A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density ̺ and temperature T . In the dilute regime, i.e., when a̺ ≪ 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2̺−[̺−̺c]+). Here, ̺c(T ) denotes the critical density for Bose-Ein...

a variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. This class of codes is applied to speed up the decoding process, for the decoder can decode from both sides of the compressed file simultaneously. In this paper, we study some basic properties of fix-free codes. We prove a sufficient and a necessary condition for the existence of fix-free cod...

Let M be a commutative cancellative atomic monoid. We use unions of sets of lengths in M to construct the V-Delta set of M . We first derive some basic properties of V-Delta sets and then show how they offer a method to investigate the asymptotic behavior of the sizes of unions of sets of lengths. A central focus of number theory is the study of number theoretic functions and their asymptotic b...

A (variable-length) code is a free subset of a free monoid; more formally, it is the basis of some free submonoid. The theory of these codes (not to be confused with error-detecting codes) was first developed by M.P. Schiitzenberger. A major problem in this theory is to factorize codes, that is, considering the characteristic formal power series of a code (in the noncommutat ive formal power se...

Stochastic categorial grammars (SCGs) are introduced as a more appropriate formalism for statistical language learners to est imate than stochastic context free grammars. As a vehicle for demonstrating SCG estimation, we show, in terms of crossing rates and in coverage, that when training material is limited, SCG estimation using the Minimum Description Length Principle is preferable to SCG est...