Abstract Several determinants with gamma functions as elements are evaluated. These kinds of determinants are encountered, for example, in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer’s symbol) and the falling factorial. ...

Let S = (s1, s2, . . .) be any sequence of nonnegative integers and let Sk = ∑k i=1 si We then define the falling (rising) factorials relative to S by setting (x)↓k,S= (x−S1)(x−S2) · · · (x−Sk) and (x)↑k,S= (x+S1)(x+S2) · · · (x+Sk) if k ≥ 1 with (x)↓0,S= (x)↑0,S= 1. It follows that {(x)↓k,S}k≥0 and {(x)↑k,S}k≥0 are bases for the polynomial ring Q[x]. We use a rook theory model due to Miceli an...

We present a method for detection and classi cation of a spatial pattern in noise contaminated binary images which is based on performing subspace decomposition on a nonnegative de nite matrix of higher order moments of the image. We introduce a method which uses normalized power moments or ascending factorial moments as descriptors. While the set of p-th order factorial moments are in one-to-o...

STUDY OBJECTIVE To examine whether exposure to long working hours predicts various forms of sleep disturbance; short sleep, difficulty falling asleep, frequent waking, early waking and waking without feeling refreshed. DESIGN Prospective study with 2 measurements of working hours (phase 3, 1991-1994 and phase 5, 1997-1999) and 2 measurements of subjective sleep disturbances (phase 5 and phase...

We survey several results on A-hypergeometric systems of linear partial differential equations introduced by Gelfand, Kapranov and Zelevinsky in the case of integer (and thus resonant) parameters, in particular, those differential systems related to sparse systems of polynomial equations. We also study in particular the case of A-hypergeometric systems for which kerA has rank 1. This allows us ...