Growing specialization and diversification have brought a host of
monographs and textbooks on increasingly specialized topics. However,
the "tree" of knowledge of mathematics and related fields does not' grow
only by putting forth new branches. It also happens, quite often in
fact, that branches which were thought to be completely disparate are
suddenly seen to be related. Further, the kind and level of
sophistication of mathematics applied in various sciences has changed
drastically in recent years: measure theory is used (non-trivially) in
regional and theoretical economics; algebraic geometry interacts with
physics; the Minkowsky lemma, coding theory arid the struc- ture of
water meet one another in packing and covering theory; quantum fields,
crystal defects and mathematical programming profit from homotopy
theory; lie algebras are relevant to filtering; and prediction and
electrical engineering can use Stein spaces. And in addition to this
there are such new emerging subdisciplines as "completely integrable
systems", "chaos, synergetics and large-5cale order", which are almost
impossible to fit into the existing classification schemes. They draw
upon widely different sections of mathematics. This program, Mathematics
and Its Applications, is devoted to such (new) interrelations as exampla
gratia: - a central concept which plays an important role in several
different mathe- matical and/or scientific specialized areas; - new
applications of the results and ideas from one area of scientific en-
deavor into another; - influences which the results, problems and
concepts of one field of enquiry have and have had on the development of
another.