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The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples, the first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.

In this paper, we consider the propagation of waves in an open waveguide in ℝ$^{2}$ where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide (which we choose to be the x$_{1}$ axis) and equal to one for |x$_{2}$| > h$_{0}$ for some h$_{0}$ > 0. Motivated by the limiting absorption principle (proven in an earlier paper by the author), we formulate a radiation condition which allows the existence of propagating modes and prove uniqueness, existence, and stability of a solution under the assumption that no bound states exist. In the second part, we determine the order of decay of the radiating part of the solution in the direction of the layer and in the direction orthogonal to it. Finally, we show that it satisfies the classical Sommerfeld radiation condition and allows the definition of a far field pattern.

In this paper, using Riemann-Liouville integral and Caputo derivative, we study a nonlinear singular integro-differential equation of Lane-Emden type with nonlocal multi-point integral conditions. We prove the existence and uniqueness of solutions by application of Banach contraction principle. Also, we prove an existence result using Schaefer fixed point theorem. Then, we present some examples to show the applicability of the main results. DGRSDT, Direction Generale de la Recherche Scientifique et du Developpement Technologique, Algeria The authors express a special thanks to the associate editor and referees for their motivated comments that made the original manuscript significant and improved. This paper is supported by DGRSDT, Direction Generale de la Recherche Scientifique et du Developpement Technologique, Algeria. WOS:000526582000001 2-s2.0-85084038419

This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\Omega\subset\mathbb{R}^N$ ($N\in{\mathbb N}$), written as \[ \frac{\partial u}{\partial t} + (-\Delta+1)\beta(u) = g \quad \mbox{in}\ \Omega\times(0, T), \] which represents the porous media, the fast diffusion equations, etc., where $\beta$ is a single-valued maximal monotone function on $\mathbb{R}$, and $T>0$. Existence and uniqueness for (P) were directly proved under a growth condition for $\beta$ even though the Stefan problem was excluded from examples of (P). This paper completely removes the growth condition for $\beta$ by confirming Cauchy's criterion for solutions of the following approximate problem (P)$_{\varepsilon}$ with approximate parameter $\varepsilon>0$: \[ \frac{\partial u_{\varepsilon}}{\partial t} + (-\Delta+1)(\varepsilon(-\Delta+1)u_{\varepsilon} + \beta(u_{\varepsilon}) + \pi_{\varepsilon}(u_{\varepsilon})) = g \quad \mbox{in}\ \Omega\times(0, T), \] which is called the Cahn--Hilliard system, even if $\Omega \subset \mathbb{R}^N$ ($N \in \mathbb{N}$) is an unbounded domain. Moreover, it can be seen that the Stefan problem is covered in the framework of this paper.

This paper is concerned with the large time behavior of solutions to the initial value problem for the damped wave equations with nonlinear convection in one-dimensional whole space. In 2007, Ueda and Kawashima showed that the solution tends to a self similar solution of the Burgers equation. However, they did not mention that their decay estimate is optimal or not. Under this situation, the aim of this paper was to find out the sharp decay estimate by studying the second asymptotic profile of solutions. The explicit representation formula and the decay estimates of the solution for the linearized equation including the lower order term play crucial roles in our analysis.

This paper deals with an adaptation of the Poincare-Lindstedt method for the determination of periodic orbits in three-dimensional nonlinear differential systems. We describe here a general symbolic algorithm to implement the method and apply it to compute periodic solutions in a three-dimensional Lotka-Volterra system modeling a chain food interaction. The sufficient conditions to make secular terms disappear from the approximate series solution are given in the paper.

Shannon and Zipf-Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well-know Jensen inequality and obtain different bounds for Shannon and Zipf-Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf-Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf-Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf-Mandelbrot entropy.

The purpose of this paper is to study the traveling wave solutions of a nonlocal reaction-diffusion system with delay arising from the spread of an epidemic by oral-faecal transmission. Under monostable and quasimonotone it is well known that the system has a minimal wave speed c* of traveling wave fronts. In this paper, we first prove the monotonicity and uniqueness of traveling waves with speed c⩾c∗. Then we show that the traveling wave fronts with speed c>c∗ are exponentially asymptotically stable.

In this paper, we introduce the notion of partial affine system that is a subset of an affine system. It has potential applications in signal analysis. A general affine system has been extensively studied; however, the partial one has not. The main focus of this paper is on partial affine system–based frames and dual frames. We obtain a necessary condition and a sufficient condition for a partial affine system to be a frame and present a characterization of partial affine system–based dual frames. Some examples are also provided.

The Bogdanov-Takens bifurcations of a Leslie-Gower predator-prey model with Michaelis-Menten–type prey harvesting were studied. In the paper “Diff. Equ. Dyn. Syst. 20(2012), 339-366,” Gupta et al proved that the Leslie-Gower predator-prey model with Michaelis-Menten–type prey harvesting has rich dynamics. Some equilibria of codimension 1 and their bifurcations were discussed. In this paper, we find that the model has an equilibrium of codimensions 2 and 3. We also prove analytically that the model undergoes Bogdanov-Takens bifurcations (cusp cases) of codimensions 2 and 3. Hence, the model can have 2 limit cycles, coexistence of a stable homoclinic loop and an unstable limit cycle, supercritical and subcritical Hopf bifurcations, and homoclinic bifurcation of codimension 1 as the values of parameters vary. Moreover, several numerical simulations are conducted to illustrate the validity of our results.

In the paper, a necessary and sufficient criterion it provided such that any local optimal solution is also global in a not necessarily differentiable constrained optimization problem. This criterion is compared to others earlier appeared in the literature, which are sufficient but not necessary for a local optimal solution to be global. The importance of the established criterion is illustrated by suitable examples of nonconvex optimization problems presented in the paper.

This paper studies the dynamics of the generalized Lengyel-Epstein reaction-diffusion model proposed in a recent study by Abdelmalek and Bendoukha. Two main results are shown in this paper. The first of which is sufficient conditions that guarantee the nonexistence of Turing patterns, ie, nonconstant solutions. Second, more relaxed conditions are derived for the stability of the system's unique steady-state solution.

In this paper, a novel simulation methodology based on the reproducing kernels is proposed for solving the fractional order integro-differential transport model for a nuclear reactor. The analysis carried out in this paper thus forms a crucial step in the process of development of fractional calculus as well as nuclear science models. The fractional derivative is described in the Captuo Riemann–Liouville sense. Results are presented graphically and in tabulated forms to study the efficiency and accuracy of method. The present scheme is very simple, effective, and appropriate for obtaining numerical simulation of nuclear science models. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, an iteration process is considered to solve linear ill-posed problems. Based on the randomness of the involved variables, this kind of problems is regarded as simulation problems of the posterior distribution of the unknown variable given the noise data. We construct a new ensemble Kalman filter-based method to seek the posterior target distribution. Despite the ensemble Kalman filter method having widespread applications, there has been little analysis of its theoretical properties, especially in the field of inverse problems. This paper analyzes the propagation of the error with the iteration step for the proposed algorithm. The theoretical analysis shows that the proposed algorithm is convergence. We compare the numerical effect with the Bayesian inversion approach by two numerical examples: backward heat conduction problem and the first kind of integral equation. The numerical tests show that the proposed algorithm is effective and competitive with the Bayesian method. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, our main aim is to establish some new fractional integral inequalities involving Hadamard-type k-fractional integral operators recently given by Mubeen et al. Furthermore, the paper discusses some of their relevance with known results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we establish finite-region stability (FRS) and finite-region boundedness analysis methods to investigate the transient behavior of discrete two-dimensional Roesser models. First, by building special recursive formulas, a sufficient FRS condition is built via solvable linear matrix inequalities constraints. Next, by designing state feedback controllers, the finite-region stabilization issue is analyzed for the corresponding two-dimensional closed-loop system. Similar to FRS analysis, the finite-region boundedness problem is addressed for Roesser models with exogenous disturbances and corresponding criteria, and linear matrix inequalities conditions are reported. To conclude the paper, we provide numerical examples to confirm the validity of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.

A discrete dynamical system named real - valued pendulum is presented in the paper. The system is developed for modeling of particles relocations on abstract graph with formalized rules of behavior (competition for space) and movement plans logistics. Logistics is given in a formal statement by the real numbers of the unit closed interval, presented in calculus with base equals to the graph power N. The central question is to study the behavior of the pendulum depending on its architecture. In the previous papers, with investigation of logistic pendulum, we have studied chaotic pendulum, where the particle plan for “tomorrow” is played “today”. A particular case of logistic pendulum, such that particle plans are time shifts of N−ary digital representation of single generating number, is called phase pendulum. In this paper, we are considering a dynamical system with generation of particles plans using a some mapping F, defined on the set of system states. Copyright © 2016 John Wiley & Sons, Ltd.

This paper examines the initial-value problem for the nonhomogeneous incompressible nematic liquid crystals system with vacuum. This paper establishes two main results. The first result is involved with the global strong solutions to the 2D liquid crystals system in a bounded smooth domain. Our second result is concerned with the small data global existence result about the 3D system in the whole space. In addition, the local existence and a blow-up criterion of strong solutions are also mentioned. 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, 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.

In this paper, we consider one-dimensional compressible viscous and heat-conducting micropolar fluid, being in a thermodynamical sense perfect and polytropic. The homogenous boundary conditions for velocity, microrotation, and temperature are introduced. This problem has a global solution with a priori estimates independent of time; with the help of this result, we first prove the exponential stability of solution in (H1(0,1))4, and then we establish the global existence and exponential stability of solutions in (H2(0,1))4 under the suitable assumptions for initial data. The results in this paper improve those previously related results. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the optimal distributed control of the viscous weakly dispersive Degasperis–Procesi equation in nonlinear shallow water dynamics. It is well known that the Pontryagin maximum principle, which unifies calculus of variations and control theory of ordinary differential equations, sets up the theoretical basis of the modern optimal control theory along with the Bellman dynamic programming principle. In this paper, we commit ourselves to infinite dimensional generalizations of the maximum principle and aim at the optimal control theory of partial differential equations. In contrast to the finite dimensional setting, the maximum principle for the infinite dimensional system does not generally hold as a necessary condition for optimal control. By the Dubovitskii and Milyutin functional analytical approach, we prove the Pontryagin maximum principle of the controlled viscous weakly dispersive Degasperis–Procesi equation. The necessary optimality condition is established for the problem in fixed final horizon case. Finally, a remark on how to utilize the obtained results is also made. Copyright © 2015 JohnWiley & Sons, Ltd.

Previously, existence and uniqueness of a class of monotone similarity solutions for a nonlinear differential equation arising in magnetohydrodynamic Falkner–Skan flow were considered in the case of accelerating flows. It was shown that a solution satisfying certain monotonicity properties exists and is unique for the case of accelerated flows and some decelerated flows. In this paper, we show that solutions to the problem can exist for decelerated flows even when the monotonicity conditions do not hold. In particular, these types of solutions have nonmonotone second derivatives and are, hence, a distinct type of solution from those studied previously. By virtue of this result, the present paper demonstrates the existence of an important type of solution for decelerated flows. Importantly, we show that multiple solutions can exist for the case of strongly decelerated flows, and this occurs because of the fact that the solutions do not satisfy the aforementioned monotonicity requirements. 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 (FHS) where α ∈ (1 ∕ 2,1), , , is a symmetric and positive definite matrix for all , , and ∇ W is the gradient of W at u. The novelty of this paper is that, assuming L is bounded in the sense that there are constants 0

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.

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.

The present paper studies a fractional-order SEIR epidemic model for the transmission dynamics of infectious diseases such as HIV and HBV that spreads in the host population. The total host population is considered bounded, and Holling type-II saturation incidence rate is involved as the infection term. Using the proposed SEIR epidemic model, the threshold quantity, namely basic reproduction number R0, is obtained that determines the status of the disease, whether it dies out or persists in the whole population. The model’s analysis shows that two equilibria exist, namely, disease-free equilibrium (DFE) and endemic equilibrium (EE). The global stability of the equilibria is determined using a Lyapunov functional approach. The disease status can be verified based on obtained threshold quantity R0. If R0 < 1, then DFE is globally stable, leading to eradicating the population’s disease. If R0 > 1, a unique EE exists, and that is globally stable under certain conditions in the feasible region. The Caputo type fractional derivative is taken as the fractional operator. The bifurcation and sensitivity analyses are also performed for the proposed model that determines the relative importance of the parameters into disease transmission. The numerical solution of the model is obtained by the generalized Adams- Bashforth-Moulton method. Finally, numerical simulations are performed to illustrate and verify the analytical results.

In a recent paper, the authors have introduced the windowed linear canonical transform and shown its good properties together with some applications such as Poisson summation formulas, sampling interpolation, and series expansion. In this paper, we prove the Paley–Wiener theorems and the uncertainty principles for the (inverse) windowed linear canonical transform. They are new in literature and has some consequences that are now under investigation. Copyright © 2012 John Wiley & Sons, Ltd.

There have been different approaches to compute the analytic instantaneous frequency with a variety of background reasoning and applicability in practice, as well as restrictions. This paper presents a new non-analytic instantaneous frequency definition for a large class of so-called simple waves. Simple wave contains a wide range of signals for which the concept instantaneous frequency has a perfect physical sense. There are a number of automatic sleep spindle detection methods in the literature, however, due to the complexity of the sleep spindle characteristics from different people and absence of generally accepted sleep spindle definition in the literature, researchers are still exploring more practically acceptable and workable methods. A novel instantaneous frequency definition based semi-automatic sleep spindle detection approach is also proposed in this paper. A set of experiments on publicly available database clearly indicate that the proposed approaches are very promising. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we give a detailed study of the global attractors for porous medium equations in a heterogeneous medium. Not only the existence but also the infinite dimensionality of the global attractors is obtained by showing that their ϵ-Kolmogorov entropy behaves as a polynomial of the variable 1 ∕ ϵ as ϵ tends to zero, which is not observed for non-degenerate parabolic equations. The upper and lower bounds for the Kolmogorov ϵ-entropy of infinite-dimensional attractors are also obtained. We believe that the method developed in this paper has a general nature and can be applied to other classes of degenerate evolution equations. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper we investigate a time dependent family of plane closed Jordan curves evolving in the normal direction with a velocity which is assumed to be a function of the curvature, tangential angle and position vector of a curve. We follow the direct approach and analyze the system of governing PDEs for relevant geometric quantities. We focus on a class of the so-called curvature adjusted tangential velocities for computation of the curvature driven flow of plane closed curves. Such a curvature adjusted tangential velocity depends on the modulus of the curvature and its curve average. Using the theory of abstract parabolic equations we prove local existence, uniqueness and continuation of classical solutions to the system of governing equations. We furthermore analyze geometric flows for which normal velocity may depend on global curve quantities like the length, enclosed area or total elastic energy of a curve. We also propose a stable numerical approximation scheme based on the flowing finite volume method. Several computational examples of various nonlocal geometric flows are also presented in this paper., submitted to MMAS

This paper considers the finite deformation theory of poroelasticity for the case in which a deformable solid constituent and an interpenetrating liquid constituent are each regarded as incompressible, and the mixing itself is regarded as taking place without the creation of voids. The resulting kinematical constraint gives rise to a Lagrange multiplier pressure in the resulting constitutive description. This pressure therefore enters into the separate momentum balance statements for each individual constituent. The formulation of boundary value problems in this context is well known in continuum mechanics. This paper examines how a systematic elimination of the Lagrange multiplier pressure from the mathematical formulation leads to a stress-like tensor that generalizes a stress tensor concept introduced by Rajagopal and Wineman in the late 1980s, which they called the saturation stress. Here, by providing a rather complete development, it is discussed how boundary value problems are naturally formulated in terms of a single such stress tensor, how the constitutive theory is framed in terms of this stress tensor, and how certain questions concerning the formulation of boundary conditions are naturally addressed. Connections to the small deformation linear poroelastic (biphasic) theory are also provided. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the inverse electromagnetic scattering by a 2D (impenetrable or penetrable) smooth periodic curve. Precisely, we establish global uniqueness results on the inverse problem of determining the grating profile from the scattered fields corresponding to a countably infinite number of quasiperiodic incident waves. For the case of an impenetrable and partially coated perfectly reflecting grating, we prove that the grating profile and its physical property can be uniquely determined from the scattered field measured above the periodic structure. For the case of a penetrable grating, we show that the periodic interface can be uniquely recovered by the scattered field measured only above the interface. A key ingredient in our proofs is a novel mixed reciprocity relation that is derived in this paper for the periodic structures and seems to be new. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we study a homogenization problem for perimeter energies in highly contrasted media; the analysis of the previous paper is carried out by removing the hypothesis that the perforated medium Rn ∖ E is composed of disjoint compact components. Assuming E to be the union of a finite number N of connected components E1, … ,EN, the Γ-limit F is a multiphase energy with a ‘decoupled’ surface part, obtained by homogenization from the surface tensions in each E j, a trivial bulk term obtained as a weak limit, and a further interacting term between the phases, involving an asymptotic formula for a family minimum problems on invading an asymptotic formula for a family of minimum problems on invading domains with prescribed boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd.

Based on the simplicity and calculability of polyline function, we consider, in this paper, the regularized regression learning algorithm associated with the least square loss and the set of polyline function . The target is the error analysis for the regression problem. The approach presented in the paper yields satisfactory learning rates. The rates depend on the approximation property of and on the capacity of measured by covering numbers. Under some certain conditions, the rates achieve m−4/5 log m. Copyright © 2012 John Wiley & Sons, Ltd.

An analysis of the transverse vibration of nonhomogeneous orthotropic viscoelastic circular plates of parabolically varying thickness in the radial direction is presented. The thickness of a circular plate varies parabolically in a radial direction. For nonhomogeneity of the circular plate material, density is assumed to vary linearly in a radial direction. This paper used the method of separation of variables in solving the governing differential equation. In this paper, an approximate but quite convenient frequency equation is derived by using the Rayleigh–Ritz technique with a two-term deflection function. Deflection, time period and logarithmic decrement for the first two modes of vibration are computed for the nonhomogeneous orthotropic viscoelastic circular plates of varying parabolic thickness with clamped edge conditions for various values of nonhomogeneity constants and taper constants and these are shown in tabular form for the Voigt–Kelvin model. Copyright © 2011 John Wiley & Sons, Ltd.

This paper deals with a porous medium system with nonlocal sources and weighted nonlocal boundary conditions. The main aim of this paper is to study how the reaction terms, the diffusion terms, and the weight functions in the boundary conditions affect the global and blow-up properties to a porous medium system. The conditions on the global existence and blow-up in finite time for nonnegative solutions are given. Furthermore, the blow-up rate estimates of the blow-up solutions are also established. Copyright © 2011 John Wiley & Sons, Ltd.

In a recent paper, we showed that the classical Bergman theory admits two possible formulations for the class of slice regular functions with quaternionic values. In the so called formulation of the first kind, we provide a Bergman kernel which is defined on and is a reproducing kernel. In the so called formulation of the second kind, we use the Representation Formula for slice regular functions to define a second Bergman kernel; this time the kernel is still defined on U, but the integral representation of f is based on an integral computed only on and the integral does not depend on , (here denotes the sphere unit of purely imaginary quaternions, and represents the complex plane with imaginary unit I). In this paper, we extend the second formulation of the Bergman theory to the case of slice monogenic functions and we focus our attention on the so-called Bergman–Sce transform. This integral transform is defined by using the Bergman kernel and the Sce mapping theorem and associates to every slice monogenic function f, an axially monogenic function . Copyright © 2011 John Wiley & Sons, Ltd.

In a previous paper, we have studied the asymptotic behavior of a viscous fluid satisfying Navier's law on a periodic rugous boundary of period e and amplitude δe, with δe/e tending to zero. In the critical size, δe∼e3/2, in order to obtain a strong approximation of the velocity and the pressure it is necessary to consider a boundary layer term in the corresponding ansatz. The purpose of this paper is to estimate the approximation given by this ansatz. Copyright © 2011 John Wiley & Sons, Ltd.

This paper establishes a mathematical model to study the long behavior of a single-species population living in a polluted environment. In this paper, we suppose that pollution tax is imposed on toxicant emitters if their emission crosses the permissible limit, limit up to which there is no harm to the population. Some sufficient conditions for the persistence of the population are obtained. Copyright © 2011 John Wiley & Sons, Ltd.

We present a mathematical model for the slow and partial combustion process of a sheet of paper ignited on one side and in the presence of a flow of air confined in a narrow gap above the paper. The model includes mass and thermal balance for the various components. After having introduced some simplifications, a suitable rescaling is performed and some limit cases are examined. Two classes of travelling wave solutions are analyzed, corresponding to the opposite cases of a sufficiently large or of a moderate air flow. Copyright © 2010 John Wiley & Sons, Ltd.

This paper is devoted to studying the initial-value problem of the Kawahara equation. By establishing some crucial bilinear estimates related to the Bourgain spaces Xs, b(R2) introduced by Bourgain and homogeneous Bourgain spaces, which is defined in this paper and using I-method as well as L2 conservation law, we show that this fifth-order shallow water wave equation is globally well-posed for the initial data in the Sobolev spaces Hs(R) with . Copyright © 2010 John Wiley & Sons, Ltd.

This paper presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(ux) in the inhomogenenous quasi-linear parabolic equation ut(x, t)=(k(ux)ux(x, t))x +F(u), with the Dirichlet boundary conditions u(0, t)=ψ0, u(1, t)=ψ1 and source function F(u). The main purpose of this paper is to investigate the distinguishability of the input–output mappings Φ[·]:C1[0, T], Ψ[·]:C1[0, T] via semigroup theory. Copyright © 2009 John Wiley & Sons, Ltd.

Tail distribution bounds play a major role in the estimation of failure probabilities in performance and reliability analysis of systems. They are usually estimated using Markov's and Chebyshev's inequalities, which represent tail distribution bounds for a random variable in terms of its mean or variance. This paper presents the formal verification of Markov's and Chebyshev's inequalities for discrete random variables using a higher-order-logic theorem prover. The paper also provides the formal verification of mean and variance relations for some of the widely used discrete random variables, such as Uniform(m), Bernoulli(p), Geometric(p) and Binomial(m, p) random variables. This infrastructure allows us to precisely reason about the tail distribution properties and thus turns out to be quite useful for the analysis of systems used in safety-critical domains, such as space, medicine or transportation. For illustration purposes, we present the performance analysis of the coupon collector's problem, a well-known commercially used algorithm.

In this paper, we deal with a new approximation of a diffusive predator--prey model with Leslie--Gower term and social behavior for the prey subject to Neumann boundary conditions. A new approach for a predator-prey interaction in the presence of prey social behavior has been considered. Our main topic in this work is to study the influence of the prey's herd shape on the predator-prey interaction in the presence of Leslie--Gower term. First of all, we examine briefly the system without spatial diffusion. By analyzing the distribution of the eigenvalues associated with the constant equilibria, the local stability of the equilibrium points and the existence of Hopf bifurcation have been investigated. Then, the spatiotemporal dynamics introduced by self diffusion was determined, where the existence of the positive solution, Hopf bifurcation, Turing driven instability, Turing-Hopf bifurcation point have been derived. Further, the effect of the prey's herd shape rate on the prey and predator equilibrium densities as well as on the Hopf bifurcating points has been discussed. Finally, by using the normal form theory on the center manifold, the direction and stability of the bifurcating periodic solutions have also been obtained. To illustrate the theoretical results, some graphical representations are given.

In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient goodness-of-fit (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fr\’{e}chet and Kumaraswamy distributions; and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fr\’{e}chet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling’s $T^2$ statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

In this paper, we present a recently developed mathematical model for short double-wall carbon nanotubes. The model is governed by a system of four hyperbolic equations representing the two Timoshenko beams coupled through the Van der Waals forces. The system is equipped with a four-parameter family of the boundary conditions and can be reduced to an evolution equation. This equation defines a strongly continuous semi-group. Spectral properties of the semi-group generator are presented in the paper. We show that it is an unbounded non-selfadjoint operator with compact resolvent. Moreover, this operator is a relatively compact perturbation of a certain selfadjoint operator. Copyright © 2008 John Wiley & Sons, Ltd.

In this paper, we suggest a new relaxation method for solving mathematical programs with complementarity constraints. This method can be regarded as a modification of a method proposed in a recent paper (J. Opt. Theory Appl. 2003; 118:81–116). We show that the main results remain true for the modified method and particularly, some conditions assumed in the previous paper can be removed. Copyright © 2007 John Wiley & Sons, Ltd.