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We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.

In this paper we study a family of operators dependent on a small parameter $\epsilon > 0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $\epsilon \to 0$, even though, for fixed $\epsilon > 0$, the eigenvalue asymptotics are quadratic., Comment: 16 pages

In this paper we address the problem of existence of inverse integrating factors for an analytic planar vector field in a neighborhood of its nonwandering sets. It is proved that there always exists a smooth inverse integrating factor in a neighborhood of a limit cycle, obtaining a necessary and sufficient condition for the existence of an analytic one. This condition is expressed in terms of the Ecalle–Voronin modulus of the associated Poincare map. The existence of inverse integrating factors in a neighborhood of an elementary singularity is also established, and we give the first known examples of analytic vector fields in R not admitting a C inverse integrating factor in any neighborhood of either a limit cycle or a weak focus. Moreover, it is shown that a C inverse integrating factor of a C planar vector field must vanish identically on the polycycles which are limit sets of its flow, thereby solving a problem posed by Garcia and Shafer (J. Differential Equations 217 (2005) 363–376).

This paper provides sufficient conditions that guarantee the global attractivity of the zero solution of a delay population model under impulsive perturbations.

For any x ∈ (0, 1], let the series [sum ]∞n=1 1/dn(x) be the Sylvester expansion of x. Galambos has shown that the Lebesgue measure of the set[formula here]is 1 when α = e, the base of the natural logarithm. This paper provides a proof that for any α [ges ] 1, A(α) has Hausdorff dimension 1 when α ≠ e.

In a previous paper, the author proved a recent Wiener–Hopf formula, established by Alili and Doney, by means of a path transform. We derive here two other results using this path transform.