Lectures in Mathematics. ETH Zürich – serie
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28 produkter
Selected Chapters in the Calculus of Variations
Av Jürgen Moser
Häftad, 2003
551 kr
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0.1 Introduction These lecture notes describe a new development in the calculus of variations which is called Aubry-Mather-Theory. The starting point for the theoretical physicist Aubry was a model for the descrip tion of the motion of electrons in a two-dimensional crystal. Aubry investigated a …
Optimal Stopping and Free-Boundary Problems
Av Goran Peskir, Albert Shiryaev
Inbunden, 2006
1534 kr
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The book aims at disclosing a fascinating connection between optimal stoppingproblems in probability and free-boundary problems in analysis using minimal toolsand focusing on key examples. The general theory of optimal stopping is exposed at thelevel of basic principles in both discrete and …
Splinefunktionen
Av Carl de Boor
Häftad, 1990
543 kr
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Der Begriff der Splinefunktionen wurde von I. J. Schoenberg 1946 eingefUhrt. "Spline" ist der Name eines Zeichengerates, welches auf mechanischem Weg Interpolatio- aufgaben lost. Dieses Gerat besteht aus einer flexiblen, oft mehrere Meter langen Latte, die auf dem Zeichenbrett aufliegt und dort an …
Numerical Methods for Conservation Laws
Häftad, 1992
498 kr
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These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, …
Teichmüller Theory in Riemannian Geometry
Häftad, 1992
660 kr
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These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical …
Compact Riemann Surfaces
Häftad, 1992
660 kr
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These notes form the contents of a Nachdiplomvorlesung given at the Forschungs- institut fur Mathematik of the Eidgenossische Technische Hochschule, Zurich from November, 1984 to February, 1985. Prof. K. Chandrasekharan and Prof. Jurgen Moser have encouraged me to write them up for inclusion in the …
Ball and Some Hilbert Problems
Häftad, 1994
551 kr
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As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine …
Convergence of Iterations for Linear Equations
Häftad, 1993
387 kr
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Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and focuses on …
Topics in Combinatorial Group Theory
Häftad, 1993
551 kr
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Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about …
Modules and Group Algebras
Häftad, 1996
332 kr
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The notes in this volume were written as a part of a Nachdiplom course that I gave at the ETH in the summer semester of 1995. The aim of my lectures was the development of some of the basics of the interaction of homological algebra, or more specifically the cohomology of groups, and modular …
Markov Processes and Differential Equations
Asymptotic Problems
Häftad, 1996
498 kr
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Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and …
Theorems on Regularity and Singularity of Energy Minimizing Maps
Av Leon Simon
Häftad, 1996
716 kr
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The aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set. Specialized knowledge in …
Some Aspects of Brownian Motion
Part II: Some Recent Martingale Problems
Av Marc Yor
Häftad, 1997
332 kr
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The following notes represent approximately the second half of the lectures I gave in the Nachdiplomvorlesung, in ETH, Zurich, between October 1991 and February 1992, together with the contents of six additional lectures I gave in ETH, in November and December 1993. Part I, the elder brother of the …
Nonpositive Curvature: Geometric and Analytic Aspects
Av Jürgen Jost
Häftad, 1997
551 kr
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The present book contains the lecture notes from a "Nachdiplomvorlesung", a topics course adressed to Ph. D. students, at the ETH ZUrich during the winter term 95/96. Consequently, these notes are arranged according to the requirements of organizing the material for oral exposition, and the level …
Topics in Disordered Systems
Häftad, 1997
333 kr
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Disordered systems are statistical mechanics models in random environments. This lecture notes volume concerns the equilibrium properties of a few carefully chosen examples of disordered Ising models. The approach is that of probability theory and mathematical physics, but the subject matter is of …
Time-dependent Partial Differential Equations and Their Numerical Solution
Av Heinz-Otto Kreiss, Hedwig Ulmer Busenhart
Häftad, 2001
551 kr
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In these notes we study time-dependent partial differential equations and their numerical solution. The analytic and the numerical theory are developed in parallel. For example, we discuss well-posed linear and nonlinear problems, linear and nonlinear stability of difference approximations and …
Spatial Branching Processes, Random Snakes and Partial Differential Equations
Häftad, 1999
552 kr
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In these lectures, we give an account of certain recent developments of the theory of spatial branching processes. These developments lead to several fas cinating probabilistic objects, which combine spatial motion with a continuous branching phenomenon and are closely related to certain …
Canonical Metrics in Kähler Geometry
Av Gang Tian
Häftad, 2000
825 kr
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There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kahler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring …
Introduction to Combinatorial Torsions
Häftad, 2001
607 kr
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This book is an extended version of the notes of my lecture course given at ETH in spring 1999. The course was intended as an introduction to combinatorial torsions and their relations to the famous Seiberg-Witten invariants. Torsions were introduced originally in the 3-dimensional setting by K. …
Geometry of the Group of Symplectic Diffeomorphism
Häftad, 2001
825 kr
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The group of Hamiltonian diffeomorphisms Ham(M, 0) of a symplectic mani fold (M, 0) plays a fundamental role both in geometry and classical mechanics. For a geometer, at least under some assumptions on the manifold M, this is just the connected component of the identity in the group of all …
Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems
Häftad, 2001
551 kr
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One of the most striking development of the last decades in the study of minimal surfaces, constant mean surfaces and harmonic maps is the discovery that many classical problems in differential geometry - including these examples - are actually integrable systems. This theory grew up mainly after …
Hyperbolic Systems of Conservation Laws
The Theory of Classical and Nonclassical Shock Waves
Häftad, 2002
551 kr
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This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000. I would like to thank the faculty of the Mathematics Department, and especially Rolf Jeltsch and Michael Struwe, for giving me …
Introduction to the Baum-Connes Conjecture
Häftad, 2002
551 kr
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A quick description of the conjecture The Baum-Connes conjecture is part of Alain Connes'tantalizing "noncommuta- tive geometry" programme [18]. It is in some sense the most "commutative" part of this programme, since it bridges with classical geometry and topology. Let r be a countable group. The …
Counting, Sampling and Integrating: Algorithms and Complexity
Av Mark Jerrum
Häftad, 2003
825 kr
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These notes had their origin in a postgraduate lecture series I gave at the Eid genossiche Technische Hochschule (ETH) in Zurich in the Spring of 2000. I am very grateful to my hosts, the Forschungsinstitut fUr Mathematik at ETH, for providing the ideal opportunity to develop and present this …
Adaptive Finite Element Methods for Differential Equations
Av Wolfgang Bangerth, Rolf Rannacher
Häftad, 2003
550 kr
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These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are …
Gradient Flows
In Metric Spaces and in the Space of Probability Measures
Av Luigi Ambrosio, Nicola Gigli m. fl.
Häftad, 2008
1316 kr
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The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. …
