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Discrete Calculus
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, prec...
Complex Analysis and Geometry
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Functional Analysis, Calculus of Variations and Optimal Control
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author pr...
Whiplash Injuries
The new edition of this book provides an up-to-date and comprehensive overview of whiplash-associated disorders, focusing in particular on a functional approach to clinical and instrumental diagnosis and rehabilitative treatment. It fully reflects the changes in our understanding of whiplash injuries since the first edition, and in particular the increased awareness that whiplash is a whole-body trauma in which forces act progressively from the lumbar region to the brain, through the cervical spine. Detailed attention is paid to the functional connections between the sense organs of the inner ear, the sympathetic system, and the spine with a view to optimizing diagnosis and treatment. It is explained how various treatment options can be employed to best effect in patients with different symptoms, following, but updating, the well-known Quebec Task Force guidelines. Underestimated aspects such as positional vertigo, somatic tinnitus, temporomandibular disorders, and back pain are also considered. This book will be an invaluable tool in everyday clinical practice for all who are involved in the diagnosis and treatment of whiplash injury.
Advances in Convex Analysis and Global Optimization
There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Societ...
