The present article deals with existence and uniqueness results for a nonlinear evolution initial-boundary value problem, which originates in an age-structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age *a* and cycle length *l*. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length *l* is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.

In this article, we study the increasing stability property for the determination of the potential in the Schrödinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat, and homogeneous boundary condition is prescribed on this part. In contrast to earlier works, we are able to deal with the case when potentials have some Sobolev regularity and also need not be compactly supported inside the domain.

]]>Controversial results concerning the effectiveness of bed net in reducing dengue fever transmission make further research necessary in this direction. At this aim, we consider a mathematical model of dengue transmission where the use by individuals of insecticide-treated bed nets is taken into account, combined or not with insecticide spraying. Furthermore, as climatic factors play a key role in mosquito-borne diseases, we model the effect of seasonality through a periodic mosquito birth rate. We numerically investigate some specific scenarios according to different rainfall and mean temperature values. We set an optimal control problem to minimize the number of human infections and the cost of efforts placed into bed net adoption and maintenance and insecticide spraying. To assess the most appropriate strategy to eliminate dengue with minimum costs, we perform a comparative cost-effectiveness analysis, which also shows how the cost-benefit of intervention efforts is affected by changes in the amplitude of seasonal variation. One general result is that in any case the combination of bed net use and insecticide spraying produces the highest ratio of infections averted, whereas in terms of cost-benefit only spraying campaigns should be implemented in control programs for regions with no large seasonality.

]]>Bor has recently obtained a main theorem dealing with absolute weighted mean summability of Fourier series. In this paper, we generalized that theorem for summability method. Also, some new and known results are obtained dealing with some basic summability methods.

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

]]>This paper deals with the blow-up solution to the following semilinear pseudo-parabolic equation

in a bounded domain
, which was studied by Luo (Math Method Appl Sci 38(12):2636-2641, 2015) with the following assumptions on *p*:

and the lifespan for the initial energy *J*(*u*_{0})<0 is considered. This paper generalizes the above results on the following two aspects:

- a new blow-up condition is given, which holds for all p> 1;
- a new lifespan is given, which holds for all p> 1 and possible
*J*(*u*_{0})≥0.

Moreover, as a byproduct, we refine the lifespan when *J*(*u*_{0})<0.

This paper deals with a stochastic system which models the population dynamics of a chemostat including species death rate. On the basis of the theory on Markov semigroup, we demonstrate that the probability densities of the distributions for the solutions are absolutely continuous. The densities will convergence in *L*^{1} to an invariant density or weakly convergence to a singular measure under appropriate conditions. We also give the sufficient criteria for extinction exponentially of the species. To be specific, when *D*_{1}>*D* and the strength of perturbation is relatively small, we derive a precise threshold for the species survival.

This paper is devoted to the study of the initial value problem of nonlinear fractional differential equations involving a Caputo-type fractional derivative with respect to another function. Existence and uniqueness results for the problem are established by means of the some standard fixed point theorems. Next, we develop the Picard iteration method for solving numerically the problem and obtain results on the long-term behavior of solutions. Finally, we analyze a population growth model and a gross domestic product model with governing equations being fractional differential equations that we have introduced in this work.

]]>We address the question of mean biomass volumetric productivity optimization, which originates from the simplification of dynamics of microalgae in a batch bioreactor process with light incidence. In particular, the stability of the model is analyzed, some optimality necessary conditions for the nonsmooth optimization problem obtained through the inclusion of different photoperiods are studied, and the model is applied in the particular case of *Chlamydomonas reinhardtii* microalgae to validate our results.

Since Compton cameras were introduced in the use of single photon emission computed tomography, various types of conical Radon transforms, which integrate the emission distribution over circular cones, have been studied. Most of previous works did not address the attenuation factor, which may lead to significant degradation of image quality. In this paper, we consider the problem of recovering an unknown function from conical projections affected by a known constant attenuation coefficient called an attenuated conical Radon transform. In the case of a fixed opening angle and vertical central axis, new explicit inversion formula is derived. Two-dimensional numerical simulations were performed to demonstrate the efficiency of the suggested algorithm.

]]>Deciding participation level of a component to dubious information is essential, particularly all things considered are displaying issues. This paper will present a participation capacity of components that has a place with unverifiable information. The fundamental instrument is the similarity classes that came about because of the likeness connection of a data framework. We will likewise express a few properties and an examination between our work and the past one.

]]>In this paper, we study the existence of ground state solutions for a Kirchhoff-type problem in involving critical Sobolev exponent. With the help of Nehari manifold and the concentration-compactness principle, we prove that problem admits at least one ground state solution.

]]>In this work, we study coexistence states for a Lotka-Volterra symbiotic system with cross-diffusion under homogeneous Dirichlet boundary conditions. By using topological degree theory and bifurcation theory, we prove the existence and multiplicity of positive solutions under certain conditions on the parameters. Asymptotic behaviors of positive solutions are respectively studied as the cross-diffusion coefficient tends to infinity and the interaction rate tends to zero. Finally, we compare our results with those of the Lotka-Volterra predator and competition systems.

]]>The purpose of this paper is to study the mixed Dirichlet-Neumann boundary value problem for the semilinear Darcy-Forchheimer-Brinkman system in *L*_{p}-based Besov spaces on a bounded Lipschitz domain in
, with *p* in a neighborhood of 2. This system is obtained by adding the semilinear term |**u**|**u** to the linear Brinkman equation. First, we provide some results about equivalence between the Gagliardo and nontangential traces, as well as between the weak canonical conormal derivatives and the nontangential conormal derivatives. Various mapping and invertibility properties of some integral operators of potential theory for the linear Brinkman system, and well-posedness results for the Dirichlet and Neumann problems in *L*_{p}-based Besov spaces on bounded Lipschitz domains in
(*n*≥3) are also presented. Then, using integral potential operators, we show the well-posedness in *L*_{2}-based Sobolev spaces for the mixed problem of Dirichlet-Neumann type for the linear Brinkman system on a bounded Lipschitz domain in
(*n*≥3). Further, by using some stability results of Fredholm and invertibility properties and exploring invertibility of the associated Neumann-to-Dirichlet operator, we extend the well-posedness property to some *L*_{p}-based Sobolev spaces. Next, we use the well-posedness result in the linear case combined with a fixed point theorem to show the existence and uniqueness for a mixed boundary value problem of Dirichlet and Neumann type for the semilinear Darcy-Forchheimer-Brinkman system in *L*_{p}-based Besov spaces, with *p*∈(2−*ε*,2+*ε*) and some parameter *ε*>0.

For the detection of *C*^{2}-singularities, we present lower estimates for the error in Schoenberg variation-diminishing spline approximation with equidistant knots in terms of the classical second-order modulus of smoothness. To this end, we investigate the behaviour of the iterates of the Schoenberg operator. In addition, we show an upper bound of the second-order derivative of these iterative approximations. Finally, we provide an example of how to detect singularities based on the decay rate of the approximation error.

This paper is focused on following time-harmonic Maxwell equation:

where
is a bounded Lipschitz domain,
is the exterior normal, and *ω* is the frequency. The boundary condition holds when Ω is surrounded by a perfect conductor. Assuming that *f* is asymptotically linear as
, we study the above equation by improving the generalized Nehari manifold method. For an anisotropic material with magnetic permeability tensor
and permittivity tensor
, ground state solutions are established in this paper. Applying the principle of symmetric criticality, we find 2 types of solutions with cylindrical symmetries in particular for the uniaxial material.

In this article, we present the equiform parameter and define the equiform-Bishop frame in Minkowski 3-space . Additionally, we investigate the equiform-Bishop formulas of the equiform spacelike case in Minkowski 3-space. Furthermore, some results of equiform spacelike normal curves according to the equiform-Bishop frame in are considered.

]]>This paper is concerned with the two-species chemotaxis-competition system

where Ω is a bounded domain in
with smooth boundary *∂*Ω, *n*≥2; *χ*_{i} and *μ*_{i} are constants satisfying some conditions. The above system was studied in the cases that *a*_{1},*a*_{2}∈(0,1) and *a*_{1}>1>*a*_{2}, and it was proved that global existence and asymptotic stability hold when
are small. However, the conditions in the above 2 cases strongly depend on *a*_{1},*a*_{2}, and have not been obtained in the case that *a*_{1},*a*_{2}≥1. Moreover, convergence rates in the cases that *a*_{1},*a*_{2}∈(0,1) and *a*_{1}>1>*a*_{2} have not been studied. The purpose of this work is to construct conditions which derive global existence of classical bounded solutions for all *a*_{1},*a*_{2}>0 which covers the case that *a*_{1},*a*_{2}≥1, and lead to convergence rates for solutions of the above system in the cases that *a*_{1},*a*_{2}∈(0,1) and *a*_{1}≥1>*a*_{2}.

The homogenization of kinetic laminates in the framework of time-dependent linearized elasticity is studied from a variational point of view through the Γ-convergence of the associated energies. The characterization of the effective coefficients is achieved by means of a finite dimensional minimization problem.

]]>In this paper, we study the homogeneous Dirichlet problem for an elliptic equation whose simplest model is

where
, *N*≥3 is an open bounded set, *θ*∈]0,1[, and *f* belongs to a suitable Morrey space. We will show that the Morrey property of the datum is transmitted to the gradient of a solution.

We study the existence of ground state solutions for the following Schrödinger-Poisson equations:

where
is the sum of a periodic potential *V*_{p} and a localized potential *V*_{loc} and *f* satisfies the subcritical or critical growth. Although the Nehari-type monotonicity assumption on *f* is not satisfied in the subcritical case, we obtain the existence of a ground state solution as a minimizer of the energy functional on Nehari manifold. Moreover, we show that the existence and nonexistence of ground state solutions are dependent on the sign of *V*_{loc}.

The issue of justifying the eddy current approximation of Maxwell's equations is reconsidered in the time-dependent setting. Convergence of the solution operators is shown in the sense of strong operator limits.

]]>In this paper, we prove a Liouville-type theorem for the steady compressible Hall-magnetohydrodynamics system in Π, where Π is whole space
or half space
. We show that a smooth solution (*ρ*,**u**,**B**,*P*) satisfying 1/*C*_{0}<*ρ*<*C*_{0},
, and **B**∈*L*^{9/2}(Π) for some constant *C*_{0}>0 is indeed trivial. This generalizes and improves 2 results of Chae.

In this paper, we consider the Cauchy problem of a fluid-particle interaction model with external forces. We first construct the asymptotic profile of the system. The global existence and uniqueness theorem for the solution near the profile is given. Finally, optimal decay rate of the solution to the background profile is obtained by combining the decay rate analysis of a linearized equation with energy estimates for the nonlinear terms. The main method used in this paper is the energy method combining with the macro-micro decomposition.

]]>Due to the huge volume and complex structure, simplification of point clouds is an important technique in practical applications. However, the traditional algorithms often lose geometric information and have no dynamic expanding structure. In this paper, a new simplification algorithm is proposed based on conformal geometric algebra. First of all, a multiresolution subdivision is constructed by the sphere tree, which computes the minimal bounding spheres with the help of k-means clustering, and then 2 kinds of simplification methods with full advantages of distance computing convenience are applied to carry out self-adapting simplification. Finally, several comparisons with original data or other algorithms are implemented from visualization to parameter contrast. The results show that the proposed algorithm has good effect not only on the local details but also on the overall error rate.

]]>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.

]]>In this article, we consider and investigate the cases when the retailer's capitals are restricted and when the supplier offers another kind of 2-level trade credit. This means that the supplier offers 2-level trade credit for the retailer to settle the account and the retailer's capitals are restricted, so the retailer decides to pay off the unpaid balance as follows: Firstly, the retailer decides to pay off the unpaid balance at the end of the first credit period if the retailer can pay off all accounts and, in addition, the retailer can use the sales revenue to earn interest throughout the replenishment cycle time. Secondly, the retailer decides to pay off all accounts either after the end of the first credit period, but before the second credit period, or after the second credit period if the retailer cannot pay off the unpaid balance at the end of the first credit period. Additionally, the delay will incur interest charges on the unpaid and overdue balance due to the difference between the interest earned and the interest charged. Consequently, the main purpose of this article is to characterize the optimal solution processes and (in accordance with the functional behavior of the cost function) to search for the optimal replenishment cycle time. Finally, numerical examples are given to illustrate the theoretical results which are proven in this article by means of mathematical solution procedures.

]]>Recently, Sanhan and Mongkolkeha introduced the concept of Berinde's cyclic contraction, and they established some results. Unfortunately, these results seem to be incorrect. In this paper, some counterexamples are given.

]]>Coevolution can impose density-dependent selection through reciprocal biotic interactions on the fitness of involved species, driving directional and disruptive trait evolution and rich evolutionary possibilities. Coevolution has since Darwin been considered a potential path leading to adaptive diversification that could explain the emergence of ecological networks of biotic interactions that harbour multiple interacting species (eg, pollination networks and food webs). Here, we present adaptive dynamics, a powerful tool of evolutionary invasion analysis that explores how quantitative traits undergo incremental evolution, to exploring the emergence of multi-species networks through coevolution. Specifically, we exemplify the feasibility of using adaptive dynamics to investigate trait evolution in 4 ecological networks, driven, respectively, by resource competition, trophic interactions, as well as bipartite mutualistic and antagonistic interactions. We use a set of ordinary differential equations to describe, at different paces, the population dynamics and trait dynamics of involved species assemblages. Through computing ecological equilibrium, invasion fitness, selection gradient and evolutionary singularity, and testing for evolutionary stability and the coexistence criterion of mutual invasibility, we illustrate the typical evolutionary dynamics and the criteria of evolutionary stability and branching in these ecological networks. Results highlight the importance of the form of trait-mediated interaction kernel (ie, interaction strength as a function of trait difference) to adaptive diversification in these coevolutionary systems. We conclude by advocating that biotic interactions between two species can indeed lead to diffuse and even escape-and-radiate coevolution, making the emerged ecological networks an ideal model for studying complex adaptive systems.

]]>Here, a system of 3 wave equations in
with infinite memories acting in the first 2 equations is considered. Using weighted spaces, we prove the polynomial stability of the system under some conditions on *μ*_{1},*μ*_{2}, and *ϕ* as
.

In this paper, we consider a viscoelastic equation with minimal conditions on the
relaxation function *g*, namely,
, where *H* is an increasing and convex function near the origin and *ξ* is a nonincreasing function. With only these very general assumptions on the behavior of *g*at infinity, we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial rates when *H*(*s*)=*s*^{p} and *p* covers the full admissible range [1,2). We get the best decay rates expected under this level of generality, and our new results substantially improve several earlier related results in the literature.

The triple conformal geometric algebra (TCGA) for the Euclidean
-plane extends CGA as the product of 3 orthogonal CGAs and thereby the representation of geometric entities to general cubic plane curves and certain cyclidic (or roulette) quartic, quintic, and sextic plane curves. The plane curve entities are 3-vectors that linearize the representation of nonlinear curves, and the entities are inner product null spaces with respect to all points on the represented curves. Each inner product null space entity also has a dual geometric outer product null space form. Orthogonal or conformal (angle preserving) operations (as versors) are valid on all TCGA entities for inversions in circles, reflections in lines, and by compositions thereof, isotropic dilations from a given center point, translations, and rotations around arbitrary points in the plane. A further dimensional extension of TCGA also provides a method for anisotropic dilations. Intersections of any TCGA entity with a point, point pair, line, or circle are possible. The TCGA defines commutator-based differential operators in the coordinate directions that can be combined to yield a general **n**-directional derivative.

We discuss minimality conditions for the speed of monotone travelling waves in a sample of smectic C^{∗} liquid crystal subject to a constant electric field, dealing with both isotropic and anisotropic cases. Such conditions are important in understanding the properties of domain wall switching across a smectic layer, and our focus here is on examining how the presence of anisotropy can affect the speed of this switching. We obtain an estimate of the influence of anisotropy on the minimal speed, sufficient conditions for linear and non-linear minimal speed selection mechanisms to hold in different parameter regimes, and a characterisation of the boundary separating the linear and non-linear regimes in parameter space.

In this paper, we obtained some useful estimates for convolution corresponding to Kontorovich-Lebedev transform (KL-transform) in Lebesgue space. Some continuity theorems for translation, convolution, and KL-transform in test function space are discussed. Then an integral representation of pseudodifferential operator involving KL-transform is found out, and its estimates in Lebesgue space is obtained. At the end, some applications of KL-transform and its convolution are discussed.

]]>The aim of this paper was to study the junction between a periodic family of beams and two thin plates. This structure depends on 3 small parameters. We use the decompositions of the displacement fields in every beam and plate to obtain a priori estimates. Then in the case for which the displacements of both plates match, we derive the asymptotic behavior of this structure.

]]>We study the Cauchy problem of the 3-dimensional nonhomogeneous heat conducting Navier-Stokes equations with nonnegative density. First of all, we show that for the initial density allowing vacuum, the strong solution to the problem exists globally if the velocity satisfies the Serrin's condition. Then, under some smallness condition, we prove that there is a unique global strong solution to the 3D viscous nonhomogeneous heat conducting Navier-Stokes flows. Our method relies upon the delicate energy estimates.

]]>An efficient method for nonlinear fractional differential equations is proposed in this paper. This method consists of 2 steps. First, we linearize the nonlinear operator equation by quasi-Newton's method, which is based on *Fréchet derivative*. Then we solve the linear fractional differential equations by the simplified reproducing kernel method. The convergence of the quasi-Newton's method is discussed for the general nonlinear case as well. Finally, some numerical examples are presented to illustrate accuracy, efficiency, and simplicity of the method.

In this work, we develop a new integrable equation by combining the KdV equation and the negative-order KdV equation. We use concurrently the KdV recursion operator and the inverse KdV recursion operator to construct this new integrable equation. We show that this equation nicely passes the Painlevé test. As a result, multiple soliton solutions and other soliton and periodic solutions are guaranteed and formally derived.

]]>We consider the undamped Klein-Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions. For any real value of the initial energy, particularly for supercritical values of the energy, we give sufficient conditions to conclude blow-up in finite time of weak solutions. The success of the analysis is based on a detailed analysis of a differential inequality. Our results improve previous ones in the literature.

]]>In this paper, we consider the time-periodic solution to a simplified version of Ericksen-Leslie equations modeling the compressible hydrodynamic flow of nematic liquid crystals with a time-periodic external force in a periodic domain in . By using an approach of parabolic regularization and combining with the topology degree theory, we establish the existence of the time-periodic solution to the model under some smallness and symmetry assumptions on the external force. Then, we give the uniqueness of the periodic solution of this model.

]]>Quaternion analytic signal is regarded as a generalization of analytic signal from 1D to 4D space. It is defined by an original signal with its quaternion partial and total Hilbert transforms. The quaternion analytic signal provides the signal features representation, such as the local amplitude and local phase angle, the latter includes the structural information of the original signal. The aim of the present study is twofold. Firstly, it attempts to analyze the Plemelj-Sokhotzkis formula associated with quaternion Fourier transform and quaternion linear canonical transform. With these formulae, we show that the quaternion analytic signals are the boundary values of quaternion Hardy functions in the upper half space of 2 complex variables space. Secondly, the quaternion analytic signal can be extended to the quaternion Hardy function in the upper half space of 2 complex variables space. Two novel types of phase-based edge detectors are proposed, namely, quaternion differential phase angle and quaternion differential phase congruency methods. In terms of peak signal-to-noise ratio and structural similarity index measure, comparisons with competing methods on real-world images consistently show the superiority of the proposed methods.

]]>In this paper, we consider the integration of the special second-order initial value problem. Hybrid Numerov methods are used, which are constructed in the sense of Runge-Kutta ones. Thus, the Taylor expansions at the internal points are matched properly in the final expression. A new family of such methods attaining eighth algebraic order is given at a cost of only 7 function evaluations per step. The new family provides us with an extra parameter, which is used to increase phase-lag order to 18. We proceed with numerical tests over a standard set of problems for these cases. Appendices implementing the symbolic construction of the methods and derivation of their coefficients are also given.

]]>Precomputed radiance transfer (PRT) methods established for handling global illumination (GI) of objects from area lights in real time and many techniques proposed for rotating the light using linear algebra rotation matrices. Rotating area lights efficiently are crucial part for computer graphics since it is one of the main components of real-time rendering. Matrices commonly used for handling such rotations are not quite efficient and require high memory consumption; as a result, the need for proposing new more efficient rotation algorithms has been established. In this work, we use the conformal geometric algebra (CGA) as the mathematical background for “GI in real-time” under distant Image-based lighting (IBL) illumination, for diffuse surfaces with self-shadowing by efficiently rotating the environment light using CGA entities. Our work is based on spherical harmonics (SH), which are used for approximating natural, area-light illumination as irradiance maps. Our main novelty is that we extend the PRT algorithm by representing SH for the first time with CGA.The main intuition is that SH of band index 1 are represented using CGA entities and SH with band index larger than 1 are represented in terms of CGA-SH of band 1. Specifically, we propose a new method for representing SH with CGA entities and rotating SH by rotating CGA entities. In this way, we can visualize the SH rotations, rotate them faster than rotation matrices, and we provide a unique visual representation and intuition regarding their rotation, in stark contrast to usual rotation matrices, and we achieve consistently better visual results from Ivanic rotation matrices during light rotation. Via our CGA expressed SH, we provide a significant boost on the PRT algorithm since we represent SH rotations by CGA rotors (4 numbers) as opposed to 9 × 9 sparse matrices that are usually used. With our algorithm, we pave the way for including scaling (dilation) and translation of light coefficients using CGA motors.

]]>The nonlinear versions of Sturm-Picone comparison theorem as well as Leighton's variational lemma and Leighton's theorem for regular and singular nonlinear impulsive differential equations with discontinuous solutions having fixed moments of impulse actions are established. Although discontinuity of the solutions causes some difficulties, these new comparison theorems cover the old ones where impulse effects are dropped.

]]>The self-adaptive intelligence gray predictive model (SAIGM) has an alterable-flexible model structure, and it can build a dynamic structure to fit different external environments by adjusting the parameter values of SAIGM. However, the order number of the raw SAIGM model is not optimal, which is an integer. For this, a new SAIGM model with the fractional order accumulating operator (SAIGM_FO) was proposed in this paper. Specifically, the final restored expression of SAIGM_FO was deduced in detail, and the parameter estimation method of SAIGM_FO was studied. After that, the Particle Swarm Optimization algorithm was used to optimize the order number of SAIGM_FO, and some steps were provided. Finally, the SAIGM_FO model was applied to simulate China's electricity consumption from 2001 to 2008 and forecast it during 2009 to 2015, and the mean relative simulation and prediction percentage errors of the new model were only 0.860% and 2.661%, in comparison with the ones obtained from the raw SAIGM model, the GM(1, 1) model with the optimal fractional order accumulating operator and the GM(1, 1) model, which were (1.201%, 5.321%), (1.356%, 3.324%), and (2.013%, 23.944%), respectively. The findings showed both the simulation and the prediction performance of the proposed SAIGM_FO model were the best among the 4 models.

]]>In this paper, a model for the spread of tuberculosis between buffaloes and lions is presented and analyzed. The most important system parameters are identified: vertical and horizontal disease transmission among the buffaloes and the influence of intraspecific competition between healthy and diseased buffaloes on the infected buffaloes population. Removal of diseased prey appears to be the most effective strategy to render the ecosystem disease free.

]]>In this paper, the 2D Navier-Stokes-Voight equations with 3 delays in
is considered. By using the Faedo-Galerkin method, Lions-Aubin lemma, and Arzelà-Ascoli theorem, we establish the global well-posedness of solutions and the existence of pullback attractors in *H*^{1}.

This paper deals with the oscillation of the fourth-order linear delay differential equation with a negative middle term under the assumption that all solutions of the auxiliary third-order differential equation are nonoscillatory. Examples are included to illustrate the importance of results obtained.

]]>We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero-Hopf equilibrium. This study is done using the averaging theory of second order.

]]>In living cells, we can observe a variety of complex network systems such as metabolic network. Studying their sensitivity is one of the main approaches for understanding the dynamics of these biological systems. The study of the sensitivity is done by increasing/decreasing, or knocking out separately, each enzyme mediating a reaction in the system and then observing the responses in the concentrations of chemicals or their fluxes. However, because of the complexity of the systems, it has been unclear how the network structures influence/determine the responses of the systems. In this study, we focus on monomolecular networks at steady state and establish a simple criterion for determining regions of influence when any one of the reaction rates is perturbed through sensitivity experiments of enzyme knock-out type. Specifically, we study the network response to perturbations of a reaction rate *j*^{∗} and describe which other reaction rates
respond by non-zero reaction flux, at steady state. Non-zero responses of
to *j*^{∗} are called flux-influence of *j*^{∗} on
. The main and most important aspect of this analysis lies in the reaction graph approach, in which the chemical reaction networks are modelled by a directed graph. Our whole analysis is function-free, ie, in particular, our approach allows a graph theoretical description of sensitivity of chemical reaction networks. We emphasize that the analysis does not require numerical input but is based on the graph structure only. Our specific goal here is to address a topological characterization of the flux-influence relation in the network. In fact we characterize and describe the whole set of reactions influenced by a perturbation of any specific reaction.

We consider a Cahn-Hilliard–type equation with degenerate mobility and single-well potential of Lennard-Jones type. This equation models the evolution and growth of biological cells such as solid tumors. The degeneracy set of the mobility and the singularity set of the cellular potential do not coincide, and the absence of cells is an unstable equilibrium configuration of the potential. This feature introduces a nontrivial difference with respect to the Cahn-Hilliard equation analyzed in the literature. We give existence results for different classes of weak solutions. Moreover, we formulate a continuous finite element approximation of the problem, where the positivity of the solution is enforced through a discrete variational inequality. We prove the existence and uniqueness of the discrete solution for any spatial dimension together with the convergence to the weak solution for spatial dimension *d*=1. We present simulation results in 1 and 2 space dimensions. We also study the dynamics of the spinodal decomposition and the growth and scaling laws of phase ordering dynamics. In this case, we find similar results to the ones obtained in standard phase ordering dynamics and we highlight the fact that the asymptotic behavior of the solution is dominated by the mechanism of growth by bulk diffusion.

In this note, we study and explore locally symmetric *f*−associated standard static spacetimes *I*_{f}×*M*. Necessary and sufficient conditions on *f*−associated standard static spacetimes to be locally symmetric are derived. Some implications for these conditions are considered.

In this paper we consider a periodic 2-dimensional quasi-geostrophic equations with subcritical dissipation. We show the global existence and uniqueness of the solution for small initial data in the Lei-Lin-Gevrey spaces . Moreover, we establish an exponential type explosion in finite time of this solution.

]]>This paper deals with an adaptation of the Poincaré-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.

]]>Human immunodeficiency virus (HIV)/AIDS and cancer coexistence both in vivo and in vitro in a cancer-immune environment leads to specific cytokines being produced by various immune cells and the cancer cells. Most of the studies have suggested that specific cytokines produced by the immune system cells and the tumor play an important role in the dynamics of non-Hodgkin lymphomas (NHLs). In this paper, a mathematical model describing the NHL-immune system interaction in the presence of the HIV, HIV treatment, and chemotherapy is developed. The formulated model, described by nonlinear ODEs, shows existence of multiple equilibria whose stability and bifurcation analysis are presented. From the bifurcation analysis, bistability regions are evident. We observe that with and without HIV treatment, the system results in a nonaggressive tumor size or aggressive tumor (full-blown tumor) depending on the initial conditions. The results further suggest that at a low endemic state, patients can live for longer period with the tumor, which might explain why some patients can live with cancer for many years. However, initiation of HIV treatment in patients with NHL is observed to lower these endemic states of the tumor. Our results explain why late initiation of HIV treatment might not be helpful to NHL patients. We further investigated the effect of chemotherapy on the dynamics of the tumor. Our simulation results might explain why a few of these chemotherapeutic drugs are more effective when given at a slow continuous rate. The model provides a unique opportunity to influence policy on HIV-related cancer treatment and management.

]]>In this article, we consider the Cauchy problem to Keller-Segel equations coupled to the incompressible Navier-Stokes equations. Using the Fourier frequency localization and the Bony paraproduct decomposition, let *u*_{F}:=*e*^{tΔ}*u*_{0}; we prove that there exist 2 positive constants *σ*_{0} and *C*_{0} such that if the gravitational potential
and the initial data (*u*_{0},*n*_{0},*c*_{0}) satisfy

for some *p*,*q* with
and
, then the global solutions can be established in critical Besov spaces.

In this paper, we study constraint minimizers of the following *L*^{2}−critical minimization problem:

where *E*(*u*) is the Schrödinger-Poisson-Slater functional

and *N* denotes the mass of the particles in the Schrödinger-Poisson-Slater system. We prove that *e*(*N*) admits minimizers for
and, however, no minimizers for *N*>*N*^{∗}, where *Q*(*x*) is the unique positive solution of
in
. Some results on the existence and nonexistence of minimizers for *e*(*N*^{∗}) are also established. Further, when *e*(*N*^{∗}) does not admit minimizers, the limit behavior of minimizers as *N*↗*N*^{∗} is also analyzed rigorously.

The determination of a space-dependent source term along with the solution for a 1-dimensional time fractional diffusion equation with nonlocal boundary conditions involving a parameter *β*>0 is considered. The fractional derivative is generalization of the Riemann-Liouville and Caputo fractional derivatives usually known as Hilfer fractional derivative. We proved existence and uniqueness results for the solution of the inverse problem while over-specified datum at 2 different time is given. The over-specified datum at 2 time allows us to avoid initial condition in terms of fractional integral associated with Hilfer fractional derivative.

We investigate the uniform regularity and vanishing viscosity limit for the incompressible chemotaxis-Navier-Stokes system with Navier boundary condition for velocity field and Neumann boundary condition for cell density and chemical concentration in a 3D bounded domain. It is shown that there exists a unique strong solution of the incompressible chemotaxis-Navier-Stokes system in a finite time interval, which is independent of the viscosity coefficient. Moreover, this solution is uniformly bounded in a conormal Sobolev space, which allows us to take the vanishing viscosity limit to obtain the incompressible chemotaxis-Euler system.

]]>Growth models are often used when modelling various processes in life sciences, ecology, demography, social sciences, etc. Dynamical growth models are usually formulated in terms of an ODE (system of ODS's) or by an explicit solution to an ODE, such as the logistic, Gompertz, and Richardson growth models. To choose a suitable growth model it is useful to know the physics-chemical meaning of the model. In many situations this meaning is best expressed by means of a reaction network that possibly induces the dynamical growth model via mass action kinetics. Such reaction networks are well known for a number of growth models, such as the saturation-decay and the logistic Verhulst models. However, no such reaction networks exist for the Gompertz growth model. In this work we propose some reaction networks using mass action kinetics that induce growth models that are (in certain sense) close to the Gompertz model. The discussion of these reaction networks aims to a better understanding of the chemical properties of the Gompertz model and “Gompertzian-type” growth models. Our method can be considered as an extension of the work of previous authors who “recasted” the Gompertz differential equation into a dynamical system of two differential equations that, apart of the basic species variable, involve an additional variable that can be interpreted as a “resource.” Two new growth models based on mass action kinetics are introduced and studied in comparison with the Gompertz model. Numerical computations are presented using some specialized software tools.

]]>No abstract is available for this article.

]]>Ren and Zeng (2013) introduced a new kind of *q*-Bernstein–Schurer operators and studied some approximation properties. Acu *et al*. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using *q*-Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's *K*-functional. Next, we introduce the bivariate case of *q*-Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's *K*-functional. Finally, we define the generalized Boolean sum operators of the *q*-Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.

In earlier literature, a version of a classical three-species food chain model, with modified Holling type IV functional response, is proposed. Results on the global boundedness of solutions to the model system under certain parametric restrictions are derived, and chaotic dynamics is shown. We prove that in fact the model possesses explosive instability, and solutions can explode/blow up in finite time, for certain initial conditions, even under the parametric restrictions of the literature. Furthermore, we derive the Hopf bifurcation criterion, route to chaos, and Turing bifurcation in case of the spatially explicit model. Lastly, we propose, analyze, and simulate a version of the model, incorporating gestation effect, via an appropriate time delay. The delayed model is shown to possess globally bounded solutions, for any initial condition. Copyright © 2017 John Wiley & Sons, Ltd.

]]>This paper is devoted to the existence of positive solutions for a fourth-order impulsive boundary value problem with integral boundary conditions on time scales. Existence results of at least two and three positive solutions are established via the double fixed point theorem and six functionals fixed point theorem, respectively. Also, an example is given to illustrate the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this work successive differentiation method is applied to solve highly nonlinear partial differential equations (PDEs) such as Benjamin–Bona–Mahony equation, Burger's equation, Fornberg–Whitham equation, and Gardner equation. To show the efficacy of this new technique, figures have been incorporated to compare exact solution and results of this method. Wave variable is used to convert the highly nonlinear PDE into ordinary differential equation with order reduction. Then successive differentiation method is utilized to obtain the numerical solution of considered PDEs in this paper. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, a time-fractional diffusion equation with singular source term is considered. The Caputo fractional derivative with order 0<*α*⩽1 is applied to the temporal variable. Under specific initial and boundary conditions, we find that the time-fractional diffusion equation presents quenching solution that is not globally well-defined as time goes to infinity. The quenching time is estimated by using the eigenfunction of linear fractional diffusion equation. Moreover, by implementing a finite difference scheme, we give some numerical simulations to demonstrate the theoretical analysis. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we establish global existence of strong solutions to the 3D incompressible two-fluid MHD equations with small initial data. In addition, the explicit convergence rate of strong solutions from the two-fluid MHD equations to the Hall-MHD equations is obtained as . Copyright © 2017 John Wiley & Sons, Ltd.

]]>This work provides sufficient conditions for the existence of homoclinic solutions of fourth-order nonlinear ordinary differential equations. Using Green's functions, we formulate a new modified integral equation that is equivalent to the original nonlinear equation. In an adequate function space, the corresponding nonlinear integral operator is compact, and it is proved an existence result by Schauder's fixed point theorem. Copyright © 2017 John Wiley & Sons, Ltd.

]]>This paper presents a method for computing numerical solutions of two-dimensional Stratonovich Volterra integral equations using one-dimensional modification of hat functions and two-dimensional modification of hat functions. The problem is transformed to a linear system of algebraic equations using the operational matrix associated with one-dimensional modification of hat functions and two-dimensional modification of hat functions. The error analysis of the method is given. The method is computationally attractive, and applications are demonstrated by a numerical example. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, we have studied a prey–predator model living in a habitat that divided into two regions: an unreserved region and a reserved (refuge) region. The migration between these two regions is allowed. The interaction between unreserved prey and predator is Crowley–Martin-type functional response. The local and global stability of the system is discussed. Further, the system is extended to incorporate the effect of time delay. Then the dynamical behavior of the system is analyzed, taking delay as a bifurcation parameter. The direction of Hopf bifurcation and the stability of the bifurcated periodic solution are determined with the help of normal form theory and centre manifold theorem. We have also discussed the influence of prey refuge on densities of prey and predator species. The analytical results are supplemented with numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd.

]]>We study Hankel transform of the sequences (*u*,*l*,*d*),*t*, and the classical Motzkin numbers. Using the method based on orthogonal polynomials, we give closed-form evaluations of the Hankel transform of the aforementioned sequences, sums of two consecutive, and shifted sequences. We also show that these sequences satisfy some interesting convolutional properties. Finally, we partially consider the Hankel transform evaluation of the sums of two consecutive shifted (*u*,*l*,*d*)-Motzkin numbers. Copyright © 2017 John Wiley & Sons, Ltd.

This paper is addressed to a study of the persistent regional null controllability problems for one-dimensional linear degenerate wave equations through a distributed controller. Different from non-degenerate wave equations, the classical null controllability results do not hold for some degenerate wave equations. Thus, persistent regional null controllability is introduced, which means finding a control such that the corresponding state of the degenerate wave equation may vanish in a suitable subset of the space domain in a period of time. In order to solve this problem, we need to establish the regional null controllability for degenerate wave equations. This problem is reduced to a suitable observability problem of a linear degenerate wave equation. The key point is to choose a suitable multiplier in order to establish this observability inequality. 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.

]]>Both numerical and asymptotic analyses are performed to study the similarity solutions of three-dimensional boundary-layer viscous stagnation point flow in the presence of a uniform magnetic field. The three-dimensional boundary-layer is analyzed in a non-axisymmetric stagnation point flow, in which the flow is developed because of influence of both applied magnetic field and external mainstream flow. Two approaches for the governing equations are employed: the Keller-box numerical simulations solving full nonlinear coupled system and a corresponding linearized system that is obtained under a far-field behavior and in the limit of large shear-to-strain-rate parameter (*λ*). From these two approaches, the flow phenomena reveals a rich structure of new family of solutions for various values of the magnetic number and *λ*. The various results for the wall stresses and the displacement thicknesses are presented along with some velocity profiles in both directions. The analysis discovered that the flow separation occurs in the secondary flow direction in the absence of magnetic field, and the flow separation disappears when the applied magnetic field is increased. The flow field is divided into a near-field (due to viscous forces) and far-field (due to mainstream flows), and the velocity profiles form because of an interaction between two regions. The magnetic field plays an important role in reducing the thickness of the boundary-layer. A physical explanation for all observed phenomena is discussed. Copyright © 2017 John Wiley & Sons, Ltd.

Calgero–Bogoyavlenskii–Schiff (CBS) equation is analytically solved through two successive reductions into an ordinary differential equation (ODE) through a set of optimal Lie vectors. During the second reduction step, CBS equation is reduced using hidden vectors. The resulting ODE is then analytically solved through the singular manifold method in three steps; First, a Bäcklund truncated series is obtained. Second, this series is inserted into the ODE, and finally, a seminal analysis leads to a Schwarzian differential equation in the eigenfunction *φ*(*η*). Solving this differential equation leads to new analytical solutions. Then, through two backward substitution steps, the original dependent variable is recovered. The obtained results are plotted for several Lie hidden vectors and compared with previous work on CBS equation using Lie transformations. Copyright © 2017 John Wiley & Sons, Ltd.

We consider general virus dynamics model with virus-to-target and infected-to-target infections. The model is incorporated by intracellular discrete or distributed time delays. We assume that the virus-target and infected-target incidences, the production, and clearance rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The non-negativity and boundedness of the solutions are studied. The existence and stability of the equilibria are determined by a threshold parameter. We use suitable Lyapunov functionals and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd.

]]>We are concerned with the identification and reconstruction of the coefficients of a linear parabolic system from finite time observations of the solution on the boundary. We present two procedures depending on whether the spectrum of the system is simple or multiple. Copyright © 2017 John Wiley & Sons, Ltd.

]]>The present contribution focuses on the estimation of the geometric acceleration and of the geometric jolt (namely, the derivative of the acceleration) of a multidimensional, structured gyroscopic signal. A gyroscopic signal encodes the instantaneous orientation of a rigid body during a full three-dimensional rotation that is regarded as a trajectory in the curved space SO(3) of the special orthogonal matrices. The geometric acceleration and jolt associated to a gyroscopic signal are evaluated through the rules of calculus prescribed by differential geometry. Such an endeavor is motivated by recent studies on the smoothness of human body movement in biomechanical engineering, sports science, and rehabilitation neuroengineering. Two indexes of smoothness are compared, namely, a normalized proper geometric acceleration index and a normalized proper geometric jolt index. Our investigation concludes that, in the considered experiments with measured signals, for relatively low values of the acceleration and of the jolt indexes, such indexes are strongly positively correlated. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, we present the approximate solution of damped Boussinesq equation using extended Raviart–Thomas mixed finite element method. In this method, the numerical solution of this equation is obtained using triangular meshes. Also, for discretization in time direction, we use an implicit finite difference scheme. In addition, error estimation and stability analysis of both methods are shown. Finally, some numerical examples are considered to confirm the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, we investigate the vanishing viscosity limit for the 3D nonhomogeneous incompressible Navier–Stokes equations with a slip boundary condition. We establish the local well-posedness of the strong solutions for initial boundary value problems for such systems. Furthermore, the vanishing viscosity limit process is established, and a strong rate of convergence is obtained as the boundary of the domain is flat. In addition, it is needed to add some additional condition for density to match well the boundary condition. Copyright © 2017 John Wiley & Sons, Ltd.

]]>This paper studies the time-averaged energy dissipation rate ⟨*ε*_{SMD}(*u*)⟩ for the combination of the Smagorinsky model and damping function. The Smagorinsky model is well known to over-damp. One common correction is to include damping functions that reduce the effects of model viscosity near walls. Mathematical analysis is given here that allows evaluation of ⟨*ε*_{SMD}(*u*)⟩ for any damping function. Moreover, the analysis motivates a modified van Driest damping. It is proven that the combination of the Smagorinsky with this modified damping function does not over-dissipate and is also consistent with Kolmogorov phenomenology. Copyright © 2017 John Wiley & Sons, Ltd.

The Riesz probability distribution on any symmetric cone and, in particular, on the cone of positive definite symmetric matrices represents an important generalization of the Wishart and of the matrix gamma distributions containing them as particular examples. The present paper is a continuation of the investigation of the properties of this probability distribution. We first establish a property of invariance of this probability distributions by a subgroup of the orthogonal group. We then show that the Pierce components of a Riesz random variable are independent, and we determine their probability distributions. Some moments and some useful expectations related to the Riesz probability distribution are also calculated. Copyright © 2017 John Wiley & Sons, Ltd.

]]>We consider the Calderón problem in an infinite cylindrical domain, whose cross section is a bounded domain of the plane. We prove log–log stability in the determination of the isotropic periodic conductivity coefficient from partial Dirichlet data and partial Neumann boundary observations of the solution. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, we study a reaction-diffusion equation where nonlinear memory and concentration effects are considered at the same time. We are specially concerned with the local solvability of this problem for singular initial data in Lebesgue spaces. We also analyze the vanishing concentration problem and prove a blow-up alternative. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, we study a model of hematopoiesis with time-varying delays and discontinuous harvesting, which is described by a nonsmooth dynamical system. Based on a newly developed method, nonsmooth analysis, and the generalized Lyapunov method, some new delay-dependent criteria are established to ensure the existence and global exponential stability of positive periodic solutions. Moreover, an example with numerical simulations is presented to demonstrate the effectiveness of theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, we investigate a backward problem for a space-fractional partial differential equation. The main purpose is to propose a modified regularization method for the inverse problem. The existence and the uniqueness for the modified regularized solution are proved. To derive the gradient of the optimization functional, the variational adjoint method is introduced, and hence, the unknown initial value is reconstructed. Finally, numerical examples are provided to show the effectiveness of the proposed algorithm. Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, we consider the almost periodic dynamics of an impulsive multispecies Lotka–Volterra competition system with time delays on time scales. By establishing some comparison theorems of dynamic equations with impulses and delays on time scales, a permanence result for the model is obtained. Furthermore, based on the permanence result, by studying the Lyapunov stability theory of impulsive dynamic equations on time scales, we establish the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results, and our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new even if for both the case of the time scale and the case of the time scale . Copyright © 2017 John Wiley & Sons, Ltd.

]]>In this paper, we use the domain decomposition method to prove well-posedness and smoothness results in anisotropic weighted Sobolev spaces for a multidimensional high-order parabolic equation set in conical time-dependent domains of . Copyright © 2017 John Wiley & Sons, Ltd.

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