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We investigate the structure of
travelling waves for a model of a fungal disease propagating over
a vineyard. This model is based on a set of ODEs of the SIR-type
coupled with two reaction-diffusion equations describing the
dispersal of the spores produced by the fungus inside and over the
vineyard. An estimate of the biological parameters in the model
suggests to use a singular perturbation analysis. It allows us to
compute the speed and the profile of the travelling waves. The
analytical results...
Due to wide range of interest in use of bio-economic models
to gain insight into the scientific management of renewable resources like
fisheries and forestry,variational iteration method (VIM) is employed to
approximate the solution of the ratio-dependent predator-prey system with
constant effort prey harvesting.The results are compared with the results
obtained by Adomian decomposition method and reveal that VIM is very
effective and convenient for solving nonlinear differential equations.
After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure...
In this article we discuss some issues related to Air Pollution modelling (as viewed by the authors): subgrid parametrization, multiphase modelling, reduction of high dimensional models and data assimilation. Numerical applications are given with POLAIR, a 3D numerical platform devoted to modelling of atmospheric trace species.
The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain D with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations...
Let be a strongly elliptic operator on a -dimensional manifold (polyhedra or boundaries of polyhedra are also allowed). An operator equation with stochastic data is considered. The goal of the computation is the mean field and higher moments , , , of the solution. We discretize the mean field problem using a FEM with hierarchical basis and degrees of freedom. We present a Monte-Carlo algorithm and a deterministic algorithm for the approximation of the moment for . The key tool...
We use the scale of Besov spaces , 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains ⊂ ℝ. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.
We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...
In this paper, we investigate the complex dynamics of a spatial plankton-fish system with
Holling type III functional responses. We have carried out the analytical study for both
one and two dimensional system in details and found out a condition for diffusive
instability of a locally stable equilibrium. Furthermore, we present a theoretical
analysis of processes of pattern formation that involves organism distribution and their
interaction of spatially...
For an SI type endemic model with one host and two parasite strains, we study the
stability of the endemic coexistence equilibrium, where the host and both parasite strains
are present. Our model, which is a system of three ordinary differential equations,
assumes complete cross-protection between the parasite strains and reduced fertility and
increased mortality of infected hosts. It also assumes that one parasite strain is
exclusively vertically...
Stable hypothesis are hypothesis that may refer either for the fixed part or for the random part of the model. We will consider such hypothesis for models with balanced cross-nesting. Generalized F tests will be derived. It will be shown how to use Monte-Carlo methods to evaluate p-values for those tests.
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