Carson Crosses Canada by L. Bailey

THE A l AND C l BAILEY TRANSFORM

Abstract. We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative “Bailey chain” concept in the setting of basic hypergeometric series very well-poised on unitary Al or symplectic Cl groups. The classical case, corresponding to A1 or equivalently U(2), contains an immense amount of the theory and application of one-variable basic hypergeometric serie...

Rachel Carson Syndrom

For years some ecologists have been convinced that pesticides are contributing to a decline in amphibian species around the globe. From an apparent epidemic of deformed frogs in Minnesota to the near disappearance of yellow-legged frogs from California’s Sierra Nevada Mountains, pesticides have been considered prime suspects. This suspicion is no doubt rooted in the belief by the ecological com...

Lifting Bailey pairs to WP-Bailey pairs

A pair of sequences (αn(a, k, q),βn(a, k, q)) such that α0(a, k, q) = 1 and βn(a, k, q) = n ∑ j=0 (k/a; q)n−j(k; q)n+j (q; q)n−j(aq; q)n+j αj(a, k, q) is termed a WP-Bailey Pair. Upon setting k = 0 in such a pair we obtain a Bailey pair. In the present paper we consider the problem of “lifting” a Bailey pair to a WPBailey pair, and use some of the new WP-Bailey pairs found in this way to derive...

Tiling R 5 by Crosses

An n-dimensional cross comprises 2n + 1 unit cubes: the center cube and reflections in all its faces. It is well known that there is a tiling of R n by crosses for all n. AlBdaiwi and the first author proved that if 2n + 1 is not a prime then there are 2 ℵ 0 non-congruent regular (= face-to-face) tilings of R n by crosses, while there is a unique tiling of R n by crosses for n = 2, 3. They conj...

Economic History Scott Carson