A new Multiscale Enrichment method based on the Partition of Unity (MEPU) method is presented. It is a synthesis of mathematical homogenization theory and the Partition of Unity method. Its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible. MEPU is perfectly suited for enriching the coarse scale...

The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is de ned by constant entropy increase. The Markov property of a quasi-free state is described by the representing block matrix. The proof is based on results on the statistical su ciency ...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

Notions of robust and " classical " states for an open quantum system are introduced and discussed in the framework of the isometric-sweeping decomposition of trace class operators. Using the predictability sieve proposed by Zurek, " quasi-classical " states are defined. A number of examples illustrating how the " quasi-classical " states correspond to classical points in phase space connected ...

Inconsistency handling in expressive description logics is an important problem because inconsistency may naturally occur in an open world. In this paper, we first present the quasi-classical semantics for description logic SHIQ, which is based on quasi-classical logic. We show that this semantics can be used to deal with inconsistency and that it is reduced to the standard semantics when there...

We examine the equilibrium properties of hot, dilute, non-relativistic plasmas. The partition function and density correlation functions of a classical plasma with several species are expressed in terms of a functional integral over electrostatic potential distributions. This is a convenient formulation for performing a well-defined perturbative expansion. The leading order, field-theoretic tre...