Semi-F-spaces are spaces such that given any pair of disjoint cozero sets, every countable subset of one is completely separated from the other. This generalizes the notion of an F-space and is stronger than the property that every countable subset is C*-embedded. Semi-F-spaces are studied and several examples are given.

R. A. Brualdi [1] presents a construction yielding matrices whose Birkhoff representation consists of the maximum number of permutation matrices and having 0(2n2) line sum. In this note a counterexample to such a construction is given. Furthermore, a new construction is presented, yielding matrices with lower line sums.

A Σ-group is an abelian group on which is given a collection of infinite sums having properties suggested by those of absolutely convergent series in R or C. It is shown that the usual decomposition of a torsion abelian group into its p-components carries over to the case of Σ-groups when the property of being torsion is replaced by an appropriate uniform version. For a certain class of Σ-groups, it turns out that being torsion is already sufficient for primary decomposition to hold.

Let ﹛zn﹜ be a sequence in the open unit disc and write In the case of pn for all n, the interpolation problems are considered.

Let n = 4t +- 2, where the integer t ≧ 2. A necessary condition is given for a particular Latin square L of order n to have a complete set of n — 2 mutually orthogonal Latin squares, each orthogonal to L. This condition extends constraints due to Mann concerning the existence of a Latin square orthogonal to a given Latin square.

A new proof of a product formula for Laguerre polynomials, due originally to Watson, is given. Considering the commutative Banach algebra of radial functions on the Heisenberg groups Hn, n ≧ 2, we observe that Watson's formula holds for z = 1,2, 3, …. Then, applying a complex function theory argument, we establish the validity of this formula for other complex values of z, i.e. for Re z > - 1/2.

Let G be a group with elements 1,…, n such that the group operation agrees with ordinary multiplication whenever the ordinary product of two elements lies in G. We show that if n is odd, then G is abelian.

In this paper p-local versions of the Rational Fibre and Cofibre Decomposition Theorems are given. In particular, if there exists an element in the nth Gottlieb group of a space F such that its image under the Hurewicz map has infinite order, then Sn for almost all primes p. A dual result is proved for cofibrations.

The self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.

The C*-algebras associated with irrational rotations of the circle were classified up to strong Morita equivalence by M. A. Rieffel. As a corollary, he gave a complete classification of the C*-algebras arising from irrational or Kronecker flows on the 2-torus up to *-isomorphism. Here, we extend the result to the socalled Denjoy homeomorphisms. Specifically, we give a necessary and sufficient condition for the strong Morita equivalence of two C*-algebras arising from homeomorphisms of the circle without periodic points. As a corollary, we show that two C*-algebras arising from flows on the 2-torus obtained from such homeomorphisms by the “flow under constant function” construction are *-isomorphic if and only if the flows themselves are topologically conjugate.

We prove that the sum of two idempotents is in a Banach algebra is itself an idempotent if and only if it is power-bounded.

We show that two maps between classifying spaces of compact, connected Lie groups are homotopic after inverting the order of the Weyl group of the source if and only if they induce the same maps on rational cohomology. We shall also give some results on maps from classifying spaces of finite groups to classifying spaces of compact Lie groups. Among other things we construct a map from B(Z/2 + Z/2 4- Z/3) into BSO(3) which is not induced by a homomorphism.

We established sufficient conditions for the oscillation of all solutions of the delay differential equation

and of the neutral delay differential equation

where p, q, r and a are nonnegative constants and n is an odd natural number.

A seven-parameter extension of Askey and Wilson's four parameter q-beta integral is written in a symmetric form as the sum of multiples of two very-well-poised balanced basic hypergeometric 10Φ9 series. Two special cases are considered in which the evaluation of the integral gives single terms by the q-Dixon formula in one case and by a special case of the Verma-Jain formula in the other. An orthogonal polynomial system is obtained in the first case and a system of biorthogonal rational function is obtained in the second. It is also shown that the biorthogonal system represents a generalization of Rogers’ q-ultraspherical polynomials.

Let (L, λ) be a locally solid Riesz space. (L, λ) is said to have the Levi property if for every increasing λ-bounded net (xα) ⊂ L+, sup xα exists. The Levi property, appearing in literature also as weak Fatou property (Luxemburg and Zaanen), condition (B) or monotone completeness (Russian terminology), is a classical object of investigation. In this paper we are interested in some variations of the property, their mutual relationships and applications in the theory of topological Riesz spaces. In the first part of the paper we clarify the status of two problems of Aliprantis and Burkinshaw. In the second part we study ideal-injective Riesz spaces.

Let V be a variety of rings and let A ∊ V. The ring A is injective in V if every triangle

with C ∊ V, m a monomorphism and f a homomorphism has a commutative completion as indicated. A ring which is injective in some variety (equivalently, injective in the variety it generates) is called injective. When only triangles with f surjective are considered we obtain the notion of weak injectivity. Directly indecomposable injective and weakly injective rings are classified.

The paper gives a good approximation of a Ck function on Rn and its derivatives by the restriction of an entire function on Cn and its derivatives respectively.

A semiderivation of a ring R is an additive mapping f:R → R together with a function g:R → R such that f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y) and f(g(x) ) = g(f(x)) for all x, y ∊ R. Motivating examples are derivations and mappings of the form x → x — g(x), g a ring endomorphism. A semiderivation f of R is centralizing on an ideal U if [f(u), u] is central for all u ∊ U. For R prime of char. ≠2, U a nonzero ideal of R, and 0 ≠ f a semiderivation of R we prove: (1) if f is centralizing on U then either R is commutative or f is essentially one of the motivating examples, (2) if [f(U), f(U) ] is central then R is commutative.