The ring decomposition technique of part I is extended to the case when the factors in the direct product decomposition are no longer fields but arbitrary chain rings. This includes not only the case of quasi-cyclic codes over rings but also the case of quasi-cyclic codes over fields whose co-index is no longer prime to the characteristic of the field. A new quaternary construction of the Leech...

We provide a method for constructing a class of multivariate copulas depending on a univariate function. We study some properties of this class and present several examples. The same circle of ideas is used in a similar construction of quasi–copulas.

We introduce the notion of a standard system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for a finite dimensional algebra to be quasi-hereditary is the existence of a full and divisible standard system. As a further application, we obtain a sufficient condition for a standardly stratified algebra. To Roger Carter on his 65th birthday

In this paper, we investigate approximation of quasi-projection operators in Besov spaces B p,q, μ > 0, 1 ≤ p, q ≤ ∞. Suppose I is a countable index set. Let (φi)i∈I be a family of functions in Lp(IR), and let (φ̃i)i∈I be a family of functions in Lp̃(IR), where 1/p+ 1/p̃ = 1. Let Q be the quasi-projection operator given by

A set is said to be amorphous if it is innnite, but cannot be written as the disjoint union of two innnite sets. The possible structures which an amorphous set can carry were discussed in 5]. Here we study an analogous notion at the next level up, that is to say replacing nite/innnite by countable/uncountable, saying that a set is quasi-amorphous if it is uncountable, but is not the disjoint un...

In this paper we provide an overview of recent developments in the methodology for the construction of composite coincident and leading indexes, and apply them to the UK. In particular, we evaluate the relative merits of factor based models and Markov switching specifications for the construction of coincident and leading indexes. For the leading indexes we also evaluate the performance of prob...