For any finitely generated torsion-free graded module over a polynomial ring, there exists a homogeneous ideal fitting into an exact sequence similar to a Bourbaki sequence even though its height is not restricted to two.

2 Regimes of 1D gases 2 2.1 Strongly versus weakly interacting regimes . . . . . . . . . . . . . . . . . . . . 4 2.2 Nearly ideal gas regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Quasi-condensate regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Density fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Phase fluc...

We study a simple one-dimensional model of ballisticaly-controlled annihilation in which the two annihilating species are initially spatially separated. The time dependent properties of the annihilation front are exactly derived. It is shown that the front wanders in a brownian fashion around its average value.

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA-->(m+k)A, nA-->(n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of nontrivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair and triplet processes.

Matrix theory and its applications make wide use of the eigenprojections of square matrices. The paper demonstrated that the eigenprojection of a matrix A can be calculated with the use of any annihilating polynomial for A, where u ≥ indA. This enables one to establish the components and the minimum polynomial of A, as well as the Drazin inverse A.