Let B be a generator of positivity preserving (shortly, positive) semi-group in L 2 on a space with-nite measure. It is supposed that the semigroup e ?tB ; t > 0; acts continuously from L 2 to L 1. For a measurable function V 0 an estimate for the number of negative eigenvalues of the operator B ? V is obtained, generalizing the similar estimate for the the Schrr odinger operator (the CLR-estim...

For a class of diffusion schemes not satisfying the property of positivity-preserving, we propose an enforcing positivity algorithm. It is locally conservative and easy to be implemented in existing codes. Moreover, this algorithm can be performed on both structured and unstructured meshes. Numerical experiments demonstrate that in terms of L2 error and conservation this algorithm is much bette...

In [19, 20, 22], we constructed uniformly high order accurate discontinuous Galerkin (DG) which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics. The technique also applies to high order accurate finite volume schemes. In this paper, we show an extension of this framework to construct positivity-preserving high order essentially non-oscillatory (E...

We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma self-gravitation modeling. The scheme is fully discrete structure preserving the sense it maintains a energy law, as well hyperbolic invariant domain properties, such positivity of density minimum principle specific entropy. A detailed discussion ...

We study ground state properties of the Kondo lattice model with an electron–phonon interaction. The is proved to be unique; in addition, total spin determined according structure. To prove assertions, extension method reflection positivity given terms order preserving operator inequalities.