In [32, 31], fast deterministic algorithms based on spectral methods were derived for the Boltzmann collision operator for a class of interactions including the hard spheres model in dimension 3. These algorithms are implemented for the solution of the Boltzmann equation in dimension 2 and 3, first for homogeneous solutions, then for general non homogeneous solutions. The results are compared t...

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to new non-trivial constraints. This fact has been used to conjecture that the resulting models correspond to the spatially hom...

We study the mean dimension of the moduli space of Brody curves. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension. 1. Main results 1.1. Moduli space of Brody curves. M. Gromov introduced a remarkable notion of mean dimension in [6] (see also Lindenstrauss-Weiss [8] and Lindenstrauss [7]). In this paper we study the mean dimension of the modu...

If R is a commutative ring, then we prove that every finitely generated R-module has a pure-composition series with indecomposable cyclic factors and any two such series are isomorphic if and only if R is a Bézout ring and a CF-ring. When R is a such ring, the length of a pure-composition series of a finitely generated R-module M is compared with its Goldie dimension and we prove that these num...

A new worm eel (Ophichthidae, Myrophinae), Muraenichthys velinasalis, is described based on five specimens (97.9-281.0 mm of total length) collected from Taiwan, Philippines, northeastern Australia, Vanuatu, and Sri Lanka. Muranichthys velinasalis is most similar to M. philippinensis and M. schultzei in the position of the dorsal-fin origin behind a vertical through mid-anus, but can be easily ...

The intrinsic dimension (see, e.g., [29, 11]) has proven to be a suitable descriptor to distinguish between different kind of image structures such as edges, junctions or homogeneous image patches. In this paper, we will show that the intrinsic dimension is spanned by two axes: one axis represents the variance of the spectral energy and one represents the a weighted variance in orientation. Mor...