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 ...

VOLUME 37 • AUGUST 2012 • www.mrs.org/bulletin © 2012 Materials Research Society Plasmonics: Converting photons into the nanoscale Recently, photonic technologies have become universal in global data communications. 1 The unprecedented data bandwidths, ever falling power consumption requirements, and reduced cost margins of on-chip photonics 2,3 have established a photonic roadmap for scaling d...

A study was conducted which aimed to determine whether varying attractiveness and character integrity significantly affected the severity of the crime which participants associated with defendant portraits. Participants were shown attractive and unattractive portraits that were paired with a positive, negative or no-character statement. It was predicated that both variables would have effects o...

The mixed cold-hot dark matter cosmological model (CHDM) with Ωtot = 1 and a falling power-law initial spectrum of Gaussian adiabatic perturbations (n > 1) is tested using recent obserbational data. It is shown that its fit to the data becomes worse with the growth of n− 1, and may be considered as unreasonable for n > 1.1 for all possible values of the Hubble constant. Thus, the CHDM model wit...

In this work we examined morphological variation at different levels to study performance and population structuring of the blue mussel Mytilus edulis. Our objectives were: (i) to develop an integrated technique for analyzing morphological variation in blue mussels and, based on this technique; (ii) to perform a morphometric description of mussels from the northern part of their range; and (iii...