Island Grooves

Island Grooves is an instructional drumset DVD aimed squarely at drummers who wish to add some Caribbean grooves to their repertoire.Dr. Hanning demonstrates several styles including Calypso, Soca, Dub, Zouk, Shango, Party Soca, Traditional Island Favourites, and Reggae. The DVD contains seven play-along tracks with the Panyard Steel Orchestra, and three play-along tracks with Deighton Revealer Charlemagne.https://digitalcommons.wcupa.edu/cvpafaculty_books/1007/thumbnail.jp

We Were There

We Were There includes thirty World War II accounts told by men who lived it and (in some cases, narrowly) lived to tell about it. These veterans, representing all branches of the military, each played a different and important role in the war. These first-hand accounts provide personal insights into the hardships, monotony, adventure, and terror of war. Readers share in the loneliness, camaraderie, fear, and success as these young men selflessly serve their country, for many of them, on hostile land. The joy of World War II victory is short-lived, however, as they return to civilian life and face the adjustments necessary for returning to their families and restarting their education and careers.https://digitalcommons.wcupa.edu/casfaculty_books/1010/thumbnail.jp

Further Combinatorial Identities Deriving from the n-th Power of a 2 X 2 Matrix

In this paper we use a formula for the n-th power of a 2×2 matrix A (in terms of the entries in A) to derive various combinatorial identities. Three examples of our results follow. 1) We show that if m and n are positive integers and s ∈ {0, 1, 2, . . . , b(mn − 1)/2c}, then X i,j,k,t 2 1+2t−mn+n (−1)nk+i(n+1) 1 + δ(m−1)/2, i+k m − 1 − i i ! m − 1 − 2i k ! × n(m − 1 − 2(i + k)) 2j ! j t − n(i + k) ! n − 1 − s + t s − t ! = mn − 1 − s s ! . 2) The generalized Fibonacci polynomial fm(x, s) can be expressed as fm(x, s) = b(mX−1)/2c k=0 m − k − 1 k ! x m−2k−1 s k . We prove that the following functional equation holds: fmn(x, s) = fm(x, s) × fn ( fm+1(x, s) + sfm−1(x, s), −(−s) m) . 3) If an arithmetical function f is multiplicative and for each prime p there is a complex number g(p) such that f(p n+1) = f(p)f(p n ) − g(p)f(p n−1 ), n ≥ 1, then f is said to be specially multiplicative. We give another derivation of the following formula for a specially multiplicative function f evaluated at a prime power: f(p k ) = b X k/2c j=0 (−1)j k − j j ! f(p) k−2j g(p) j . We also prove various other combinatorial identities

The Convergence behavior of q-Continued Fractions on the Unit Circle

In a previous paper, we showed the existence of an uncountable set of points on the unit circle at which the Rogers-Ramanujan continued fraction does not converge to a finite value. In this present paper, we generalise this result to a wider class of qcontinued fractions, a class which includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fractions. We show, for each q-continued fraction, G(q), in this class, that there is an uncountable set of points, YG, on the unit circle such that if y ∈ YG then G(y) does not converge to a finite value. We discuss the implications of our theorems for the convergence of other q-continued fractions, for example the G¨ollnitz-Gordon continued fraction, on the unit circle