Closed ideals in A(G) with bounded approximate identities are characterized for amenable [SIN]-groups and arbitrary discrete groups. This extends a result of Liu, van Rooij and Wang for abelian groups.

Some oscillation criteria for solutions of a general second order ordinary superlinear differential equation with alternating coefficients are given. The results generalize and complement some existing results in the literature.

This paper is concerned with a new notion of coherency for monoids. A monoid S is right coherent if the first order theory of right S-sets is coherent; this is equivalent to the property that every finitely generated S-subset of every finitely presented right S-set is finitely presented. If every finitely generated right ideal of S is finitely presented we say that S is weakly right coherent. As for the corresponding situation for modules over a ring, we show that our notion of coherency is related to products of flat left S-sets, although there are some marked differences in behaviour from the case for rings. Further, we relate our work to ultraproducts of flat left S-sets and so to the question of axiomatisability of certain classes of left S-sets.

We show that a monoid S is weakly right coherent if and only if the right annihilator congruence of every element is finitely generated and the intersection of any two finitely generated right ideals is finitely generated. A similar result describes right coherent monoids. We use these descriptions to recognise several classes of (weakly) right coherent monoids. In particular we show that any free monoid is weakly right (and left) coherent and any free commutative monoid is right (and left) coherent.

Soit D I'opérateur de Laplace-Beltrami sur le bi-disque. On démontre que les fonctions ζ → Plgr; (ζ, u) provenant du noyau de Poisson associé au bi-disque sont les seules solutions réelles normalisées du système. qui satisfont une certaine hypothèse.

Three differently defined classes of two-symbol sequences, which we call the two-distance sequences, the linear sequences and the characteristic sequences, have been discussed by a number of authors and some equivalences between them are known. We present a self-contained proof that the three classes are the same (when ambiguous cases of linear sequences are suitably in terpreted). Associated with each sequence is a real invariant (having a different appropriate definition for each of the three classes). We give results on the relation between sequences with the same invariant and on the symmetry of the sequences. The sequences are closely related to Beatty sequences and occur as digitized straight lines and quasicrystals. They also provide examples of minimal word proliferation in formal languages.

We prove Theorem 1: suppose G is a simple graph of order n having Δ(G) = n − k where k ≥ 5 and n ≥ max (13, 3k −3). If G contains an independent set of k − 3 vertices, then the TCC (Total Colouring Conjecture) is true. Applying Theorem 1, we also prove that the TCC is true for any simple graph G of order n having Δ(G) = n −5. The latter result together with some earlier results confirm that the TCC is true for all simple graphs whose maximum degree is at most four and for all simple graphs of order n having maximum degree at least n − 5.

We adapt the Toeplitz operator proof of Bott periodicity to give a short direct proof of Bott periodicity for the representable K-theory of σ-C*-algebras. We further show how the use of this proof and the right definitions simplifies the derivation of the basic properties of representable K-theory.

Some fixed point theorems on H-spaces are presented. These theorems are then applied to generalize a theorem of Fan concerning sets with convex sections to H-spaces and to prove the existence of equilibrium points of abstract economics in which the commodity space is an H-space.

In this paper, we consider a class of strong symmetric distributions, which we refer to as the strong c-symmetric distributions. We provide, as the main result of this paper, conditions satisfied by the recurrence relations of certain polynomials associated with these distributions.

We discuss the application of nonstandard methods to local versions of certain lattice notions. In a particular case, we find that imposition of certain local conditions imply a surprising global one, namely boundedness of the given lattice.

This paper answers a recent question concerning the relationship between two notions of paracompactness for bitopological spaces. Romaguera and Marin defined pairwise paracompactness in terms of pair open covers, motivated by a characterization of paracompactness due to Junnila. On the other hand, Raghavan and Reilly defined a bitopological space (X, τ, σ) to be δ-pairwise paracompact if and only if every τ open (σ open) cover of X admits a τ V σ open refinement which is τ V σ locally finite. It is shown that pairwise paracompactness implies δ-pairwise paracompactness, and that the converse is false.