Michael C. Berg (Loyola Marymount Univ.)

The Fourier-Analytic Proof of Quadratic Reciprocity

A unique synthesis of the three existing Fourier-analytic treatments of quadratic reciprocity.

The relative quadratic case was first settled by Hecke in 1923, then recast by Weil in 1964 into the language of unitary group
representations. The analytic proof of the general n-th order case is still an open problem today, going back to the end of Hecke's famous
treatise of 1923. The Fourier-Analytic Proof of Quadratic Reciprocity provides number theorists interested in analytic methods applied to
reciprocity laws with a unique opportunity to explore the works of Hecke, Weil, and Kubota.

This work brings together for the first time in a single volume the three existing formulations of the Fourier-analytic proof of quadratic
reciprocity. It shows how Weil's groundbreaking representation-theoretic treatment is in fact equivalent to Hecke's classical approach,
then goes a step further, presenting Kubota's algebraic reformulation of the Hecke-Weil proof. Extensive commutative diagrams for
comparing the Weil and Kubota architectures are also featured.

The author clearly demonstrates the value of the analytic approach, incorporating some of the most powerful tools of modern number
theory, including adeles, metaplectric groups, and representations. Finally, he points out that the critical common factor among the three
proofs is Poisson summation, whose generalization may ultimately provide the resolution for Hecke's open problem.

Contents
Hecke's Proof of Quadratic Reciprocity.
Two Equivalent Forms of Quadratic Reciprocity.
The Stone-Von Neumann Theorem.
Weil's "Acta" Paper.
Kubota and Cohomology.
The Algebraic Agreement Between the Formalisms of Weil and Kubota.
Hecke's Challenge: General Reciprocity and Fourier Analysis on the March.
Bibliography.
Index.

Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts
ISBN: 0-471-35830-4
Hardcover
Pages: 118
Copyright: 2000

Merran Evans (Monash University, Australia)
Nicholas Hastings (Queensland Univ. of Technology, Australia)
J. Brian Peacock (General Motors Advanced Engineering)

Statistical Distributions, 3rd Ed.

Since the previous edition of this popular guide to the most commonly used statistical distributions was published in 1993, statistical
methods have found many new applications in science, medicine, engineering, business/finance, and the social sciences. To keep pace
with these developments and to highlight the growing influence of statistical software and data management techniques, this new edition is
now thoroughly updated and revised. Through clear, concise, easy-to-follow presentations, the authors discuss the key facts and formulas
for 40 major probability distributions, fine-tune all existing material, and continue to offer ready access to vital information gleaned from
hard-to-find places across the literature. Highly useful both as an introduction to basic principles and as a quick reference guide, Statistical
Distributions, Third Edition:

Presents the 40 distributions in alphabetical order
Provides all key formulas for each distribution
Adds a new chapter on the Empirical Distribution Function
Expands the Weibull Distribution to cover the 3 and 5 parameter versions
Incorporates diagrams and tables illustrating the characteristics of each distribution
Discusses the types of application for which distributions are used
Features references to relevant software packages

Wiley Series in Probability and Statistics: Texts and References Sectio
ISBN: 0-471-37124-6
Paperback
Projected Pub Date: Jun 2000

Lorenzo Farina (Univ. of Rome, La Sapienza, Italy)
Sergio Rinaldi (Politecnico di Milano, Italy)

Positive Linear Systems: Theory and Applications

A complete study on an important class of linear dynamical systems朴ositive linear systems

One of the most often-encountered systems in nearly all areas of science and technology, positive linear systems is a specific but
remarkable and fascinating class. Renowned scientists Lorenzo Farina and Sergio Rinaldi introduce readers to the world of positive linear
systems in their rigorous but highly accessible book, rich in applications, examples, and figures.

This professional reference is divided into three main parts: The first part contains the definitions and basic properties of positive linear
systems. The second part, following the theoretical exposition, reports the main conceptual results, considering applicable examples taken
from a number of widely used models. The third part is devoted to the study of some classes of positive linear systems of particular
relevance in applications (such as the Leontief model, the Leslie model, the Markov chains, the compartmental systems, and the queueing
systems). Readers familiar with linear algebra and linear systems theory will appreciate the way arguments are treated and presented.

Extraordinarily comprehensive, Positive Linear Systems features:
Applications from a variety of backgrounds including modeling, control engineering, computer science, demography, economics,
bioengineering, chemistry, and ecology
References and annotated bibliographies throughout the book
Two appendices concerning linear algebra and linear systems theory for readers unfamiliar with the mathematics used

Farina and Rinaldi make no effort to hide their enthusiasm for the topics presented, making Positive Linear Systems: Theory and
Applications an indispensable resource for researchers and professionals in a broad range of fields.

Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts
ISBN: 0-471-38456-9
Hardcover
Projected Pub Date: Jun 2000

Howard Raiffa
Robert Schlaifer, (deceased), (both of Harvard Business School)

Applied Statistical Decision Theory

Contents
EXPERIMENTATION AND DECISION: GENERAL THEORY.
The Problem and the Two Basic Modes of Analysis.
Sufficient Statistics and Noninformative Stopping.
Conjujgate Prior Distributions.
EXTENSIVE-FORM ANALYSIS WHEN SAMPLING AND TERMINAL UTILITIES ARE ADDITIVE.
Additive Utility, Opportunity Loss, and the Value of Information: Introduction to Part II.
Linear Terminal Analysis.
Selection of the Best of Several Processes.
Problems in Which the Act and State Spaces Coincide.
DISTRIBUTION THEORY.
Univariate Normalized Mass and Density Functions.
Multivariate Normalized Density Functions.
Bernoulli Process.
Poisson Process.
Independent Normal Process.
Independent Multinormal Process.
Normal Regression Process.

Wiley Classics Library Editions
ISBN: 0-471-38349-X
Paperback
Pages: 356
Published: May 2000