PURPOSE To compare the peak 5-min period of high-velocity running (HiVR) during a soccer match using a predefined vs a rolling time interval. METHODS Player movement data were collected from 19 elite Australian soccer players over 11 competitive matches (77 individual match files) using a 5-Hz global-positioning system. Raw velocity data were analyzed to determine the period containing the gr...

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