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Старый 18.09.2008, 20:54   #1
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Старый 05.01.2009, 15:11   #21
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Название работы: The Gamma function
Автор: Artin E.
Загрузил: Denis aka Rock Lee
Описание: A generation has passed since the late Emil Artin\'s little classic on the gamma function appealed in the Hamburger Mathematische Einzelschriften. Since that time, it has №en read with joy and fascination by many thousands of mathematicians and students of mathematics. In the United States (and presumably elsewhere as well), it has for many years been hard to find, and dog-eared copies and crude photocopies have been passed from hand to hand. Professor Artin\'s monograph has given many a student his first look at genuine analysis—the delicacy of its arguments, the precision of its results. Artin had a deep feeling for these aspects of analysis, and he treated them with a master\'s hand. His undergraduate lectures in the calculus, for example, were filled with elegant constructions and theorems which, alas, Artin never had time to put into printed form. We may be all the more grateful for this beautiful essay, and for its appearance in a new English edition. Various changes made by Artin himself have been incorporated in the present edition. In particular a small error following formula (59) (this edition) was corrected on the basis of a suggestion by Professor Borge Jessen.
Finally, thanks are due to the translator, Mr. Michael Butler, and to the firm of B. G. Teubner for English-language rights.
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Старый 05.01.2009, 15:12   #22
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Название работы: The geometric calculus of variations: a short survey and a list of open problems
Автор: Jost J.
Загрузил: Denis aka Rock Lee
Описание: Since my presentation of open problems at the Oberwolfach meeting on the \"Calculus of variations\" in April 1986 met with much interest from the side of the participants, it seemed useful to have the present notes available in written form.
The aim is to describe some of the major open problems in the area and thereby to show the potential and the limits of the mathematical methods presently available. Although some of the problems seem too hard to be solvable in the immediate future, I believe that even for a beginner it is very useful to know what the essential difficulties in a specific area of mathematics are. I also tried to describe some background for some of the problems.
Many of the problems are wellknown, and sometimes I was unable to find a specific origin or reference for a problem. Many of the problems also already appear in other problem lists. Because of the scope of the present list and since of course I could update and expand some of the older presentations, I nevertheless believe that my collection represents a useful documentation of the present state of our insight into the geometric aspects of the calculus of variations.
Before discussing the individual problem, I shall give a general overview of the geometric calculus of variations, in order to provide the framework within which the problems acquire their meaning. In this overview, I shall focus on area, energy, and curvature integrals, although the problem list has a somewhat broader scope, in order to point out the major lines of developments, the guiding underlying principles, and the interplay of geometry and analysis that is characteristic for the subject.
My main sources for the problems were Yau\'s differential geometric problem section in [Y2] (an updated version is under preparation), the list of problems on harmonic
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Старый 05.01.2009, 15:14   #23
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Название работы: The geometry of four-manifolds
Автор: Donaldson S. K., Kronheimer P.B.
Загрузил: Denis aka Rock Lee
Описание: This book grew out of two lecture courses given by the first author in Oxford in 1985 and 1986. These dealt with the applications of Yang-Mills theory to 4-manifold topology, which, beginning in 1982, have grown to occupy an important place in current research. The content of the lectures was governed by two main aims, and although the treatment of the material has been expanded considerably in the intervening years, some of the resulting structure is preserved in the present work. The primary aim is to give a self-contained and comprehensive treatment of these new techniques as they have been applied to the study of 4-manifolds. The second aim is to bring together some of the developments in Yang-Mills theory itself, placed in the framework of contemporary differential and algebraic geometry. Leaving aside the topological applications, ideas from Yang-Mills theory—developed by many mathematicians since the late 1970\'s—have played a large part in fixing the direction of modern research in geometry. We have tried to present some of these ideas at a level which bridges the gap between general text books and research papers.
These two aims are reflected in the organization of the book. The first provides the main thread of the material and begins in Chapter I with the mysteries of 4-manifold topology—problems which have been well-known in that field for a quarter of a century. It finishes in the last chapters, when some of these problems are, in part, resolved. On the way to this goal we make a number of detours, each with the purpose of expounding a particular area of interest. Some are only tangentially related, but none are irrelevant to our principal topic. It may help the reader to signpost here the main digressions.
The first is in Chapter 3, which deals for the most part with the description of instanton solutions on the 4-sphere; some of the facts which emerge are an ingredient in later arguments (in Chapters 7 and 8, for example) and serve as a model for more general results, but their derivation is essentially independent from the rest of the book. Chapter 6 is concerned with the proof of a key theorem which provides a route from differential to algebraic geometry. This result underpins calculations in Chapters 9 and 10, but it could be taken on trust by some readers. In Chapter 7, only the last section is central to the subject matter of the book, and the main topological results can be obtained without the rather lengthy analysis which it contains. The reader who wants only to discover how Yang-Mills theory has been applied to 4-manifold topology might want to read only Chapter 1, the first part of Chapter 2, and Chapters 4, 5, 8, and 9.
The ten chapters are each reasonably self-contained and could, to a large extent, be read as individual articles on different topics. In general we have tried to avoid duplicating material which is readily available elsewhere.
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Старый 05.01.2009, 15:16   #24
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Название работы: The Kobayashi-Hitchin correspondence
Автор: Luebke M., Teleman A.
Загрузил: Denis aka Rock Lee
Описание: When in 1993, encouraged by several colleagues, we decided to write this book, we had two main reasons to do so.
On the one hand, we were able to give a complete proof of the Kobayashi-Hitchin correspondence, i.e. the natural isomorphy of the moduli spaces of stable holomor-phic structures respectively irreducible Hermitian-Einstein connections in a differ-entiable complex vector bundle over a compact complex manifold. In particular, we could give this proof in the most general Hermitian context, whereas in most of the existing literature on this subject only algebraic or Kahler manifolds were considered; even for these cases, there was no single reference containing a complete proof of the correspondence in detail.
On the other hand, the Kobayashi-Hitchin correspondence had found important applications. In Donaldson theory, it had been used in the algebraic context to compute moduli spaces of instantons by algebraic-geometric methods, and thus had been an important tool in proving spectacular results in 4-diinensional differential topology. (In fact, this was our main motivation.) Furthermore, it had been used in the non-Kahler case to give a new and comparatively simple proof of Bogomolov\'s theorem on surfaces of type Vila-
Therefore, we thought it might be useful to present a complete, as far as possible self-contained, and hopefully readable proof of the correspondence and some of its applications.
Although at the end of 1994 it became apparent that many results in Donaldson theory can be proved in a much simpler way, by means of the newly discovered Seiberg-Witten invariants, and using only a very simple variant of the Kobayashi-Hitchin correspondence, we still think that this fundamental result is important and interesting enough to justify the publication of this book.
Acknowledgements.
First of all, we are most grateful to Christian Okonek for his steady encouragement and financial support, which made several visits of the first author to Zurich possible.
Furthermore, we would like to thank the Stieltjes Institute for Mathematics in Leiden, the EC Science project Geometry of Algebraic Varieties (no. SCI-0398-C(A)), and the HCM project AGE-Algebraic Geometry in Europe (contr. no. ER-
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Старый 05.01.2009, 15:16   #25
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Название работы: The method of multiple scales: Asymptotic solutions and normal forms for nonlinear oscillatory probl
Автор: Sanchez N. E.
Загрузил: Denis aka Rock Lee
Описание: The method of multiple scales is implemented in Maple V Release 2 to generate a uniform asymptotic solution 0(er) for a weakly nonlinear oscillator. In recent work, it has been shown that the method of multiple scales also transforms the differential equations into normal form, so the given algorithm can be used to simplify the equations describing the dynamics of a system near a fixed point. These results are equivalent to those obtained with the traditional method of normal forms which uses a near-identity coordinate transformation to get the system into the \"simplest\" form. A few Duffing type oscillators are analysed to illustrate the power of the procedure. The algorithm can be modified to take care of systems of ODEs, PDEs and other nonlinear cases.
© 1996 Academic Press Limited
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Старый 05.01.2009, 15:17   #26
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Название работы: The Raman effect
Автор: Long D.A.
Загрузил: Denis aka Rock Lee
Описание: Raman spectroscopy is now rinding wide-ranging application in pure and applied science and the number of original papers devoted to this area of spectroscopy continues to grow. This is largely the result of significant advances in the equipment available, particularly laser excitation sources, spectrometers, detectors, signal processors and computers.
It seems timely, therefore, to provide an integrated treatment of the theory underlying Raman spectroscopy. Of course there are already a number of edited books and reviews dealing with various aspects of the subject, but this book is the result of the phenomenon of Raman spectroscopy falling \'under the consideration of one man\'s mind\' as Francis Bacon put it. My objective has been to present a unified theoretical treatment which is reasonably complete and adequately rigorous but nonetheless readable. My hope is that this will provide a sound basis for the effective use of more highly specialized review articles.
As to completeness, I have had to put some restrictions on the coverage, partly because the subject is so vast and partly because of my own limitations. Therefore the treatments developed here relate mainly to scattering by a system of freely orienting, non-interacting molecules or by systems which approximate to this. As to rigour, I have endeavoured to explain in words, as far as possible, the inwardness of the mathematics and physics which are necessarily involved. I have particularly tried to avoid taking refuge behind that often overworked phrase \'as is well known\'.
An effective theoretical treatment demands a variety of carefully honed mathematical and physical tools. To keep the treatment in the main text uncluttered, these tools are
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Старый 05.01.2009, 15:20   #27
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Название работы: The Theory of Elastic Waves and Waveguides
Автор: Miklowitz J.
Загрузил: Denis aka Rock Lee
Описание: The primary objective of this book is to give the reader a basic understanding of waves and their propagation in a linear elastic continuum. The studies presented here, of elastodynamic theory and its application to fundamental boundary value problems, should prepare the reader to tackle many physical problems of modern general interest in engineering and geophysics, and particular interest in mechanics and seismology.
The book focuses on transient wave propagation reflecting the strong interest in this topic exhibited in the literature and my research interest for the past twenty years. Chapters 5-8, and part of 2 are exclusively on transient waves, bringing to the reader a detailed physical and mathematical exposition of the fundamental boundary value problems in the subject. The approach is through the governing partial differential equations with integral transforms, integral equations and analytic function theory and applications being the tools. Transient waves in the infinite and semi-infinite medium and waveguides (rods, plates, etc.) are covered, as well as pulse diffraction problems. Chapters 3 and 4 with their extensive discussions of time harmonic waves in a half space, two half spaces in welded contact and waveguides are of interest per se. They are also important as necessary background for the later chapters.
The book will also serve as a reference source for workers in the subject since many important works are involved in the presentation. Many others are cited, but I make no claim to an extensive literature search since time precluded that. In this connection my survey covers the literature through 1964 (see reference [4.4] at the end of Chapter 4).
I found my way into this subject long ago and quite accidentally. In experiments with plexiglas tension specimens, preliminary ones in an investigation of dynamic stress-strain properties, a few of the specimens in these static tests broke suddenly and in a brittle manner in two places. The frontispiece p. VI) depicts this phenomenon (also for high-speed tool steel). Simple wave
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Старый 05.01.2009, 15:35   #28
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Название работы: The Transforms and Applications Handbook (second edition)
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Автор: A.D. Poularikas
Загрузил: Denis aka Rock Lee
Описание: The purpose of The Transforms and Applications Handbook, Second Edition is to include in a single volume the most important mathematical transforms frequently used by engineers and scientists. The book also was written with the advanced undergraduate and graduate students in mind. Each chapter covers one of the transforms, accompanied by a number of examples that are included to elucidate the use of the transform and its properties. Applications to different areas are included in each chapter as well. This inclusion gives readers of different backgrounds the opportunity to become familiar with the wide spectrum of applications of these transforms. We believe that having all of these useful transforms included in one book will be of great value to scientists, engineers, and students.
The information is now organized into 15 chapters, each covering one of the transforms, except for Chapter 1 which enhances some topics that are treated less extensively in the other chapters. Over the past 3 years, a number of communications have been received concerning different aspects of the Handbook. All of the comments regarding typographical errors have been incorporated in the second edition. The editor and the contributors wish to thank the readers for their contributions and encouragement which prompted this second edition.
In the second edition to the Handbook, we have added three new chapters: Lapped Transforms, Discrete Time and Discrete Fourier Transforms, and Fractional Fourier Transforms. In the original chapters, we have corrected typographical errors, replaced the table of Laplace transforms with another table containing a larger number of entries, the chapter on Mellin transforms was rewritten, the cosine and sine transforms were rewritten, and the Wavelet transforms were updated.
The Editor would be extremely grateful if the readers forwarded their opinion about the Handbook, any errors they may detect, suggestions for new material in new editions, and material that they feel may be neglected. The reader also may consult the following references:
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Старый 05.01.2009, 15:36   #29
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Название работы: The umbral calculus
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Автор: Roman S.
Загрузил: Denis aka Rock Lee
Описание: This monograph is intended to be an elementary introduction to the modern umbral calculus. Since we have in mind the largest possible audience, the only prerequisite is an acquaintance with the basic notions of algebra, and perhaps a dose of applied mathematics (such as differential equations) to help put the theory in some mathematical perspective.
The title of this work really should have been The Modern Classical Umbral Calculus, Within the past few years many, indeed infinitely many, distinct umbral calculi have begun to be studied. Actually, the existence of distinct umbral calculi was recognized in a vague way as early as the 1930s but seems to have remained largely ignored until the past decade.
In any case, we shall occupy the vast majority of our time in studying one particular umbral calculus—the one that dates back to the 1850s and that has received the attention (both good and bad) of mathematicians up to the present time. For this, we use the term classical umbral calculus. Only in the last chapter do we glimpse the newer, much less well established, nonclassi-cal umbral calculi.
The classical umbral calculus, as it was from 1850 to about 1970, consisted primarily of a symbolic technique for the manipulation of sequences, whose mathematical rigor left much to be desired. To drive this point home one need only look at Eric Temple Bell's unsuccessful attempt (in 1940) to convince the mathematical community to accept the umbral calculus as a legitimate mathematical tool. (Even now some are still trying to achieve Eric Temple Bell's original goal.) This old-style umbral calculus was, however, useful in deriving certain mathematical results; but unfortunately these results had to be verified by a different, more rigorous method.
In the 1970s Gian-Carlo Rota, a mathematician with a superlative talent for handling just this sort of situation, began to construct a completely rigorous foundation for the theory—one that was based on the relatively

IK
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Старый 05.01.2009, 15:38   #30
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Название работы: Topology Without Tears
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Автор: Morris S. A.
Загрузил: Denis aka Rock Lee
Описание: Topology is an important and interesting area of mathematics, the study of which will not only introduce you to new concepts and theorems but also put into context old ones like continuous functions. However, to say just this is to understate the significance of topology. It is so fundamental that its influence is evident in almost every other branch of mathematics. This makes the study of topology relevant to all who aspire to be mathematicians whether their first love is (or will be) algebra, analysis, category theory, chaos, continuum mechanics, dynamics, geometry, industrial mathematics, mathematical biology, mathematical economics, mathematical finance, mathematical modelling, mathematical physics, mathematics of communication, number theory, numerical mathematics, operations research or statistics. (The substantial bibliography at the end of this book suffices to indicate that topology does indeed have relevance to all these areas, and more.) Topological notions like compactness, connectedness and denseness are as basic to mathematicians of today as sets and functions were to those of last century.
Topology has several different branches — general topology (also known as point-set topology), algebraic topology, differential topology and topological algebra — the first, general topology, being the door to the study of the others. We aim in this book to provide a thorough grounding in general topology. Anyone who conscientiously studies about the first ten chapters and solves at least half of the exercises will certainly have such a grounding.
For the reader who has not previously studied an axiomatic branch of mathematics such as abstract algebra, learning to write proofs will be a hurdle. To assist you to learn how to write proofs, quite often in the early chapters, we include an aside which does not form part of the proof but outlines the thought process which led to the proof.
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