In the present paper, we generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic LCT (QLCT). Using the properties of the LCT, we establish an uncertainty principle for the two-sided QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternionic signal minimizes the uncertainty. Copyright © 2016 John Wiley & Sons, Ltd.

]]>An adaptive mesh method combined with the optimality criteria algorithm is applied to optimal shape design problems of fluid dynamics. The shape sensitivity analysis of the cost functional is derived. The optimization problem is solved by a simple but robust optimality criteria algorithm, and an automatic local adaptive mesh refinement method is proposed. The mesh adaptation, with an indicator based on the material distribution information, is itself shown as a shape or topology optimization problem. Taking advantages of this algorithm, the optimal shape design problem concerning fluid flow can be solved with higher resolution of the interface and a minimum of additional expense. Details on the optimization procedure are provided. Numerical results for two benchmark topology optimization problems are provided and compared with those obtained by other methods. Copyright © 2016 John Wiley & Sons, Ltd.

]]>We start recalling the characterizing property of the ‘partial symmetries’ of a differential problem, that is, the property of transforming solutions into solutions only in a proper subset of the full solution set. This paper is devoted to analyze the role of partial symmetries in the special context of dynamical systems and also to compare this notion with other notions of ‘weak’ symmetries, namely, the *λ*-symmetries and the orbital symmetries. Particular attention is addressed to discuss the relevance of partial symmetries in dynamical systems admitting homoclinic (or heteroclinic) manifolds, which can be ‘broken’ by periodic perturbations, thus giving rise, according to the (suitably rewritten) Mel'nikov theorem, to the appearance of a chaotic behavior of Smale-horseshoes type. Many examples illustrate all the various aspects and situations. Copyright © 2016 John Wiley & Sons, Ltd.

We review the theory of hypercomplex numbers and hypercomplex analysis with the ultimate goal of applying them to issues related to the integration of systems of ordinary differential equations (ODEs). We introduce the notion of *hypercomplexification,* which allows the lifting of some results known for scalar ODEs to systems of ODEs. In particular, we provide another approach to the construction of superposition laws for some Riccati-type systems, we obtain invariants of Abel-type systems, we derive integrable Ermakov systems through hypercomplexification, we address the problem of linearization by hypercomplexification, and we provide a solution to the inverse problem of the calculus of variations for some systems of ODEs. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we first address the space-time decay properties for higher-order derivatives of strong solutions to the Boussinesq system in the usual Sobolev space. The decay rates obtained here are optimal. The proof is based on a parabolic interpolation inequality, bootstrap argument, and some weighted estimates. Secondly, we present a new solution integration formula for the Boussinesq system, which will be employed to establish the existence of strong solutions for small initial data in some scaling invariant function spaces. The smallness conditions are somehow weaker than those presented by Brandolese and Schonbek. We further investigate the asymptotic profiles and decay properties of these strong solutions. Copyright © 2016 John Wiley & Sons, Ltd.

]]>The objective of this paper is to investigate the almost periodic dynamics for a class of delayed predator–prey model with mutual interference and Beddington–DeAngelis type functional response, in which the harvesting policies are modeled by discontinuous functions. Based on the theory of functional differential inclusions theory and set-valued analysis, the solution in sense of Filippov of system with the discontinuous harvesting policies is given, and the local and global existence of positive the solution in sense of Filippov of the system is studied. By employing generalized differential inequalities, some useful Lemmas are obtained. After that, sufficient conditions which guarantee the permanence of the system are obtained in view of the constructed Lemmas. By constructing some suitable generalized Lyapunov functional, a series of useful criteria on existence, uniqueness, and global attractivity of the almost positive periodic solution to the system are derived in view of functional differential inclusions theory and nonsmooth analysis theory. Some suitable examples together with their numeric simulations are given to substantiate the theoretical results and to illustrate various dynamical behaviors of the system. Copyright © 2016 John Wiley & Sons, Ltd.

]]>This paper deals with the existence of traveling wave solutions for *n*-dimensional delayed reaction–diffusion systems. By using Schauder's fixed point theorem, we establish the existence result of a traveling wave solution connecting two steady states by constructing a pair of upper–lower solutions that are easy to construct. As an application, we apply our main results to a four-dimensional delayed predator–prey system and obtain the existence of traveling wave solutions. Copyright © 2016 John Wiley & Sons, Ltd.

We consider the initial boundary problem for a compressible non-Newtonian fluid with density-dependent viscosity. The local existence of strong solution is established that is based on some compatibility condition. Moreover, it is also proved that the solutions are to blow up, and the maximum norm of velocity gradients controls the possible break down of the strong solutions. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this article, the local well-posedness of Cauchy's problem is explored for a system of quadratic nonlinear Schrödinger equations in the space *L*^{p}(**R**^{n}). In a special case of mass resonant 2 × 2 system, it is well known that this problem is well posed in *H*^{s}(*s*≥0) and ill posed in *H*^{s}(*s* < 0) in two-space dimensions. By translation on a linear semigroup, we show that the general system becomes locally well posed in *L*^{p}(**R**^{2}) for 1 < *p* < 2, for which *p* can arbitrarily be close to the scaling limit *p*_{c}=1. In one-dimensional case, we show that the problem is locally well posed in *L*^{1}(**R**); moreover, it has a measure valued solution if the initial data are a Dirac function. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we establish some new interior regularity criteria for suitable weak solutions of the liquid crystals flow in terms of the smallness of the scaled *L*^{p,q}-norm of the velocity field or the vorticity, which extends the results by Scheffer in [*Communications in Mathematical Physics* 1980; **73**:1–42]. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we are concerned with the existence of solutions of systems determined by abstract functional differential equations with infinite and state-dependent delay. We establish the existence of mild solutions and the existence of periodic solutions. Our results are based on local Lipschitz conditions of the involved functions. We apply our results to study the existence of periodic solutions of a partial differential equation with infinite and state-dependent delay. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, we introduce the concept of Berinde's cyclic contraction that is a generalized cyclic contraction mapping by using the idea of weak contraction mapping which is defined by Berinde and prove best proximity point theorems for such a mapping in metric space with proximally complete property, Our results improve and extend the recent results of Eldred and Veeramani and some authors. Copyright © 2016 John Wiley & Sons, Ltd.

]]>The *p*-Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model problem for special types of nonlinearities. The *p*-Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the *p*-Laplace equation for 1 < *p* < 2 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the *p*-Laplace equation into the *p*-Dirac equation. This equation will be solved iteratively by using a fixed-point theorem. Applying operator-theoretical methods for the *p*-Dirac equation and *p*-Laplace equation, the existence and uniqueness of solutions in certain Sobolev spaces will be proved. Copyright © 2016 John Wiley & Sons, Ltd.

We present a comparison between two different mathematical models used in the description of the Ebola virus propagation currently occurring in West Africa. In order to improve the prediction and the control of the propagation of the virus, numerical simulations and optimal control of the two models for Ebola are investigated. In particular, we study when the two models generate similar results. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, a class of neutral-type neural networks with delays in the leakage term on time scales are considered. By using the Banach fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solutions for this class of neural networks. The results of this paper are new and complementary to the previously known results. Finally, an example is presented to illustrate the effectiveness of our results. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, a reaction-diffusion predator–prey system that incorporates the Holling-type II and a modified Leslie-Gower functional responses is considered. For ODE, the local stability of the positive equilibrium is investigated and the specific conditions are obtained. For partial differential equation, we consider the dissipation and persistence of solutions, the Turing instability of the equilibrium solutions, and the Hopf bifurcation. By calculating the normal form, we derive the formulae, which can determine the direction and the stability of Hopf bifurcation according to the original parameters of the system. We also use some numerical simulations to illustrate our theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this article, the new exact travelling wave solutions of the nonlinear space-time fractional Burger's, the nonlinear space-time fractional Telegraph and the nonlinear space-time fractional Fisher equations have been found. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order in the sense of the Jumarie's modified Riemann–Liouville derivative. The -expansion method is effective for constructing solutions to the nonlinear fractional equations, and it appears to be easier and more convenient by means of a symbolic computation system. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, we apply the dual reciprocity boundary elements method for the numerical solution of two-dimensional linear and nonlinear time-fractional modified anomalous subdiffusion equations and time-fractional convection–diffusion equation. The fractional derivative of problems is described in the Riemann–Liouville and Caputo senses. We employ the linear radial basis function for interpolation of the nonlinear, inhomogeneous and time derivative terms. This method is improved by using a predictor–corrector scheme to overcome the nonlinearity which appears in the nonlinear problems under consideration. The accuracy and efficiency of the proposed schemes are checked by five test problems. The proposed method is employed for solving some examples in two dimensions on unit square and also in complex regions to demonstrate the efficiency of the new technique. Copyright © 2016 John Wiley & Sons, Ltd.

]]>A two-grid variational multiscale method based on two local Gauss integrations for solving the stationary natural convection problem is presented in this article. A significant feature of the method is that we solve the natural convection problem on a coarse mesh using finite element variational multiscale method based on two local Gauss integrations firstly, and then find a fine grid solution by solving a linearized problem on a fine grid. In the computation, we introduce two local Gauss integrations as a stabilizing term to replace the projection operator without adding other variables. The stability estimates and convergence analysis of the new method are derived. Ample numerical experiments are performed to validate the theoretical predictions and demonstrate the efficiency of the new method. Copyright © 2016 John Wiley & Sons, Ltd.

]]>We simulate a fractional feed-forward network. This network consists of three coupled identical ‘cells’ (aka, oscillators). We study the behaviour of the associated coupled cell system for variation of the order of the fractional derivative, 0 < *α* < 1. We consider the Caputo derivative, approximated by the Grünwald–Letnikov approach, using finite differences of fractional order. There is observed amplification of the small signals by exploiting the nonlinear response of each oscillator near its intrinsic Hopf bifurcation point for each value of *α*. The value of the Hopf bifurcation point varies with the order of the fractional derivative *α*. Copyright © 2016 John Wiley & Sons, Ltd.

An existence result of smooth solutions for a complex material flow problem is provided. The considered equations are of hyperbolic type including a nonlocal interaction term. The existence proof is based on a problem-adapted linear iteration scheme exploiting the structure conditions of the nonlocal term. 35Q70, 35L65 Copyright © 2016 John Wiley & Sons, Ltd.

]]>We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species, Holling III and Holling II functional response for the predator and the top-predator, respectively. We prove that this model has stable periodic orbits for adequate values of its parameters. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo sense. The approach we use to prove necessary conditions of optimality in the form of Pontryagin maximum principle for fractional nonlinear optimal control problems is new in this context. Moreover, a new method based on a generalization of the Mittag–Leffler function is used to solving this class of fractional optimal control problems. A simple example is provided to illustrate the effectiveness of our main result. Copyright © 2016 John Wiley & Sons, Ltd.

]]>We present a numerical method based on the fuzzy transform for solving second-order differential equations with boundary conditions. We demonstrate the effectiveness of the method by some examples. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In the present paper, we consider the Bézier variant of an operator involving Laguerre polynomials of degree k, with *α*≥1, for bounded functions *f* defined on the interval [0,1]. In particular, by using the Chanturia modulus of variation, we estimate the rate of pointwise convergence of (*P*_{n,α}*f*)(*x*,*t*) at those points *x*∈(0,1) at which the one-sided limits *f*(*x*+),*f*(*x*−) exist. To prove our main result, we have used some methods and techniques of probability theory. Our result extends and generalizes the very recent results of very recent results of the authors to more general classes of functions. Copyright © 2016 John Wiley & Sons, Ltd.

The construction of Brownian motion paths is the most important part of simulation methods for option pricing. Particularly, there are several commonly used path generation methods in the context of quasi-Monte Carlo, including the standard method and the Brownian bridge method. To apply each method, an inevitable step is to decide how many points are used to discretize the time interval. This paper implements an iterative algorithm to select a suitable number of time steps by successively adding discretization nodes until a specific convergence criterion is met. Numerical results with this algorithm are presented in the valuation of Asian options. Copyright © 2016 John Wiley & Sons, Ltd.

]]>Computer simulations of the injection molding process of fiber-reinforced plastics critically depend on the accuracy of the constitutive models. Of prime importance for the process simulation is the precise knowledge of the viscosity. Industrial applications generally feature both high shear rates and high fiber volume fractions. Thus, both the shear-thinning behavior of the melt and the strong anisotropic effects induced by the fibers play a dominant role. Unfortunately, the viscosity cannot be determined experimentally in its full anisotropy, and analytical models cease to be accurate for the high fiber volume fractions in question. Computing the effective viscosity by a simplified homogenization approach serves as a possible remedy. This paper is devoted to the analysis of a cell problem determining the effective viscosity. We provide primal as well as dual formulations and prove corresponding existence and uniqueness theorems for Newtonian and Carreau fluids in suitable Sobolev spaces. In the Newtonian regime, the primal formulation leads to a saddle point problem, whereas a dual formulation can be obtained in terms of a coercive and symmetric bilinear form. This observation has deep implications for numerical formulations. As a by-product, we obtain the invertibility of the effective viscosity, considered as a function, mapping the macroscopic shear rate to the macroscopic shear stress. Copyright © 2016 John Wiley & Sons, Ltd.

]]>We consider continuous random dynamical systems with jumps. We estimate the dimension of the invariant measures and apply the results to a model of stochastic gene expression. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, the robust dissipativity and passivity criteria for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time-varying delays have been investigated. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strictly monotonic. Furthermore, the description of the activation functions is more general than the commonly used Lipschitz conditions. By using a Lyapunov–Krasovskii functional and employing the quadratic convex combination approach, a set of sufficient conditions are established to ensure the dissipativity of the proposed model. The obtained conditions are presented in terms of linear matrix inequalities, so that its feasibility can be checked easily via standard numerical toolboxes. The quadratic convex combination approach used in our paper gives a reduced conservatism without using Jensen's inequality. In addition to that, numerical examples with simulation results are given to show the effectiveness of the obtained linear matrix inequality conditions. Copyright © 2016 John Wiley & Sons, Ltd.

]]>This paper is dedicated to the Oldroyd-B model with fractional dissipation (−Δ)^{α}*τ* for any *α* > 0. We establish the global smooth solutions to the Oldroyd-B model in the corotational case with arbitrarily small fractional powers of the Laplacian in two spatial dimensions. Moreover, in the Appendix, we provide some a priori estimates to the Oldroyd-B model in the critical case, which may be useful and of interest for future improvement. Therefore, our result is closer to the resolution of the well-known global regularity issue on the critical 2D Oldroyd-B model. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the exponential stabilization and *L*_{2}-gain for a class of uncertain switched nonlinear systems with interval time-varying delay. Based on Lyapunov–Krasovskii functional method, novel delay-dependent sufficient conditions of exponential stabilization for a class of uncertain switched nonlinear delay systems are developed under an average dwell time scheme. Then, novel criteria to ensure the exponential stabilization with weighted *L*_{2}-gain performance for a class of uncertain switched nonlinear delay systems are established. Furthermore, an effective method is proposed for the designing of a stabilizing feedback controller with *L*_{2}-gain performance. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we consider the split feasibility problem (SFP) in infinite-dimensional Hilbert spaces and propose some subgradient extragradient-type algorithms for finding a common element of the fixed-point set of a strict pseudocontraction mapping and the solution set of a split feasibility problem by adopting Armijo-like stepsize rule. We derive convergence results under mild assumptions. Our results improve some known results from the literature. Copyright © 2016 John Wiley & Sons, Ltd.

]]>Wavelet bi-frames with uniform symmetry are discussed in this paper. Every refinable function in the bi-frame system is symmetric, which is very useful in the image processing and curve and surface multiresolution processing. By the aid of the lifting scheme, bi-frame multiresolution algorithms can be divided into several iterative steps, and each step can be shown by a symmetric template. The template-based procedure is established for constructing bi-frames with uniform symmetry and *N* > 2 generators. In particular, we take the bi-frame with three generators as an example to provide a clearer picture of the template-based procedure for constructing bi-frames. Three types of bi-frames with three generators are studied, and some examples with certain smoothness are constructed. These examples include some bi-frames with interpolating property. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we develop a spectral method for mixed inhomogeneous Dirichlet/Neumann/Robin boundary value problems defined on rectangle. Some results on two-dimensional Legendre approximation in Jacobi-weighted Sobolev space are established. As examples of applications, spectral schemes are provided for two model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms are proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy and confirm the theoretical analysis well. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, we consider a one-dimensional porous thermoelastic system of type III with viscoelastic damping and constant time delay on boundary. Using the energy method, we prove the general stability of the system under suitable assumptions on the relaxation function and the time delay. Copyright © 2016 John Wiley & Sons, Ltd.

]]>At first, the existence of a unique solution for the Cauchy problem to nondegenerate fractional differential equation was proved. These results were used for research of the unique solvability for the initial Cauchy and Showalter–Sidorov problems to differential equations in Banach spaces with degenerate operator at fractional Caputo derivative in linear and nonlinear cases. Abstract results are applied to the research of an initial boundary value problem for time-fractional order Oskolkov system of equations. Copyright © 2016 John Wiley & Sons, Ltd.

]]>Given a joint probability density function of *N* real random variables,
, obtained from the eigenvector–eigenvalue decomposition of *N* × *N* random matrices, one constructs a random variable, the linear statistics, defined by the sum of smooth functions evaluated at the eigenvalues or singular values of the random matrix, namely,
. For the joint PDFs obtained from the Gaussian and Laguerre ensembles, we compute, in this paper, the moment-generating function
, where
denotes expectation value over the orthogonal (*β* = 1) and symplectic (*β* = 4) ensembles, in the form one plus a Schwartz function, none vanishing over
for the Gaussian ensembles and
for the Laguerre ensembles. These are ultimately expressed in the form of the determinants of identity plus a scalar operator, from which we obtained the large *N* asymptotic of the linear statistics from suitably scaled *F*(·). Copyright © 2016 John Wiley & Sons, Ltd.

In the design of mathematical methods for a medical problem, one of the kernel issues is the identification of symptoms and measures that could help in the diagnosis. Discovering connections among them constitute a big challenge because it allows to reduce the number of parameters to be considered in the mathematical model. In this work, we focus on formal concept analysis as a very promising technique to address this problem. In previous works, we have studied the use of formal concept analysis to manage attribute implications. In this work, we propose to extend the knowledge that we can extract from every context using positive and negative information, which constitutes an open problem.

Based on the main classical algorithms, we propose new methods to generate the lattice concept with positive and negative information to be used as a kind of map of attribute connections. We also compare them in an experiment built with datasets from the UCI repository for machine learning. We finally apply the mining techniques to extract the knowledge contained in a real data set containing information about patients suffering breast cancer. The result obtained have been contrasted with medical scientists to illustrate the benefits of our proposal. Copyright © 2016 John Wiley & Sons, Ltd.

In the given paper, a special method of representation of the Mittag-Leffler functions and their multivariate generalizations in the form of the Laplace integrals is suggested. The method is based on the usage of the generalized multiplication Efros theorem. The possibilities of a new method are demonstrated on derivation of the integral representations for relaxation functions used in the anomalous dielectric relaxation in time domain. Copyright © 2016 John Wiley & Sons, Ltd.

]]>This paper aims to present the generalized Kudryashov method to find the exact traveling wave solutions transmutable to the solitary wave solutions of the ubiquitous unsteady Korteweg–de Vries equation and its two famed alternatives, namely, the regularized long-wave equation and the time regularized long-wave equation. The exact analytic solutions of the studied equations are constructed explicitly in three forms, namely, hyperbolic, trigonometric, and rational function. The validity of our solutions is verified with MAPLE by putting them back into the original equation and found correct. Moreover, it has shown that the generalized Kudryashov method is an easy and reliable technique over the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, we study the exponential stability of a two-dimensional Schrödinger–heat interconnected system in a torus region, where the interface between the Schrödinger equation and the heat equation is of natural transmission conditions. By using a polar coordinate transformation, the two-dimensional interconnected system can be reformulated as an equivalent one-dimensional coupled system. It is found that the dissipative damping of the whole system is only produced from the heat part, and hence, the heat equation can be considered as an actuator to stabilize the whole system. By a detailed spectral analysis, we present the asymptotic expressions for both eigenvalues and eigenfunctions of the closed-loop system, in which the eigenvalues of the system consist of two branches that are asymptotically symmetric to the line Re*λ* =− Im*λ*. Finally, we show that the system is exponentially stable and the semigroup, generated by the system operator, is of Gevrey class *δ* > 2. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study the following Kirchhoff-type elliptic problem

where is a bounded domain with smooth boundary *∂*Ω, *a*,*b*,*λ*,*μ* > 0 and 1 < *q* < 2^{∗}=2*N*/(*N* − 2). When *N* = 4, we obtain that there is a ground state solution to the problem for *q*∈(2,4) by using a variational methods constrained on the Nehari manifold and also show the problem possesses infinitely many negative energy solutions for *q*∈(1,2) by applying usual Krasnoselskii genus theory. In addition, we admit that there is a positive solution to the equations for *N*≥5 under some suitable conditions. Copyright © 2016 John Wiley & Sons, Ltd.

We address various topologies (de Bruijn, chordal ring, generalized Petersen, and meshes) in various ways (isometric embedding, embedding up to scale, and embedding up to a distance) in a hypercube or a half-hypercube. Example of obtained embeddings: infinite series of hypercube embeddable bubble sort and double chordal rings topologies, as well as of regular maps. Copyright © 2016 John Wiley & Sons, Ltd.

]]>In this paper, we are interested in the nonlinear Schrödinger equation with non-local regional diffusion

- (1)

where 0 < *α* < 1 and
is a variational version of the regional Laplacian, whose range of scope is a ball with radius *ρ*(*x*) > 0. The novelty of this paper is that, assuming *f* is of subquadratic growth as |*u*|+*∞*, we show that (1) possesses infinitely many solutions via the genus properties in critical point theory. Furthermore, if *f*(*x*,*u*) = *γ**a*(*x*)|*u*|^{γ − 1}, where
is a nonincreasing radially symmetric function, then the solution of (1) is radially symmetric. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we investigate a predator–prey model with Gompertz growth function and impulsive dispersal of prey between two patches. Using the dynamical properties of single-species model with impulsive dispersal in two patches and comparison principle of impulsive differential equations, necessary and sufficient criteria on global attractivity of predator-extinction periodic solution and permanence are established. Finally, a numerical example is given to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

]]>We deal with the scattering of an acoustic medium modeled by an index of refraction *n* varying in a bounded region Ω of
and equal to unity outside Ω. This region is perforated with an extremely large number of small holes *D*_{m}'s of maximum radius *a*, *a* << 1, modeled by surface impedance functions. Precisely, we are in the regime described by the number of holes of the order *M*:=*O*(*a*^{β − 2}), the minimum distance between the holes is *d* ∼ *a*^{t}, and the surface impedance functions of the form *λ*_{m}∼*λ*_{m,0}*a*^{−β} with *β* > 0 and *λ*_{m,0} being constants and eventually complex numbers. Under some natural conditions on the parameters *β*,*t*, and *λ*_{m,0}, we characterize the equivalent medium generating approximately the same scattered waves as the original perforated acoustic medium. We give an explicit error estimate between the scattered waves generated by the perforated medium and the equivalent one, respectively, as *a*0. As applications of these results, we discuss the following findings:

- If we choose negative-valued imaginary surface impedance functions, attached to each surface of the holes, then the equivalent medium behaves as a passive acoustic medium only if it is an acoustic metamaterial with index of refraction $\tilde {n}(x)=-n(x),\; x \in \upOmega $ñ(x)=−n(x),x∈Ω and $\tilde {n}(x)=1,\; x \in \mathbb {R}^{3}\setminus {\overline {\upOmega }}$ñ(x)=1,x∈R3∖Ω¯. This means that with this process, we can switch the sign of the index of the refraction from positive to negative values.
- We can choose the surface impedance functions attached to each surface of the holes so that the equivalent index of refraction $\tilde {n}$ñ is $\tilde {n}(x)=1,\; x \in \mathbb {R}^{3}$ñ(x)=1,x∈R3. This means that the region Ω modeled by the original index of refraction n is approximately cloaked.

Copyright © 2015 John Wiley & Sons, Ltd.

Determination of effective physical parameters of gas-filled porous media is of practical interest to a wide spectrum of applications from construction industry to petrophysics. The classical equations of thermal conductivity are not applicable for sufficiently small pores, the characteristic size of which is comparable with the mean free path of gas molecules. In this case, for description of the gas behavior, it is necessary to use the methods of physical kinetics and rarefied gas dynamics. In this work, we have considered so-called slip flow regime, 0 < Kn < 1, where Kn =*λ*/*R* is the Knudsen number, *λ* is the mean free path, and *R* is the characteristic pore size. In this regime, we can use the classical equations of mechanics of continuum media with modified boundary conditions that take into account the temperature and energy flux jumps on the pore boundaries. We have solved the so-called one-particle problem of thermal polarization of gas-filled inclusion. The obtained solution was then used in some self-consistent homogenization methods to calculate the effective conductivity coefficient. Our calculations have shown that the effective conductivity depends substantially on the pore size (the Knudsen number). The obtained results demonstrate the feasibility of pore sizes determination by using measurements of effective thermal conductivity. Copyright © 2015 John Wiley & Sons, Ltd.

A two dimensional version of a reconstruction problem of an unknown weld on the interface between two electric conductive plates is considered. It is assumed that the two plates have a same known isotropic homogeneous conductivity, and the line where the welding area is located is known. Under these assumptions, an explicit extraction formula of the location of the tips of the welding area on the line from a single set of an electric current density and the corresponding voltage potential on the boundary of the material formed by the plates is given. This result may have possibility of application to quality evaluation of spot welding fixation strength of a lamina. Copyright © 2015 John Wiley & Sons, Ltd.

]]>By incorporating the Monotone Upwind Scheme of Conservation Law (MUSCL) scheme into the smoothed particles hydrodynamics (SPH) method and making use of an interparticle contact algorithm, we present a MUSCL–SPH scheme of second order for multifluid computations, which extends the Riemann-solved-based SPH method. The numerical tests demonstrate high accuracy and resolution of the scheme for both shocks, contact discontinuities, and rarefaction waves in the one-dimensional shock tube problem. For the two-dimensional cylindrical Noh and shock-bubble interaction problems, the MUSCL–SPH scheme can resolve shocks well. Copyright © 2015 John Wiley & Sons, Ltd.

]]>An asymptotic model for a thin, soft, linearly elastic joint imperfectly bonded to two linearly elastic bodies is derived by studying the variational convergence of the total mechanical energy when the thickness and the stiffness of the joint go to zero. The joint is replaced by a mechanical constraint between the adherents which correspond to the connection in series of the classical limit constraint induced by the soft joint and constraints between the joint and the adherents.74K3074G65 Copyright © 2015 John Wiley & Sons, Ltd.

]]>A sufficient condition for blowup of solutions to a class of pseudo-parabolic equations with a nonlocal term is established in this paper. In virtue of the potential wells method, we first extend the results obtained by Xu and Su in [J. Funct. Anal., 264 (12): 2732-2763, 2013] to the nonlocal case and describe successfully the behavior of solutions by using the energy functional, Nehari functional, and the ground state energy of the stationary equation. Sequently, we study the boundedness and convergency of any global solution. Finally, we achieve a criterion to guarantee the blowup of solutions without any limit of the initial energy.Copyright © 2015 John Wiley & Sons, Ltd.

]]>We consider the time-dependent magnetic induction model as a step towards the resistive magnetohydrodynamics model in incompressible media. Conforming nodal-based finite element approximations of the induction model with inf-sup stable finite elements for the magnetic field and the magnetic pseudo-pressure are investigated. Based on a residual-based stabilization technique proposed by Badia and Codina, SIAM J. Numer. Anal. 50 (2012), pp. 398–417, we consider a stabilized nodal-based finite element method for the numerical solution. Error estimates are given for the semi-discrete model in space. Finally, we present some examples, for example, for the magnetic flux expulsion problem, Shercliff's test case and singular solutions of the Maxwell problem. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we introduce a general Bayesian abstract fuzzy economy model of product measurable spaces, and we prove the existence of Bayesian fuzzy equilibrium for this model. Our results extend and improve the corresponding recent results announced by Patriche and many authors from the literature. It captures the idea that the uncertainties characterize the individual feature of the decisions of the agents involved in different economic activities. In this paper, the uncertainties can be described by using random fuzzy mappings. Further attention is needed for the study of applications of the established result in the game theory and the fuzzy economic field.Copyright © 2015 John Wiley & Sons, Ltd.

]]>The paper is devoted to the investigation of a parabolic partial differential equation with non-local and time-dependent boundary conditions arising from ductal carcinoma *in situ* model. Approximation solution of the present problem is implemented by the Ritz–Galerkin method, which is a first attempt at tackling parabolic equation with such non-classical boundary conditions. In the process of dealing with the difficulty caused by integral term in non-local boundary condition, we use a trick of introducing the transition function *G*(*x*,*t*) to convert non-local boundary to another non-classical boundary, which can be handled with the Ritz–Galerkin method. Illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we study the nonlinear Schrödinger equation on Zoll manifolds with odd order nonlinearities. We will obtain the local well-poesdness in the critical space
. This extends the recent results in the literature to the Zoll manifolds of dimension *d*≥2 with general odd order nonlinearities and also partially improves the previous results in the subcritical spaces of Yang to the critical cases. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with a SIR model with saturated and periodic incidence rate and saturated treatment function. By using differential inequality technique, we employ a novel argument to show that the disease-free equilibrium is globally exponentially stable. The obtained results improve and supplement existing ones. We also use numerical simulations to demonstrate our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior, which is uniformly Lipschitz and nonlinear terms, are concentrated in a region, which neighbors the boundary of domain. We prove that this family of solutions converges to the solutions of a limit problem in *H*^{1}an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.Copyright © 2015 John Wiley & Sons, Ltd.

The inverse problem with unknown source function is studied for the nonlinear Oskolkov's system of partial differential equations that describes the dynamics of viscoelastic Kelvin–Voigt fluid. It is reduced to the problem for a first order semilinear ordinary differential equation with operator coefficients in Banach spaces. The main difficulty of the problem is a presence of the operator with a nontrivial kernel at the derivative. By the results on the unique solvability of the abstract problem, obtained by the authors before, the existence of a unique classical solution for the Oskolkov's system inverse problem is proved. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper deals with fractional differential equations with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters. Copyright © 2015 John Wiley & Sons, Ltd.

]]>Entropy plays an important role in the simulation of traffic flow distribution. This paper studies the entropy condition for the Lighthill–Whitham–Richards model of the fractal traffic flows described by local fractional calculus. We also discuss the solutions of non-differentiability with graphs by using the local fractional variational iteration method. Copyright © 2015 John Wiley & Sons, Ltd.

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]]>The task of this paper is to study and analyse *transformed localization* and *generalized localization* for ensemble methods in *data assimilation*. Localization is an important part of *ensemble methods* such as the *ensemble Kalman filter* or *square root filter*. It guarantees a sufficient number of degrees of freedom when a small number of ensembles or particles, respectively, are used. However, when the observation operators under consideration are *non-local*, the localization that is applicable to the problem can be severly limited, with strong effects on the quality of the assimilation step. Here, we study a transformation approach to change non-local operators to local operators in transformed space, such that localization becomes applicable. We interpret this approach as a generalized localization and study its general algebraic formulation. Examples are provided for a compact integral operator and a non-local Matrix observation operator to demonstrate the feasibility of the approach and study the quality of the assimilation by transformation. In particular, we apply the approach to temperature profile reconstruction from infrared measurements given by the infrared atmospheric sounding interferometer (IASI) infrared sounder and show that the approach is feasible for this important data type in atmospheric analysis and forecasting. 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 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.

]]>In this work, we develop the negative-order modified Korteweg–de Vries (nMKdV) equation. By means of the recursion operator of the modified KdV equation, we derive negative order forms, one for the focusing branch and the other for the defocusing form. Using the Weiss–Tabor–Carnevale method and Kruskal's simplification, we prove the Painlevé integrability of the nMKdV equations. We derive multiple soliton solutions for the first form and multiple singular soliton solutions for the second form. 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.

]]>In this paper, we study an American option-pricing model with an uncertain volatility. Some properties for the option price are derived. Particularly, a global spread for the option price is proved when the volatility depends on the underlying security and time. This result confirms the observed fact from the real financial data in option markets. 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 consider a nonlinear age structured McKendrick–von Foerster population model with diffusion term. Here we prove existence and uniqueness of the solution of the equation. We consider a particular type of nonlinearity in the renewal term and prove Generalized Relative Entropy type inequality. Longtime behavior of the solution has been addressed for both linear and nonlinear versions of the equation. In linear case, we prove that the solution converges to the first eigenfunction with an exponential rate. In nonlinear case, we have considered a particular type of nonlinearity that is present in the mortality term in which we can predict the longtime behavior. 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.

]]>This paper is devoted to global asymptotic stability of cellular neural networks with impulses and multi-proportional delays. First, by means of the transformation *v*_{i}(*t*) = *u*_{i}(*e*^{t}), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Second, we prove the global exponential stability of the latter by nonlinear measure, and that the exponential stability of the latter implies the asymptotic stability of the former. We furthermore provide a sufficient condition to the existence, uniqueness, and the global asymptotic stability of the equilibrium point of the former. Our results are generalizations of some existing ones. Finally, an example and its simulation are presented to illustrate effectiveness of our method. Copyright © 2015 John Wiley & Sons, Ltd.

With the aid of Lenard recursion equations, we derive the Wadati–Konno–Ichikawa hierarchy. Based on the Lax matrix, an algebraic curve
of arithmetic genus *n* is introduced, from which Dubrovin-type equations and meromorphic function *φ* are established. The explicit theta function representations of solutions for the entire WKI hierarchy are given according to asymptotic properties of *φ* and the algebro-geometric characters of
. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we prove the unique continuation property for the weak solution of the plate equation with the low regular coefficient. Then, we apply this result to study the global attractor for the semilinear plate equation with a localized damping. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper is concerned with a suspension bridge equation with memory effects , defined in a bounded domain of . For the suspension bridge equation without memory, there are many classical results. Existing results mainly devoted to existence and uniqueness of a weak solution, energy decay of solution and existence of global attractors. However the existence of global attractors for the suspension bridge equation with memory was no yet considered. The object of the present paper is to provide some results on the well-posedness and long-time behavior to the suspension bridge equation in a more with past history. Copyright © 2015 John Wiley & Sons, Ltd.

]]>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+*ρ*^{β}(*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.

K. Guerlebeck In this paper, we consider the following nonlinear Dirac equation

By applying the variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou, we prove the existence of nontrivial and ground state solutions for the aforementioned system under conditions weaker than those in Zhang *et al.* (Journal of Mathematical Physics, 2013). John Wiley & Sons, Ltd.

The paper explores an eco-epidemiological model of a predator–prey type, where the prey population is subject to infection. The model is basically a combination of S-I type model and a Rosenzweig–MacArthur predator–prey model. The novelty of this contribution is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We explicitly separate the competition between non-infected and infected individuals. This emergent carrying capacity is markedly different to the explicit carrying capacities that have been considered in many eco-epidemiological models. We observed that different intra-class and inter-class competition can facilitate the coexistence of susceptible prey-infected prey–predator, which is impossible for the case of the explicit carrying capacity model. We also show that these findings are closely associated with bi-stability. The present system undergoes bi-stability in two different scenarios: (a) bi-stability between the planner equilibria where susceptible prey co-exists with predator or infected prey and (b) bi-stability between co-existence equilibrium and the planner equilibrium where susceptible prey coexists with infected prey; have been discussed. The conditions for which the system is to be permanent and the global stability of the system around disease-free equilibrium are worked out. 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:

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.

]]>This paper deals with the long-term properties of the thermoelastic nonlinear string-beam system related to the well-known Lazer–McKenna suspension bridge model

- (0.1)

In particular, no mechanical dissipation occurs in the equations, because the loss of energy is entirely due to thermal effects. The existence of regular global attractors for the associated solution semigroup is proved (without resorting to a bootstrap argument) for time-independent supplies *f*,*g*,*h* and any
. 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.

]]>In thiswork,we present two new(3+1)-dimensional nonlinear equationswith Korteweg-de Vries equation constituting its main part. We show that the dispersive relation is distinct for each model, whereas the phase shift remains the same. We determine multiple solitons solutions, with distinct physical structures, for each established equation. The architectures of the simplified Hirota's method is implemented in this paper. The constraint conditions that fall out which must remain valid in order for themultiple solitons to exist are derived.Copyright © 2015 John Wiley & Sons, Ltd.

]]>We present the improved three-dimensional axially symmetric incompressible magnetohydrodynamics (MHD) equations with nonzero swirl. We consider three kinds of smooth axially symmetric particular solutions to the MHD equations: (1) *u*^{θ}=0,*B*^{r}=*B*^{z}=0, (2) *B*^{r}=*B*^{z}=0, and (3) *B*^{θ}=0. In particular, we derive new regularity criteria for these three kinds of the three-dimensional axially symmetric smooth solutions to the MHD equations. Our results also reveal some interesting dynamic behavior of the interaction by the angular vorticity field *ω*^{θ} and the angular current density field *j*^{θ}. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we will study the lower bounds of the life span (the maximal existence time) of solutions to the initial-boundary value problems with small initial data and zero Neumann boundary data on exterior domain for one-dimensional general quasilinear wave equations *u*_{tt}−*u*_{xx}=*b*(*u*,*D**u*)*u*_{xx}+*F*(*u*,*D**u*). Our lower bounds of the life span of solutions in the general case and special case are shorter than that of the initial-Dirichlet boundary value problem for one-dimensional general quasilinear wave equations. We clarify that although the lower bounds in this paper are same as that in the case of Robin boundary conditions obtained in the earlier paper, however, the results in this paper are not the trivial generalization of that in the case of Robin boundary conditions because the fundamental Lemmas 2.4, 2.5, 2.6, and 2.7, that is, the priori estimates of solutions to initial-boundary value problems with Neumann boundary conditions, are established differently, and then the specific estimates in this paper are different from that in the case of Robin boundary conditions. Another motivation for the author to write this paper is to show that the well-posedness of problem is the essential precondition of studying the lower bounds of life span of classical solutions to initial-boundary value problems for general quasilinear wave equations. The lower bound estimates of life span of classical solutions to initial-boundary value problems is consistent with the actual physical meaning. Finally, we obtain the sharpness on the lower bound of the life span in the general case and in the special case. Copyright © 2015 John Wiley & Sons, Ltd.

A coefficient inverse problem for a parabolic equation is considered. Using a Carleman weight function, a globally strictly convex cost functional is constructed for this problem. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper is concerned with the oscillation of numerical solution for the Nicholson's blowflies model. Using two kinds of *θ*-methods, namely, the linear *θ*-method and the one-leg *θ*-method, several conditions under which the numerical solution oscillates are derived. Moreover, it is shown that every non-oscillatory numerical solution tends to equilibrium point of the original continuous-time model. Finally, numerical experiments are provided to illustrate the analytical results. Copyright © 2015 John Wiley & Sons, Ltd.

Milling chatter leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Thus, it is desirable to predict and avoid the onset of this instability. Considering that the stability of milling with variable pitch cutter or tool runout case is characterized by multiple delays, in this paper, an improved semi-discretization method is proposed to predict the stability lobes for milling processes with multiple delays. Taking the variable pitch milling, for example, a comparisonwith prior methods is conducted to verify the accuracy and efficiency of the proposed approach for the stability prediction both in low and high radial immersion ratios. In addition, the rate of convergence of the proposed method is also evaluated. The results show that the proposed method has high computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.