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The band preserving and phase retrieval problems have long been interested and studied. In this paper, we, for the first time, give solutions to these problems in terms of backward shift invariant subspaces. The backward shift method among other methods seems to be direct and natural. We show that a function , with , that makes the band of fg to be within that of f if and only if g divided by an inner function related to f, belongs to some backward shift invariant subspace in relation to f. By the construction of backward shift invariant space, the solution g is further explicitly represented through the span of the rational function system whose zeros are those of the Laplace transform of f. As an application, we also use the backward shift method to give a characterization for the solutions of the phase retrieval problem. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with neutral bidirectional associative memory neural networks with time-varying delays in leakage terms on time scales. Some sufficient conditions on the existence, uniqueness, and global exponential stability of almost-periodic solutions are established. An example is presented to illustrate the feasibility and effectiveness of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.

This paper investigates the existence of solutions for multi-point boundary value problems of higher-order nonlinear Caputo fractional differential equations with p-Laplacian. Using the five functionals fixed-point theorem, the existence of multiple positive solutions is proved. An example is also given to illustrate the effectiveness of ourmain result. Copyright © 2015 John Wiley & Sons, Ltd.

Y. Wang In this paper, the finite time extinction of solutions to the fast diffusion system ut=div(|∇u|p − 2∇u) + vm, vt=div(|∇v|q − 2∇v) + un is investigated, where 1 0 and is a bounded smooth domain. After establishing the local existence of weak solutions, the authors show that if mn > (p − 1)(q − 1), then any solution vanishes in finite time provided that the initial data are ‘comparable’; if mn = (p − 1)(q − 1) and Ω is suitably small, then the existence of extinction solutions for small initial data is proved by using the De Giorgi iteration process and comparison method. On the other hand, for 1 < p = q < 2 and mn < (p − 1)2, the existence of at least one non-extinction solution for any positive smooth initial data is proved. Copyright © 2015 John Wiley & Sons, Ltd.

S. G. Georgiev, Complete orthogonal systems of monogenic polynomials over 3D prolate spheroids have recently experienced an upsurge of interest because of their many remarkable properties. These generalized polynomials and their applications to the theory of quasi-conformal mappings and approximation theory have played a major role in this development. In particular, the underlying functions of three real variables take on values in the reduced quaternions (identified with ) and are generally assumed to be null-solutions of the well-known Riesz system in . The present paper introduces and explores a new complete orthogonal system of monogenic functions as solutions to this system for the space exterior of a 3D prolate spheroid. This will be made in the linear spaces of square integrable functions over . The representations of these functions are explicitly given. Some important properties of the system are briefly discussed, from which several recurrence formulae for fast computer implementations can be derived. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the initial-boundary value problem for a variable coefficient beam equation with nonlinear damping. Such a model arises from the vertical deflections of a damped extensible elastic inhomogeneous beam whose density depends on time and position. By using the Faedo–Galerkin method and energy method, we obtain the existence and uniqueness of global strong solution. Furthermore, the exponential decay estimate for the total energy is also derived. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the stability of positive periodic solutions for the Mackey–Glass model of respiratory dynamics with a control term. We prove the existence, positivity, and permanence of solutions, which help to deduce the global exponential stability of positive periodic solutions for this model. Our method relies upon a differential inequality technique and a Lyapunov functional. At the end, we give an example with numerical simulations to demonstrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

T. Qian In this paper, we prove two theorems on normal families of meromorphic functions, which improve a few of results from several authors. Copyright © 2015 John Wiley & Sons, Ltd.

This paper deals with the quasilinear Keller–Segel system with rotation where is a bounded domain with smooth boundary, D(u) is supposed to be sufficiently smooth and satisfies D(u)≥D0um − 1(m≥1) and D(u)≤D1(u + 1)K − mum − 1(K≥1) for all u≥0 with some positive constants D0 and D1, and f(u) is assumed to be smooth enough and non-negative for all u≥0 and f(0) = 0, while S(u,v,x) = (sij)n × n is a matrix with and with l≥2, where is nondecreasing on [0,∞). It is proved that when , the system possesses at least one global and bounded weak solution for any sufficiently smooth non-negative initial data. Copyright © 2015 John Wiley & Sons, Ltd.

We investigate in this paper the solutions and the periodicity of the following rational systems of difference equations of three-dimensional with initial conditions x−2,x−1,x0,y−2,y−1,y0,z−2,z−1andz0 are nonzero real numbers. 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 are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian systems

In the present paper, we study the problem of multiple non semi-trivial solutions for the following systems of Kirchhoff-type equations with discontinuous nonlinearities (1.1) where F∈C1(RN×R+×R+,R),V∈C(RN,R), and By establishing a new index theory, we obtain some multiple critical point theorems on product spaces, and as applications, three multiplicity results of non semi-trivial solutions for (1.1) are obtained. 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.

In this paper, we investigate the generalized Stieltjes-Wigert and q-Laguerre polynomials. We derive the second- and the third-order nonlinear difference equations for the subleading coefficients of these polynomials and use them to find a few terms of the formal expansions in powers of q(n/2). We also show how the recurrence coefficients in the three-term recurrence relation for these polynomials can be computed efficiently by using the nonlinear difference equations for the subleading coefficient. Moreover, we obtain systems of difference equations with one of the equations being q-discrete Painleve III or V equations and analyze them by a singularity confinement. We also discuss certain generalized weights.

In this paper, we generalize Fueter's theorem to the higher spin setting. To do so, we consider an alternative proof for the celebrated theorem that uses the Fischer decomposition. This decomposition is then extended to spaces of polynomials that depend on wedge variables, after which we can finish the proof of our higher spin Fueter theorem.

The purpose of this paper is the presentation of a new extragradient algorithm in 2-uniformly convex real Banach spaces. We prove that the sequences generated by this algorithm converge strongly to a point in the solution set of split feasibility problem, which is also a common element of the solution set of a generalized equilibrium problem and fixed points of of two relatively nonexpansive mappings. We give a numerical example to investigate the behavior of the sequences generated by our algorithm.

In this paper, the stability and Hopf bifurcation of a delayed viral infection model with logistic growth and saturated immune impairment is studied. It is shown that there exist 3 equilibria. The sufficient conditions for local asymptotic stability of the infection-free equilibrium and no-immune equilibrium are given. We also discussed the local stability of positive equilibrium and the existence of Hopf bifurcation. Moreover, the direction and stability of Hopf bifurcation is obtained by using standard form theory and the center manifold theorem. Finally, numerical simulations are performed to verify the theoretical conclusions.

In this paper, amodel problem that can be used for mathematical modeling and investigation of arc phenomena in electrical contacts is considered. An analytical approach for the solution of a two-phase inverse spherical Stefan problem where along with unknown temperature functions heat flux function has to be determined is presented. The suggested solution method is obtained from a new form of integral error function and its properties that are represented in the form of series whose coefficients have to be determined. Using integral error function and collocation method, the solution of a test problem is obtained in exact form and approximately.

This paper is dedicated to the study of a family of nonlinear Volterra equations coming from the theory of viscoelasticity. We analyze the existence of local mild solutions to the problem and their possible continuation to a maximal interval of existence. We also consider the problem of continuous dependence with respect to initial data.

In this paper, the existence of antiperiodic solutions for fourth-order impulsive differential equation is obtained by variational approaches and results on the auxiliary system. It is interesting that there is no growth restraint on nonlinear terms and impulsive terms. Besides, any minimizing sequence is bounded in a closed convex set of a space composed of Lipschitzian functions with the appearance of antiperiodic boundary value conditions.

This paper deals with the blow-up solution to the following semilinear pseudo-parabolic equation ut=Δut+Δu+|u|p−1u in a bounded domain Ω⊂Rn, which was studied by Luo (Math Method Appl Sci 38(12):2636-2641, 2015) with the following assumptions on p: 1 1; a new lifespan is given, which holds for all p> 1 and possible J(u0)≥0. Moreover, as a byproduct, we refine the lifespan when J(u0)

The subject of statistical convergence has attracted a remarkably large number of researchers due mainly to the fact that it is more general than the well-established theory of the ordinary (classical) convergence. In the year 2013, Edely et al[17] introduced and studied the notion of weighted statistical convergence. In our present investigation, we make use of the (presumably new) notion of the deferred weighted statistical convergence to present Korovkin-type approximation theorems associated with the periodic functions 1,cosx, and sinx defined on a Banach space C2π(R). In particular, we apply our concept of the deferred weighted statistical convergence with a view to proving a Korovkin-type approximation theorem for periodic functions and also to demonstrate that our result is a nontrivial extension of several known Korovkin-type approximation theorems which were given in earlier works. Moreover, we establish another result for the rate of the deferred weighted statistical convergence for the same set of functions. Finally, we consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.

WOS: 000427318700016 Bor has recently obtained amain theorem dealing with absolute weighted mean summability of Fourier series. In this paper, we generalized that theorem for vertical bar A, theta(n)vertical bar k summability method. Also, some new and known results are obtained dealing with some basic summability methods.

C. Miao In this paper, we are concerned with the 1D Cauchy problem of the compressible Navier–Stokes equations with the viscosity μ(ρ) = 1+ρβ(β≥0). The initial density can be arbitrarily large and keep a non-vacuum state at far fields. We will establish the global existence of the classical solution for 0≤β < γ via a priori estimates when the initial density contains vacuum in interior interval or is away from the vacuum. We will show that the solution will not develop vacuum in any finite time if the initial density is away from the vacuum. To study the well-posedness of the problem, it is crucial to obtain the upper bound of the density. Some new weighted estimates are applied to obtain our main results. 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.

In this paper, we first establish some user-friendly versions of fixed-point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed-point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed-point theorem. Next, with these obtained fixed-point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra-type integral equations. Copyright © 2015 John Wiley & Sons, Ltd.

The maximum-likelihood expectation-maximization (EM) algorithm has attracted considerable interest in single-photon emission computed tomography, because it produces superior images in addition to be being flexible, simple, and allowing a physical interpretation. However, it often needs a large number of calculations because of the algorithm's slow rate of convergence. Therefore, there is a large body of literature concerning the EM algorithm's acceleration. One of the accelerated means is increasing an overrelaxation parameter, whereas we have not found any analysis in this method that would provide an immediate answer to the questions of the convergence. In this paper, our main focus is on the continuous version of an accelerated EM algorithm based on Lewitt and Muehllenner. We extend their conclusions to the infinite-dimensional space and interpret and analyze the convergence of the accelerated EM algorithm. We also obtain some new properties of the modified algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

The purpose of this paper is to give a proof of global existence of solutions for Gierer–Meinhardt systems with homogeneous Neumann boundary conditions. Our technique is based on Lyapunov functional argument that yields the uniform boundedness of solutions. The asymptotic behaviour of the solutions under suitable conditions is also studied. Moreover, under reasonable conditions on the exponents of the nonlinear term, we show the blow up in finite time of the solutions for the considered system. These results are valid for any positive initial data in , without any differentiability conditions. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we study a class of integral boundary value problem for fractional order impulsive differential equations, where both the nonlinearity and the impulsive terms contain the fractional order derivatives. By using fixed-point theorems, the existence results of solution for the boundary value problem are established. Finally, some examples are presented to illustrate the existence results. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a study of immiscible compressible two-phase, such as water and gas, flow through double porosity media. The microscopic model consists of the usual equations derived from the mass conservation laws of both fluids, along with the standard Darcy–Muskat law relating the velocities to the pressure gradients and gravitational effects. The problem is written in terms of the phase formulation, that is, where the phase pressures and the phase saturations are primary unknowns. The fractured medium consists of periodically repeating homogeneous blocks and fractures, where the absolute permeability of the medium becomes discontinuous. Consequently, the model involves highly oscillatory characteristics. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. We obtain the convergence of the solutions, and a macroscopic model of the problem is constructed using the notion of two-scale convergence combined with the dilatation technique. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the multidimensional Cahn–Hilliard equation with a constraint. The existence of periodic solutions of the problem is mainly proved under consideration by the viscosity approach. More precisely, with the help of the subdifferential operator theory and Schauder fixed point theorem, the existence of solutions to the approximation of the original problem is shown, and then the solution is obtained by using a passage-to-limit procedure based on a prior estimate. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is devoted to the attraction–repulsion chemotaxis system with nonlinear diffusion: where χ > 0, ζ > 0, αi>0, βi>0 (i = 1,2) and f(s)≤κ − μsτ. In two-space dimension, we prove the global existence and uniform boundedness of the classical solution to this model for any μ > 0. 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 study the time-decay rates of the solution to the Cauchy problem for a nematic liquid crystals system via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. Copyright © 2015 John Wiley & Sons, Ltd.

This is the peer reviewed version of the following article: Magaña, A., and Quintanilla, R. (2016) Exponential decay in nonsimple thermoelasticity of type III. Math. Meth. Appl. Sci., 39: 225–235. doi: 10.1002/mma.3472, which has been published in final form at http://dx.doi.org/10.1002/mma.3472. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving This paper deals with the model proposed for nonsimple materials with heat conduction of type III.We analyze rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.

In this paper, we consider the nonlinear oscillation of the following second-order neutral delay dynamic equations with distributed delay on a time scale , where Z(t) = x(t) + p(t)x(τ(t)),α,β > 0 are constants. By using some new techniques, we obtain oscillation criteria for the equation when β > α,β = α, and β < α, respectively. Those results established here complete and develop the oscillation criteria in the literature. Also, our main results are illustrated with some examples. 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.

Interval-valued fuzzy sets are an extension of fuzzy sets and are helpful when there is not enough information to define a membership function. This paper studies the behavior of a construction method for an interval-valued fuzzy relation built from a fuzzy relation. The behavior of this construction method is analyzed depending on the used t-norms and t-conorms, showing that different combinations of them produce a big variation in the results. Furthermore, a hybrid construction method that considers weight functions and a smoothing procedure is also introduced. Among the different applications of this method, the detection of edges in images is one of the most challenging. Thus, the performance of the proposal in detecting image edges is tested, showing that the hybrid approach that combines weights and a smoothing procedure provides better results than the non-weighted methods. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we study the Navier–Stokes equations with Navier boundary conditions in a bounded domain of . We prove the existence of weak solution in W1,p(Ω) × Lp(Ω) for by using fixed point theorem for the case . Copyright © 2015 John Wiley & Sons, Ltd.

The paper deals with the two-dimensional problem of the elastic equilibrium of a body containing a thin rigid inclusion. The rigid inclusion is considered to be soldered into elastic medium. The volume forces act on the body; at the external boundary the body is fixed. The first and second variations of the solution with respect to the shape of the domain are calculated. As an illustrative application of the results, the optimal shape design problem is considered. The necessary and sufficient conditions for local optimality are written. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we study the nonexistence result for the weighted Lane–Emden equation: −Δu=f(|x|)|u|p−1u,x∈RN(0.1) and the weighted Lane–Emden equation with nonlinear Neumann boundary condition: −Δu=f(|x|)|u|p−1u,x∈R+N,∂u∂ν=g(|x|)|u|−1u,x∈∂R+N,(0.2) where f(|x|) and g(|x|) are the radial and continuously differential functions, R+N={x=(x′,xN)∈RN−1×R+} is an upper half space in RN, and ∂R+N={x=(x′,0),x′∈RN−1}. Using the method of energy estimation and the Pohozaev identity of solution, we prove the nonexistence of the nontrivial solutions to problems (0.1) and (0.2) under appropriate assumptions on f(|x|) and g(|x|). Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we prove the existence and uniqueness of a solution for a class of backward stochastic differential equations driven by G-Brownian motion with subdifferential operator by means of the Moreau–Yosida approximation method. Moreover, we give a probabilistic interpretation for the viscosity solutions of a kind of nonlinear variational inequalities. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we are concerned with the existence of ground state solution for the following fractional differential equations with tempered fractional derivative: D−α,λ(D+α,λu(t))=f(t,u(t)),t∈Ru∈Wα,2(R),(FD) where α∈(1/2,1), λ>0, D±α,λu are the left and right tempered fractional derivatives, Wα,2(R) is the fractional Sobolev spaces, and f∈C(R×R,R). Assuming that f satisfies the Ambrosetti–Rabinowitz condition and another suitable conditions, by using mountain pass theorem and minimization argument over Nehari manifold, we show that (FD) has a ground state solution. Furthermore, we show that this solution is a radially symmetric solution. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we use the arrowhead matrices as a tool to study graph theory. More precisely, we deal with an interesting class of directed multigraphs, the hub-directed multigraphs. We associate the arrowhead matrices with the adjacency matrices of a class of directed multigraph, and we obtain new properties of the second objects by using properties of the first ones. The hub-directed multigraphs with potential use in applications are also defined. As main result, we show that a hub-directed multigraph G(H) with adjacency matrix H∗ is a dominant hub-directed multigraph if and only if H∗=CE, where C is the adjacency matrix of another directed multigraph and E is the adjacency matrix of a particular elementary dominant hub-directed pseudo-graph. Another decomposition of its Gram (arrowhead) matrix A=H∗TH∗ is also given. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we prove that if the initial data is small enough, we obtain an explicit L∞(QT)-estimate for a two-dimensional mathematical model of cancer invasion, proving an explicit bound with respect to time T for the estimate of solutions. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we consider a Timoshenko system in the presence of an infinite memory, where the relaxation function satisfies a relation of the form Under the same hypothesis on g and ξ imposed for the finite memory case, we establish some general decay results for the equal and nonequal speed propagation cases. Our results improve in some situations some known decay rates. Also, some applications to other problems are discussed. 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.

In this paper, we consider nonlinear age-structured equation with diffusion under nonlocal boundary condition and non-negative initial data. More precisely, we prove that under some assumptions on the nonlinear term in a model of McKendrickVon Foerster with diffusion in age, solutions exist and converge (long-time convergence) towards a stationary solution. In the first part, we use classical analysis tools to prove the existence, uniqueness, and the positivity of the solution. In the second part, using comparison principle, we prove the convergence of this solution towards the stationary solution. Copyright (c) 2012 John Wiley & Sons, Ltd. Mathematical Methods in the Applied Sciences, DOI : 10.1002/mma.2591,Issue : 3, Volume :36, pp. 323–335, February 2013.