We consider the Liénard equation and we give a sufficient condition to ensure existence and uniqueness of limit cycles. We compare our result with some other existing ones and we give some applications.

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vignéras multiple gamma functions by considering the classical limit of the multiple q-gamma functions.

Article history: Received 6 November 2009 Received in revised form 14 February 2010 Accepted 15 February 2010 Available online 19 February 2010 Communicated by C.R. Doering

In this paper we develop multiple hypotheses testing procedures to compare a new treatment with a set of standard treatments in a clinical trial. The aim is to classify the new treatment with respect to each of the standards, by specifying those to which the new treatment is superior, those to which the new treatment is equivalent and those to which one can establish neither superiority nor equ...

We undertake a case study of two series of nonclassical Zariski geometries. We show that these geometries can be realised as representations of certain noncommutative C∗-algebras and introduce a natural limit construction which for each of the two series produces a classical U(1)-gauge field over a 2-dimensional Riemann surface.

Errors are found in example problems from Henri Poincaré’s paper “Mémoire sur les courbes définies par une équation différentielle.” Examples four and five from chapter seven and examples one, two, and three from chapter nine do not have the limit cycles at infinity predicted by Poincaré. Instead they have fixed points at every point at infinity. In order to understand the errors made by Poinca...

Monte Carlo experiments have been used to test the robustness of distribution-free confidence limits for the parameters of the MichaelisMenten equation (Porter & Trager, 1977). When used in conjunction with the modified form of the direct linear plot (Cornish-Bowden & Eisenthal, 1978), they prove to be more robust than least-squares confidence limits. In circumstances where the least-squares as...