P Adic Numbers

Autor: Fernando Gouvea
Publisher: Springer Science & Business Media
ISBN: 9783540629115
File Size: 45,58 MB
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There are numbers of all kinds: rational, real, complex, p-adic... The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This book is an elementary introduction to p-adic numbers.Most other books on the subject are written for more advanced students. This book can almost be viewed as an introduction to be read in preparation for reading these more advanced texts. Readers who want to have an idea and appreciation of the subject but do not need to become specialists will probably find what they need in this book, while other texts may be too technical.

New Horizons In Pro P Groups

Autor: Marcus du Sautoy
Publisher: Springer Science & Business Media
ISBN: 9780817641719
File Size: 34,51 MB
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A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.

Tau P A Plane Wave Approach To The Analysis Of Seismic Data

Autor: Paul Stoffa
Publisher: Springer Science & Business Media
ISBN: 9780792300380
File Size: 50,76 MB
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In exploration seismology, data are acquired at multiple source and receiver posi tions along a profile line. These data are subsequently processed and interpreted. The primary result of this process is a subsurface image of the exploration target. As part of this procedure, additional information is also obtained about the subsurface material properties, e.g., seismic velocities. The methods that are employed in the acquisition and processing of exploration seismic data are internally consistent. That is, principally near vertical incidence seismic waves are generated, recorded and subsequently imaged. The data processing methods commonly used are based upon a small angle of incidence approximation, thus making the imaging problem tractable for existing data processing technology. Although tremendously successful, the limitations of this method are generally recognized. Current and future exploration goals will likely require the use of additional seismic waves, i.e., both compressional and shear precritical and postcritical reflections and refractions. Also, in addition to making better use of seismic travel times, recent efforts to directly incorporate seismic amplitude variations show that the approach may lead to a better understanding of subsurface rock properties. In response to more demanding exploration goals, recent data acquisition techniques have improved significantly by increasing the spatial aperture and incorporating a large number of closely spaced receivers. The need for better subsurface resolution in depth and position has encouraged the use of 240, 512, and even 1024 recorded data channels with receiver separations of 5 to 25 m.

A Course In P Adic Analysis

Autor: Alain Robert
Publisher: Springer Science & Business Media
ISBN: 9780387986692
File Size: 29,55 MB
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Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.

P Adic Analysis And Mathematical Physics

Autor: Vasili? Sergeevich Vladimirov
Publisher: World Scientific
ISBN: 9789810208806
File Size: 26,48 MB
Format: PDF
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p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.


Autor: Avis H. Anderson
Publisher: Arcadia Publishing
ISBN: 9780738510385
File Size: 53,42 MB
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In 1859, the Great Atlantic & Pacific Tea Company, known everywhere as A&P, began as a mail-order business located at 31 Vesey Street in downtown Manhattan. In 1925, A&P operated more than thirteen thousand grocery stores nationwide, with more than forty thousand employees. By 1950, approximately ten cents out of every dollar spent on food in the United States passed over A&P counters. A&P: The Story of the Great Atlantic & Pacific Tea Company tells the story of how cofounder George Huntington Hartford and his sons John and George brought A&P to a popularity with consumers that few companies have ever achieved. This stunning collection of vintage photographs shows such nostalgic scenes as the elegant early stores, their gleaming window displays, and the red horse-drawn delivery wagons with the A&P logo emblazoned on their sides. Shoppers choose from rows of colorful merchandise and fresh produce; uniformed storekeepers make change from ornate registers; and the founder's son tastes A&P's Eight O'Clock coffee. A&P is still an industry leader, and A&P: The Story of the Great Atlantic & Pacific Tea Company shows why, from the Hartford family's legacy to the generations of shoppers who depend on A&P for fair prices and quality food. This is the history of the supermarket where America grew up shopping.

Lectures On P Adic L Functions

Autor: Kenkichi Iwasawa
Publisher: Princeton University Press
ISBN: 9780691081120
File Size: 57,60 MB
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An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet. Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.

P Adic Functional Analysis

Autor: W.H. Schikhof
Publisher: CRC Press
ISBN: 9780824700386
File Size: 34,95 MB
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"Contains research articles by nearly 40 leading mathematicians from North and South America, Europe, Africa, and Asia, presented at the Fourth International Conference on p-adic Functional Analysis held recently in Nijmegen, The Netherlands. Includes numerous new open problems documented with extensive comments and references."