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Predicative Arithmetic (Mathematical Notes, Vol. 32)

  This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previou...

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Discontinuous Groups and Automorphic Functions

Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. The purpose of this book is to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation. The emphasis in this book is on the fundamental parts of the subject. The book is directed to three classes of ...

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Fourier Analysis In Convex Geometry

The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems.One of the results discussed in the book ...

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In-Depth Analysis of Linear Programming

Along with the traditional material concerning linear programming (the simplex method, the theory of duality, the dual simplex method), In-Depth Analysis of Linear Programming contains new results of research carried out by the authors. For the first time, the criteria of stability (in the geometrical and algebraic forms) of the general linear programming problem are formulated and proved. New regularization methods based on the idea...

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Nonhomogeneous Matrix Products

Infinite products of matrices are used in nonhomogeneous Markov chains, Markov set-chains, demographics, probabilistic automata, production and manpower systems, tomography, and fractals. More recent results have been obtained in computer design of curves and surfaces.This book puts together much of the basic work on infinite products of matrices, providing a primary source for such work. This will eliminate the rediscovery of known ...

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Proof Complexity and Feasible Arithmetics: Dimacs Workshop April 21-24, 1996

Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether logical inferences can be made, but also what resources are required to carry them out. Understanding the resources required ...

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Lattice Sums Then and Now

For over a century lattice sums have been studied by mathematicians and scientists in diverse areas of science, in some cases unwittingly duplicating previous work. Here, at last, is a comprehensive overview of the substantial body of knowledge that now exists on lattice sums and their applications.

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A Half-Century of Automata Theory: Celebration and Inspiration

This volume gathers lectures by 8 distinguished pioneers of automata theory, including two Turing Award winners. In each contribution, the early developments of automata theory are reminisced about and future directions are suggested. Although some of the contributions go into rather intriguing technical details, most of the book is accessible to a wide audience interested in the progress of the age of computers.The book is a must fo...

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Growth Curve Modeling: Theory and Applications

Title of the book is well chosen, in that it lays out (in about 400 pages) a very wide range of growth models of 10 chapters. I liked this book a lot, in that is written at the upper undergraduate/graduate level and really is aimed at showing a range of models (with derivations, some of which are in appendices) and their use. The book uses mostly standard algebra (at the level of a good regression) with limited use of matrix notation...