Quasi-interpolation is a important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain Πm = Πm(IR ) the d–variate polynomials of degree ≤ m. In particular, the reproduction of Πm leads to an approximation order of m + 1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the ...

An infinite f.g. group G is quasi-finitely axiomatizable (QFA) if there is a first-order sentence j such that G ! j, and if H is a f.g. group such that H ! j, then GGH. The first result is that all Baumslag–Solitar groups of the form ha; d j d"1ad 1⁄4 ai are QFA. A f.g. group G is a prime model if and only if there is a tuple g1; . . . ; gn generating G whose orbit (under the automorphisms of G...

In this paper, we consider various problems concerning quasi-matchings and semimatchings in bipartite graphs, which generalize the classical problem of determining a perfect matching in bipartite graphs. We prove a vast generalization of Hall’s marriage theorem, and present an algorithm that solves the problem of determining a lexicographically minimum g-quasi-matching (that is a set F of edges...

We present a general and simple procedure to construct quasi-interpolants in hierarchical spaces, which are composed of a hierarchy of nested spaces. The hierarchical quasi-interpolants are described in terms of the truncated hierarchical basis. Once for each level in the hierarchy a quasi-interpolant is selected in the corresponding space, the hierarchical quasi-interpolants are obtained witho...

We construct an example of a quasi-o-minimal group without the Exchange Property. A structure hM;<;:::i is called quasi-o-minimal 1] if in any structure elementarily equivalent to it the deenable subsets are exactly the Boolean combinations of 0-deenable subsets and intervals. A complete theory T is said to have the Exchange Property if, for any model M of T and for any X M and b; c 2 M, if b 2...