In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...

In this study, we present a numerical scheme to solve the drift-diffusion traffic flow model under the steady state. The drift-diffusion traffic flow model consists of a continuity equation and a nonlinear Poisson equation. The continuity equation describes the propagation of density along the road, and the Poisson equation describes the interaction among vehicles. The system equations cannot b...

In crash frequency studies, correlated multivariate data are often obtained for each roadway entity longitudinally. The multivariate models would be a potential useful method for analysis, since they can account for the correlation among the specific crash types. However, one issue that arises with this correlated multivariate data is the number of zero counts increases as crash counts have man...

In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis (this is well known), while the converse requires a dimension condition (which appears not to be known). We also provide examples illustrating the necessity of ...

On the local systems Hamiltonian in the weakly nonlocal Poisson brackets. Abstract We study in this work the important class of nonlocal Poisson Brackets (PB) which we call weakly nonlocal. They appeared recently in some investigations in the Soliton Theory. However there was no theory of such brackets except very special first order case. Even in this case the theory was not developed enough. ...

A smooth manifold M is endowed by a Poisson pair if two linearly independent bivectors c1, c2 are defined on M and moreover cλ = λ1c1+ λ2c2 is a Poisson bivector for any λ = (λ1, λ2) ∈ R 2. A bihamiltonian structure J = {cλ} is the whole 2-dimensional family of bivectors. The structure J (the pair (c1, c2)) is degenerate if rank cλ < dim M,λ ∈ R 2. The degenerate bihamiltonian structures play i...

where ρ is the mass density, S is the entropy density, and p is the pressure. It was shown in Morrison and Greene [1980] that this system, as well as its magnetohydrodynamic extension, admit a noncanonical Poisson formulation, that is, equation (1.1) can be written as ḟ = {f, h}, relative to a Hamiltonian function h. The study of the relativistic case was initiated in Bia lynicki-Birula, Hubbar...

A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson–Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson–Boltzmann equation is introduced as an auxiliary problem, making it possible to study the original nonlinear equation with delta distribution sources. A priori error estimates for the f...

In this paper we find a certain solution of Poisson type fractional differential equation using theory tensor product Banach spaces.