by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

We study the class of quasi-alphabetic relations, i.e., tree transformations de ned by tree bimorphisms (';L; ) with '; quasi-alphabetic tree homomorphisms and L a regular tree language. We present a canonical representation of these relations; as an immediate consequence, we get the closure under union. Also, we show that they are not closed under intersection and complement, and do not preser...

For cardinals κ, λ,μ we let bκ,λ,μ be the smallest size of a subset B of λμ unbounded in the sense of ≤κ ; that is, such that there is no function f ∈ λμ such that {α < λ : g(α) > f (α)} has size less than κ for all g ∈ B. Similarly for dκ,λ,μ, the general dominating number, which is the smallest size of a subset B of λμ such that for every g ∈ λμ there is an f ∈ B such that the above set has s...

Two models are presented that compute a quasi-regular mapping. One was based on localist representations of items in the quasi-regular domain, the other was based on distributed representations. In each model, a control parameter termed input gain was modulated over the one and only level of representation that mapped inputs to outputs. Input gain caused both models to shift between regularityb...

We present some related families of orthogonal polynomials of a discrete variable and survey some of their applications in the study of (distance-regular) graphs and (completely regular) codes. One of the main peculiarities of such orthogonal systems is their non-standard normalization condition, requiring that the square norm of each polynomial must equal its value at a given point of the mesh...

Quasi-nearness biframes provide an asymmetric setting for the study of nearness; in [1] a completion (called a quasi-completion) was constructed for such structures and in [2] completeness was characterized in terms of the convergence of regular Cauchy bifilters. In this talk, questions of functoriality for this quasi-completion are considered and one sees that having enough regular Cauchy bifi...