In this paper we present a new proof of the equivalence of the analytic and the geometric characterization of the class of functions convex in the negative or positive direction of the imaginary axis.

This paper proposes matrix variate generalization of Kummer-Beta family of distributions which has been studied recently by Ng and Kotz. This distribution is an extension of Beta distribution. Its characteristic function has been derived and it is shown that the distribution is orthogonally invariant. Some results on distribution of random quadratic forms have also been derived.

In this note we examine the relationships between a subnormal shift, the measure its moment sequence generates, and those of a large family of weighted shifts associated with the original shift. We examine the effects on subnormality of adding a new weight or changing a weight. We also obtain formulas for evaluating point mass at the origin for the measure associated with the shift. In addition, we examine the relationship between the measure associated with a subnormal shift and those of a family of shifts substantially different from the original shift.

The Hopf bifurcation and homoclinic bifurcation of the quintic Hamiltonian system is analyzed under quintic perturbations by using unfolding theory in this paper. We show that a quintic system can have at least 29 limit cycles.

For each positive integer n let N2, n denote the variety of all groups which are nilpotent of class at most 2 and which have exponent dividing n. For positive integers m and n, let N2, mN2, n denote the variety of all groups which have a normal subgroup in N2, m with factor group in N2, n. It is shown that if G ∈N2, mN2, n, where m and n are coprime, then G has a finite basis for its identities.

Suppose that V is a finite dimensional vector space over a finite field of characteristic 2, G is the symplectic group on V and a is a non-zero vector of V. Here we classify irreducible subgroups of G containing a certain subgroup of O2(StabG(a)) all of whose non-trivial elements are 2-transvections.

The notions of limits and colimits are studied in the category of C*-algebras. It is shown that limits and colimits of diagrams of C*-algebras are stable under tensor product by a fixed C*-algebra, and crossed product by a locally compact group.

Additive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, if Ad denotes the generalized Drazin inverse of a bounded linear operator A on an arbitrary complex Banach space, then in some special cases (A + B)d is computed in terms of Ad and Bd. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl. 322 (2001), 207–217) are extended to infinite dimensional settings with simplified proofs.

Pseudo-BL algebras are noncommutative generalizations of BL-algebras and they include pseudo-MV algebras, a class of structures that are categorically equivalent to l-groups with strong unit. In this paper we characterize directly indecomposable pseudo-BL algebras and we define and study different classes of these structures: local, good, perfect, peculiar, and (strongly) bipartite pseudo-BL algebras.