It is of frequent occurrence in problems of both pure and applied mathematics that certain values sought may be specified and must be determined as the roots of a tran-scendental equation. In particular, the equation may be of the class in which the unknown is involved only through the medium of exponential or trigonometric functions, with coefficients… (More)
1. Introduction. From the title of my address you will already have observed that it is my intention to discuss with you the asymptotic representation of the solutions of certain differential equations, and that my point in doing this is largely to dwell upon the Stokes phenomenon which arises in that theory. There are at least two good reasons why I have… (More)
We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable, basic case.
Materials discovery provides the opportunity to identify novel materials that are tailored to complex biological environments by using combinatorial mixing of monomers to form large libraries of polymers as micro arrays. The materials discovery approach is predicated on the use of the largest chemical diversity possible, yet previous studies into human… (More)
The ring of symmetric functions Λ, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the symmetric group. One may define a coproduct on Λ by the plethystic addition on alphabets. In this way the ring of symmetric functions… (More)
Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. As in the reverse plane partition case, the right hand side of this identity admits a simple factorization form in terms of the " hook lengths " of the… (More)