This is the fourth volume in the series "Mathematics in Industrial Prob-
lems." The motivation for these volumes is to foster interaction between
Industry and Mathematics at the "grass roots"; that is, at the level of
spe- cific problems. These problems come from Industry: they arise from
models developed by the industrial scientists in ventures directed at
the manufac- ture of new or improved products. At the same time, these
problems have the potential for mathematical challenge and novelty. To
identify such problems, I have visited industries and had discussions
with their scientists. Some of the scientists have subsequently
presented their problems in the IMA Seminar on Industrial Problems. The
book is based on questions raised in the seminar and subsequent
discussions. Each chapter is devoted to one of the talks and is
self-contained. The chap- ters usually provide references to the
mathematical literature and a list of open problems which are of
interest to the industrial scientists. For some problems partial
solution is indicated briefly. The last chapter of the book contains a
short description of solutions to some of the problems raised in the
third volume, as well as references to papers in which such solutions
have been published.