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...

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 ...

Whereas public information campaigns have failed to reverse the rising trend in obesity, economists support food taxes as they suggest they can force individuals to change their eating behavior and make the agro-food industry think more about healthy food products. Excise taxes based on the unhealthy nutrient content would be more effective since they impact more on unhealthy food products than...

The ultimate goal of antenatal and intranatal care is to have not only a healthy mother and a healthy baby, but also to achieve a successful vaginal delivery, keeping in mind the rising rates of caesarean deliveries. induced for various maternal and fetal indications. It has been stated that nearly about 13 patients requires induction of labour ultrasound examin assessing cervical findings for ...

non-discogenic sciatica can be caused by any lesion along the course of the lumbosacral nerve roots and sciatic nerve. we aim to present a rare case of refractory sciatica in an otherwise healthy 25-year-old man. he complained of left leg pain without significant back pain. extensor hallucis longus muscle was weak on the left side with limited straight leg rising. on magnetic resonance imaging,...

We use i and i for the falling and rising factorials respectively and we adopt the convention a binomial coeÆcient is zero if either of its parameters is negative. Let Fn;r denote the n-by-n matrix (i 1) j i j 1 r 1 1 i;j n . Note that Fn;r is a block matrix 0 0 Gn;r 0 with Gn;r lower triangular of size n r. Let Hn;r denote the (n r)-by-(n r) lower triangular banded matrix ( 1) j) i 1 j 1 r j ...

Insomnia affects about 33% of Americans according to Harvey & Tang (2003) who called for new cognitive treatments. We will report preliminary results from a test of (a) the Somnolent Mentation theory (SMT) of sleep onset (SO) and (b) a new cognitive treatment for insomnia, the cognitive shuffle (CS), derived from the SMT (Beaudoin, 2013, 2014). According to SMT, incoherent mentation characteris...

We give eecient algorithms for listing equivalence classes of k-ary strings under reversal and permutation of alphabet symbols. As representative of each equivalence class we choose that string which is lexicographically smallest. These algorithms use space O(n) and time O(p kN), where N is the total number of strings generated and n is the length of each string. For k = 2, we obtain a recursiv...

Abstract Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered 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. It is a special ...