Well-posedness of the derived system is studied as well as the stability of the particle system. Same examples of potentials that yield stable and unstable systems are given. Copyright © 2012 John Wiley & Sons, Ltd.

We introduce higher-order duality (Mangasarian type and Mond–Wier type) of variational problems. Under higher-order generalized invexity assumptions on functions that compose the primal problem, higher-order duality results (weak duality, strong duality, and converse duality) are derived for this pair of problems. Also, we establish many examples and counter-examples to support our investigation. Copyright © 2012 John Wiley & Sons, Ltd.

The basic linear model for describing an age structured population spreading in a limited habitat is considered with the purpose of investigating an approximation procedure based on parabolic regularization. In fact, a viscosity model is introduced by considering an appropriate approximating regularized parabolic problem and it is proved that the sequence of the approximating solutions tends to the solution to the original problem. The advantage of this approach is that it leads to the numerical solution of a parabolic problem that has more stable solutions than the hyperbolic-parabolic original problem and avoids the restrictions (compatibility conditions) needed to treat the latter. Moreover, for the solution of the approximating problem, it is possible to take advantage of established software packages dedicated to parabolic problems. Some examples of the approach are provided using COMSOL Multiphysics. Copyright © 2012 John Wiley & Sons, Ltd.

We consider the viscous hyperelastic-rod wave equation subject to an external force, where the viscous term is given by second order differential operator in divergence form. Under some mild assumptions on the viscous term, first, we establish the global well-posedness in both the periodic case and the case of the whole line, afterwards, we show the existence of global attractors for the two cases, respectively. Copyright © 2012 John Wiley & Sons, Ltd.

In this article, we give some results on the S-essential spectra of a linear operator defined on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in the Banach space L_p([−a,a] × [−1,1]),p ≥ 1 and a > 0. Copyright © 2012 John Wiley & Sons, Ltd.

We study how the inclusion of a fractal array of conductive thin fibers affects, and interacts with, the dynamical properties of the surrounding medium. Our approach is variational and is based on singular homogenization. We introduce the energy forms that describe the composite media formed by a two-dimensional Euclidean domain reinforced by an increasing number of thin conductive fibers developing fractal geometry. We study the convergence of the energy, under suitable assumptions for the relative strength of the fibers in relation to the embedding medium. Our results establish convergence of energy and of the spectral measures of the singular elliptic operators describing the composite medium. Copyright © 2012 John Wiley & Sons, Ltd.

We show that any non-periodic nonlinear elliptic homogenization problem can be approximated by periodic homogenization problems. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we study the 3D Helmholtz equation in perturbed stratified media, allowing the presence of guided waves. Our assumptions on the perturbed and source terms are too few. On the basis of the knowledge of the Green's function for the 3D homogeneous Helmholtz equation in unperturbed stratified media, we introduce a generalized (out-going) Sommerfeld–Rellich radiation condition, and then we prove the uniqueness and existence of solutions for the studied 3D Helmholtz equation satisfying our radiation condition. Copyright © 2012 John Wiley & Sons, Ltd.

We reduce an exterior initial boundary value problem for the wave equation in three space dimensions to an initial boundary value problem on a bounded computational domain bounded by an artificial boundary as well as the original boundary. From a Kirchhoff representation formula for the solution of wave equation in an exterior domain, we derive on the artificial boundary (exact) transparent boundary conditions that are nonlocal in space and time. These lead to local approximate transparent boundary conditions of the first and second orders. It is shown that these approximate transparent conditions are satisfied exactly for a related spherically symmetric problem. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we give a new sufficient condition for oscillation of first-order delay dynamic equations on time scales, which generalize the main results of the papers [Proc. Amer. Math. Soc. 124 (1996), no. 12, 3729–3737] by Li and [Comput. Math. Appl. 37 (1999), no. 7, 11–20] by Tang and Yu. To emphasize the significance of the new result, an example for which all the results fail is also given on a nonstandard time scale. Copyright © 2013 John Wiley & Sons, Ltd.

The Ginzburg–Landau equation appears as a universal amplitude equation for spatially extended pattern forming systems close to the first instability. It can be derived via multiple scaling analysis for the Marangoni convection problem that is driven by temperature-dependent surface tension and is the subject of our interest. In this paper, we prove estimates between this formal approximation and true solutions of a scalar pattern forming model problem showing the same spectral picture as the Marangoni convection problem in case of a thin fluid. The new difficulties come from neutral modes touching the imaginary axis for the wave number k = 0 and from identical group velocities at the critical wave number k = k_c and the wave number k = 0. The problem is solved by using the reflection symmetry of the system and by using the fact that the modes concentrate at integer multiples of the critical wave number k = k_c. The paper presents a method that is applicable whenever this kind of instability occurs. Copyright © 2012 John Wiley & Sons, Ltd.

The set of associated homogeneous distributions (AHDs) with support in R is an important subset of the tempered distributions because it contains the majority of the (one-dimensional) distributions typically encountered in physics applications (including the δ distribution). In a previous work of the author, a convolution and multiplication product for AHDs on R was defined and fully investigated. The aim of this paper is to give an easy introduction to these new distributional products.

Prolate spheroidal wave functions (PSWFs) possess many remarkable properties. They are orthogonal basis of both square integrable space of finite interval and the Paley–Wiener space of bandlimited functions on the real line. No other system of classical orthogonal functions is known to obey this unique property. This raises the question of whether they possess these properties in Clifford analysis. The aim of the article is to answer this question and extend the results to more flexible integral transforms, such as offset linear canonical transform. We also illustrate how to use the generalized Clifford PSWFs (for offset Clifford linear canonical transform) we derive to analyze the energy preservation problems. Clifford PSWFs is new in literature and has some consequences that are now under investigation. Copyright © 2012 John Wiley & Sons, Ltd.

A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of hypercomplex algebra and hypercomplex calculus, some of which have been neglected in existing learning approaches (e.g., for quaternions). Already in the case of quaternions, we can predict improvements in performance of hypercomplex processes. The convergence of the proposed algorithms is rigorously analyzed. Copyright © 2012 John Wiley & Sons, Ltd.

We consider the inverse source problem for a time fractional diffusion equation. The unknown source term is independent of the time variable, and the problem is considered in two dimensions. A biorthogonal system of functions consisting of two Riesz bases of the space L²[(0,1) × (0,1)], obtained from eigenfunctions and associated functions of the spectral problem and its adjoint problem, is used to represent the solution of the inverse problem. Using the properties of the biorthogonal system of functions, we show the existence and uniqueness of the solution of the inverse problem and its continuous dependence on the data. Copyright © 2012 John Wiley & Sons, Ltd.

This study is intended to provide a modified variational algorithm for the numerical solution of a class of self-adjoint singularly perturbed boundary value problem, which is equally applicable to other classes of problems. The principle of the method lies in the introduction of a mixed piecewise domain decomposition and manipulating the variational iterative approach for tackling this class of problems. The uniform convergence of the technique to the exact solution is demonstrated. Numerical results, computational comparisons, suitable error measures and illustrations are provided to testify efficiently and demonstrate the convergence, efficiency and applicability of the method. Copyright © 2012 John Wiley & Sons, Ltd.

It has been found recently that there exists a theory of functions with quaternionic values and in two real variables, which is determined by a Cauchy–Riemann-type operator with quaternionic variable coefficients, and that is intimately related to the so-called Mathieu equations. In this work, it is all explained as well as some basic facts of the arising quaternionic function theory. We establish analogues of the basic integral formulas of complex analysis such as Borel–Pompeiu's, Cauchy's, and so on, for this version of quaternionic function theory. This theory turns out to be in the same relation with the Schrödinger operator with special potential as the usual holomorphic functions in one complex variable, or quaternionic hyperholomorphic functions, or functions of Clifford analysis, are with the corresponding Laplace operator. Moreover, it is similar to that of α-hyperholomorphic functions and the Helmholtz operator. Copyright © 2012 John Wiley & Sons, Ltd.

In the present paper, the two-step difference scheme for the Cauchy problem for the stochastic hyperbolic equation is presented. The convergence estimate for the solution of the difference scheme is established. In applications, the convergence estimates for the solution of difference schemes for the numerical solution of four problems for hyperbolic equations are obtained. The theoretical statements for the solution of this difference scheme are supported by the results of the numerical experiment. Copyright © 2012 John Wiley & Sons, Ltd.

A high-order convection-bounded scheme is constructed by combining the total variational diminishing constraint and convection boundedness criterion condition in the normalized variable formulation. It employs the Hermite polynomial interpolation to design its characteristic line in the normalized variable diagram. Numerical results of the convection-dominated problems with smooth or discontinuous initial distributions demonstrate the present scheme possesses high resolution and good robustness. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we consider the following elliptic systems involving critical Sobolev growth and Hardy potential:

where N ≥ 3,λ₁,λ₂ ∈ [0,Λ_N), is the best Hardy constant. is the critical Sobolev exponent. a₁,a₂, b are positive parameters, α,β > 0 and 1 < α + β : = q < 2 < 2*. with . By means of the concentration-compactness principle and Kajikiya's new version of symmetric mountain pass lemma, we obtain infinitely many solutions that tend to zero for suitable positive parameters a₁,a₂,b and λ₁,λ₂. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we investigate the Cauchy problem for a class of the system of semilinear hyperbolic equations with damping. With the use of the L_p → L_q type estimation for the corresponding linear problem and the method of comparison of functional, the existence and nonexistence criteria of global solutions are found. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we establish a blow-up criterion of strong solutions for 3D viscous-resistive compressible magnetohydrodynamic equations, which depends only on and . Our result improves the previous criterion in Lu's paper (Journal of Mathematical Analysis and Applications 2011; 379: 425–438.) for compressible magnetohydrodynamic equations by removing a stringent condition on the viscous coefficients μ > 4λ. In addition, initial vacuum states are also allowed in our cases. Copyright © 2012 John Wiley & Sons, Ltd.