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Factorization calculus and geometric probability
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Ambartzumian
This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their ...
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Algorithmic Number Theory
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Joe Buhler (Editor)
Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic ...
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Project Factorisations in Partial Evaluation
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John Launchbury
Programming frequently requires that problems are broken down into subproblems and then each subproblem solved independently. These solutions may then be combined to provide a solution to the original problem. Partial evaluation is a serious attempt to tackle this issue, allowing the programmer to write programs in a highly interpretive style ...
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Control System Synthesis: A Factorization Approach
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M Vidyasagar
This book is the first comprehensive treatment of the "fractional representation" approach to linear feedback system design and analysis, an approach that has recently taken the control theory field by storm.
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Primes and Programming: An Introduction to Number Theory with Computing
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by
Peter Giblin
Numbers are part of our everyday experience and their properties have fascinated mankind since ancient times. Deciding whether a number is prime and if not, what its factors are, are both fundamental problems. In recent years analysis and solution of these problems have assumed commercial significance since large primes are an essential feature of ...
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Prime numbers and computer methods for factorization
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by
Hans Riesel
In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ...
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Rings and Factorization
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David Sharpe
This textbook is an introduction to the concept of factorization and its application to problems in algebra and number theory. With the minimum of prerequisites, the reader is introduced to the notion of rings, fields, prime elements and unique factorization. The author shows how concepts can be applied to a variety of examples such as factorizing ...
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Factorization and Primality Testing
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David M Bressoud
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Factorization Method in Quantum Mechanics
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by
Shi-Hai Dong
This work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader's disposal. For this purpose a comprehensive description is provided of the factorization method ...
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Factorization in Integral Domains
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by
Daniel D Anderson
The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of ...
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Scientific Ballooning: Technology and Applications of Exploration Balloons Floating in the Stratosphere and the Atmospheres of Other Planets
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by
Nobuyuki Yajima, Naoki Izutsu, Takeshi Imamura
The aim of this book is to introduce scientific ballooning to the many people who are interested in the use of balloons for scientific applications. The book offers a basic understanding of the engineering details and the scientific research giving rise to balloon activities going on today. Above all, the book will serve as a guidebook for young ...
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From Polynomials to Sums of Squares
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by
Terence H Jackson
"From Polynomials to Sums of Squares" describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is ...
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Factorization Theory of Meromorphic Functions, and Related Topics
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by
Chung-Chun Yang
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The Factorization Method for Inverse Problems
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by
Andreas Kirsch, Natalia Grinberg
The factorization method is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. Aimed at students and researchers in Applied Mathematics, Physics and Engineering, this text introduces the reader to this promising approach for solving important classes of inverse problems. The wide ...
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Factoring Groups Into Subsets
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by
Sandor Szabo, Arthur D Sands
Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups. ...
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One-Factorizations
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by
W D Wallis
This is a specialized textbook on graph factorizations, an area which lies partly in graph theory and partly in the theory of combinational designs. It is the first full-size book on its particular subject, which has previously been treated only in survey papers and in chapters in books on design theory and on graph decompositions and matching ...
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Abstract Band Method Via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation
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by
L Rodman, F R Gantmakher
New versions are developed of an abstract scheme, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract ...
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From Polynomial to Sums of Squares
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by
T. H. Jackson
This text and software describes a "journey" through algebra and number theory based on the central theme of factorization. It begins with basic knowledge of rational polynomials, gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The treatment is made very concrete throughout the main text with ...
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Convolution Operators and Factorization of Almost Periodic Matrix Functions
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by
Albrecht Bottcher, Ilya M. Spitkovskii, Yuri I. Karlovich
This book is an introduction to convolution operators with matrix-valued almost periodic or semi-almost periodic symbols. The basic tools for the treatment of the operators are Wiener-Hopf factorization and almost periodic factorization. These factorizations are systematically investigated and explicitly constructed for interesting concrete ...
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Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory
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by
Alfred Geroldinger, Franz Halter-Koch
From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, "Non-Unique ...
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Factorization and Integrable Systems: Summer School in Faro, Portugal, September 2000
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by
Nenad Manojlovic (Editor), Israel Gohberg (Editor), Antonio Ferreira Dos Santos (Editor)
In September 2000 a Summer School on "Factorization and Integrable Systems" was held at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the ...
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Prime Numbers and Computer Methods for Factorization
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Hans Riesee, Hans Riesel
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Iterative Incomplete Factorization Methods
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by
V. P. Il'in
This book is devoted to numerical methods for solving sparse linear algebra systems of very large dimension which are arising in the implementation of the mesh approximations of the partial differential equations. Incomplete factorization is the basis of the wide class of preconditioning interative processes with acceleration by conjugate ...
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The determination of units in real cyclic sextic fields
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by
Sirpa Maki
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Analytic Methods in the Analysis and Design of Number Theoretic Algorithms
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by
Eric Bach
This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic algorithms and to the construction of cryptographic protocols.
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