The Goodwin model is a 3-variable model demonstrating the emergence of oscillations in a delayed negative feedback-based system at the molecular level. This prototypical model and its variants have been commonly used to model circadian and other genetic oscillators in biology. The only source of non-linearity in this model is a Hill function, characterizing the repression process. It was mathem...

Closed integral form expressions are derived for the Mathieu-type a-series and for the associated alternating series whose terms contain Fox’s H -function. In the final section, two similar results on Mathieu-type series with the Fox–Wright Psi-function pΨq and the generalized hypergeometric function pFq which can be expressed in terms of Fox’s H -functions are deduced respectively. c © 2006 El...

In this paper we show that the image of any locally finite k-derivation of the polynomial algebra k[x, y] in two variables over a field k of characteristic zero is a Mathieu subspace. We also show that the two-dimensional Jacobian conjecture is equivalent to the statement that the image ImD of every k-derivation D of k[x, y] such that 1 ∈ ImD and divD = 0 is a Mathieu subspace of k[x, y].

Lubka T. Roumenina,1-3 Mathieu Jablonski,1-3 Christophe Hue,1-3 Jacques Blouin,4 Jordan D. Dimitrov,1-3 Marie-Agnes Dragon-Durey,1-4 Mathieu Cayla,1-3 Wolf H. Fridman,1-4 Marie-Alice Macher,5 David Ribes,6 Luc Moulonguet,7 Lionel Rostaing,6 Simon C. Satchell,8 Peter W. Mathieson,8 Catherine Sautes-Fridman,1-3 Chantal Loirat,5 Catherine H. Regnier,1-3 Lise Halbwachs-Mecarelli,9 and Veronique Fre...