Cytogenetics of the genus Musa

This book provides important information resulting from a lifetime dedicated to banana research. Ken Shepherd has not only devoted his life to studying bananas, but has focused on an area much neglected by other researchers, Musa cytology. The publishing of this book is especially timely given the recent upsurge in interest in Musa karyology and the new methods that are now available for studying Musa chromosomes

On the Waring--Goldbach problem for eighth and higher powers

Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for the function $H(k)$ in the Waring--Goldbach problem. We obtain new results for all exponents $k\ge 8$, and in particular establish that $H(k)\le (4k-2)\log k+k-7$ when $k$ is large, giving the first improvement on the classical result of Hua from the 1940s

Smooth deformations of piecewise expanding unimodal maps

In the space of C^k piecewise expanding unimodal maps, k>=1, we characterize the C^1 smooth families of maps where the topological dynamics does not change (the "smooth deformations") as the families tangent to a continuous distribution of codimension-one subspaces (the "horizontal" directions) in that space. Furthermore such codimension-one subspaces are defined as the kernels of an explicit class of linear functionals. As a consequence we show the existence of C^{k-1+Lip} deformations tangent to every given C^k horizontal direction, for k>=2.Comment: 19 pages. Few misprints fixed. Minor improvement