A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions of complexity classes, on finite model theory, on models of feasible computation for real numbers, on vector spaces and on recursion theory. The vVorkshop on Feasible Mathematics was sponsored by the Mathematical Sciences Institute and was held at Cornell University, June 26-28, 1989.

In this volume, Lambek and Scott reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher-order logic, and cartesian closed categories, are essentially the same. Part II demonstrates that another formulation of higher-order logic, (intuitionistic) type theories, is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given.The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludeds with a set of exercises.

The ultimate reference guide to the synthesis of radiopharmaceuticals The Radiochemical Syntheses series provides scientists and professionals with a comprehensive reference to proven synthetic methods for radiochemical reactions, along with step-by-step guidance on how to replicate these syntheses in the laboratory. Volume 1 in the series focuses on the synthesis and purification of radiopharmaceuticals in clinical use today. It brings together in one complete, self-contained volume a collection of monographs containing a wealth of practical information from across the literature, demonstrating in meticulous detail how to prepare radiopharmaceuticals for positron emission tomography (PET) imaging, especially in tumor studies, cardiology, and neuroscience. Readers have key experimental details culled from the literature at their fingertips, greatly simplifying the process of qualifying a site for the clinical production of new radiopharmaceuticals.