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Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications (Stochastic Modelling and Applied Probability)
Guy Fayolle ,
Roudolf Iasnogorodski , and
Vadim Malyshev
Manufacturer: Springer
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ASIN: 3540650474 |
Book Description
This monograph aims at promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes are of interest in several areas of mathematical research and are encountered in pure probabilistic problems, as well as in applications involving queuing theory. Using Riemann surfaces and boundary value problems, the authors propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behavior of random walks in the quarter plane.
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Univalent Functions and Teichmüller Spaces (Graduate Texts in Mathematics)
O. Lehto
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
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ASIN: 0387963103 |
Book Description
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the Écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated.
Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.
Customer Reviews:
Great Book.......2005-02-01
This is a wonderful book by a master of the subject.
It is packed with penetrating insights, illuminating
some of the deepest results on dynamics. Its great
strength is the bird's-eye view it gives.
It is a great place to start the study of complex dynamics.
It is not self-contained, so to get the detail on essential
ingredients such as uniformization and solving the Beltrami
equation one has to go elsewhere. I recommend students
to read it alongside Carleson and Gamelin, who take pains
to supply full details.
Product Description
In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of a one semester of complex variable! theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.
Customer Reviews:
An excellent Introduction.......2005-09-03
This book gives a very readable account of Riemann Surfaces-- a good course in Complex Analysis is all that's required as a prereq. The proofs are very clear, the material is presented beautifully, and (most of) the exercises are fairly straight forward and supplement the book very well. The notion of divisors, proof of the Riemann Roch theorem and Abel's theorem are explained very nicely. It serves as the perfect transition into more advanced books in algebraic geometry and on complex manifolds.
An incredible book for any mathematician !! .......2004-08-23
If you want to learn the basic properties of compact Riemann surfaces this is the book to read. If you want to know the "motivations" of modern Algebraic geometry this is again a book to read.
First of all the pace and the style are very casual. You really don't feel overwhelm by a mountain of definitions. The author always favor simplicity and concreteness instead of abstractions and generality. This is really a book that I should have read before taking a class on Schemes. For exemple in the context of Riemann surfaces an "very ample divisor" is simply a linear system without fixed base point that gives rise to an holomorphic embedding. This definition (at least for me) is much much more satisfactory and illuminating than the definition of a very ample sheaf that you can find in Hartshorne (even though his definition is much more general).
There is a very nice chapter on meromorphic differentials which explains how those object can be used to define line integral on any riemann surface. Topics like divisors, Riemann-Roch and curves are treated with a lot of depth. There are not a lot of pictures but having pictures supported by an unclear text is quite useless. Here the writing is so clear (not to say flawless) that on the first reading you really get the idea of what's going on.
There are very few mistakes in this book which is another reason why I like it. I'm really pissed off by those mathematicians
that are rushing to publish their books crowded by mistakes.
But don't get me wrong, I don't have anything against mathematicians that are writing books (this is a learning experience) but don't feel force to publish them unless they are very polished and "innovative".
Finally the last chapters treat of Abel's theorem ( which tells us exactly when a divisor is principal), Sheaves, Cech cohomologies and line bundles. Again the exposition is very well
motivated with a good supply of interesting exemples.
This is the best book that I read on subject and honestly if professor Miranda is writing another book related to my field of research you can be sure that I will have it my collection.
Hugo Chapdelaine,
McGill
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
Manufacturer: American Mathematical Society
ProductGroup: Book
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ASIN: 0821831674 |
Book Description
This is a collection of articles that grew out of a workshop organized to discuss deep links among various topics that were previously considered unrelated. Rather than a typical workshop, this gathering was unique as it was structured more like a course for advanced graduate students and research mathematicians.
In the book, the authors present applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations. Chapter 1 gives an introduction to Teichmüller space that is more concise than the popular textbooks, yet contains full proofs of many useful results which are often difficult to find in the literature. This chapter also contains an introduction to moduli spaces of curves, with a detailed description of the genus zero case, and in particular of the part at infinity. Chapter 2 takes up the subject of the genus zero moduli spaces and gives a complete description of their fundamental groupoids, based at tangential base points neighboring the part at infinity; the description relies on an identification of the structure of these groupoids with that of certain canonical subgroupoids of a free braided tensor category. It concludes with a study of the canonical Galois action on the fundamental groupoids, computed using Grothendieck-Teichmüller theory. Finally, Chapter 3 studies strict ribbon categories, which are closely related to braided tensor categories: Here they are used to construct invariants of 3-manifolds which in turn give rise to quantum field theories. The material is suitable for advanced graduate students and researchers interested in algebra, algebraic geometry, number theory, and geometry and topology.
Product Description
This well-known book is a self-contained treatment of the classical theory of abstract Riemann surfaces. The first five chapters cover the requisite function theory and topology for Riemann surfaces. The second five chapters cover differentials and uniformization. For compact Riemann surfaces, there are clear treatments of divisors, Weierstrass points, the Riemann-Roch theorem and other important topics. Springer's book is an excellent text for an introductory course on Riemann surfaces. It includes exercises after each chapter and is illustrated with a beautiful set of figures.
Book Description
This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented, as are alternate proofs for the most important results, showing the diversity of approaches to the subject. Of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.
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Gromov's Compactness Theorem for Pseude-holomorphic Curves (Progress in Mathematics)
Christoph Hummel
Manufacturer: Birkhauser
ProductGroup: Book
Binding: Hardcover
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ASIN: 3764357355 |
Book Description
Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. Since then, pseudo-holomorphic curves have taken on great importance in many fields. The aim of this book is to present the original proof of Gromov's compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint. Properties of particular interest are isoperimetric inequalities, a monotonicity formula, gradient bounds and the removal of singularities. A special chapter is devoted to relevant features of hyperbolic surfaces, where pairs of pants decomposition and thickthin decomposition are described. The book is essentially self-contained and should also be accessible to students with a basic knowledge of differentiable manifolds and covering spaces.
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Bieberbach Groups and Flat Manifolds (Universitext)
Leonard S. Charlap
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback
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ASIN: 0387963952 |
Book Description
Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This is the only English-language collection of these important papers, some of which are extremely hard to find. Contributors include Helmholtz, Klein, Clifford, Poincaré, and Cartan.
Customer Reviews:
Very interesting.......2007-05-07
There are many interesting articles in this collection. I shall give some highlights. Helmholtz, "The Origin and Meaning of Geometrical Axioms". "We can ... infer how the objects in a pseudospherical world, were it possible to enter one, would appear to an observer whose eye-measure and experiences of space had been gained like ours in Euclid's space. Such an observer would continue to look upon rays of light or the lines of vision as straight lines, such as are met with in flat space and as they really are in the spherical representation of pseudospherical geometry [i.e., the three-dimensional version of the projective disc model]. The visual image of the objects in pseudospherical space would thus make the same impression upon him as if he were at the center of Beltrami's sphere. He would think he saw the most remote objects round about him at a finite distance, let us suppose a hundred feet off. But as he approached these distant objects, they would dilate before him ... while behind him they would contract. He would know that his eye judged wrongly. If he saw two straight lines that in his estimate ran parallel to his world's end, he would find on following them that the farther he advanced the more they diverged" (p. 65). "There would be an illusion of the opposite description, if, with eyes practised to measure in Euclid's space, we entered a spherical space of three dimensions. We should suppose the more distant objects to be more remote and larger than they are, and should find on approaching them that we reached them more quickly than we expected from their appearance. ... The strangest sight, however, in the spherical world would be the back of our own head" (p. 66). For the two-dimensional case we should imagine mapping the sphere from its center onto a tangent plane ("gnomonic projection"), which of course sends great circles to lines. The inverse of this map is approximated by the image on a spherical mirror, so it is easy to imagine what a Euclidean world would look like to a spherical creature: he would think distant objects were pretty close (about a quarter of the circumference of the sphere) and very small. His illusion is thus the opposite of ours, as it would be in the hyperbolic case as well (a hyperbolic creature would impose the projective disc metric on our Euclidean plane, so things would seem distant and big). Clifford, "The Postulates of the Science of Space", interprets Euclidean axiomatics using modern concepts, e.g. "all right angles are equal" is a postulate to exclude singular points such as the vertex of a cone: "I can make two lines cross at the vertex of a cone so that the four adjacent angles shall be equal, and yet not one of them equal to a right angle" (p. 81). Poincaré, "On the Foundations of Geometry": "Our sensations cannot give us the notion of space. That notion is built up by the mind from elements which pre-exist in it ... What could a man see who possessed but a single immovable eye? ... Suppose that two points A and B are very near to each other, and that the distance AC is very great. Would our hypothetical man be cognisant of the difference? We perceive it, who can move our eyes, because a very slight movement is sufficient to cause an image to pass from A to B. But for him the question whether the distance AB was very small as compared with the distance AC would not only be insoluble, but would be devoid of meaning" (pp. 117-118), just as our sense of taste does not enable us to say whether water is further from milk than wine is from beer. Geometry is thus a creation of the mind, and it is not "imposed by experience. It is simply guided by experience. ... To ask whether the geometry of Euclid is true or that of Lobachevsky is false, is as absurd as to ask whether the metric system is true and that of the yard, foot, and inch, is false." (p. 145). This is one of the many articles that have been translated before and OCRed for this printing, creating a few glitches such as "superf1ous" for "superfluous" (p. 133). Pesic adds many notes, usually full of references. Many are useful, some are strange (I disagree with note 12, p. 70, and find note 1, p. 33, presumptuous). Pesic's reference hysteria is especially marked in his disorganised 16-page introduction, which has 49 footnotes. I think many readers would have benefited more from some pictures; this is a geometry book after all---why not some pictures of models of hyperbolic geometry, for instance?
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Mires: Swamp, Bog, Fen and Moor : Regional Studies
A. J. P., Ed. Gore
Manufacturer: Elsevier Science Publishing Company
ProductGroup: Book
Binding: Hardcover
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Wetlands
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ASIN: 0444420045 |
Book Description
Hardbound.
Books:
- Relativity Simply Explained
- Research Methods: A Process of Inquiry (4th Edition)
- Rosalind Franklin: The Dark Lady of DNA
- Science Instruction in the Middle and Secondary Schools: Developing Fundamental Knowledge and Skills for Teaching (6th Edition)
- Selected Papers on the Analysis of Algorithms
- Single Variable Calculus: Concepts and Contexts (with Tools for Enriching Calculus, Interactive Video Skillbuilder CD-ROM, and iLrn Homework/Personal Tutor with SMARTHINKING)
- Solar Observing Techniques (Patrick Moore's Practical Astronomy Series)
- Statistics: A Bayesian Perspective (Statistics)
- Still Life with Bombers: Israel in the Age of Terrorism
- Supreme Conflict: The Inside Story of the Struggle for Control of the United States Supreme Court
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