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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.
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.
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.
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