Author: Jing-song Huang
Publisher: World Scientific
ISBN: 9814495379
Category : Mathematics
Languages : en
Pages : 200
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Book Description
This book is an expanded version of the lectures given at the Nankai Mathematical Summer School in 1997. It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory. It only assumes that the reader has a good knowledge of linear algebra and some basic knowledge of abstract algebra.Parts I-III of the book cover the relatively elementary material of representation theory of finite groups, simple Lie algebras and compact Lie groups. These theories are natural continuation of linear algebra. The last chapter of Part III includes some recent results on extension of Weyl's construction to exceptional groups. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.
Author: Ariel Rubinstein
Publisher: Princeton University Press
ISBN: 1400842468
Category : Business & Economics
Languages : en
Pages : 167
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Book Description
Ariel Rubinstein's well-known lecture notes on microeconomics—now fully revised and expanded This book presents Ariel Rubinstein's lecture notes for the first part of his well-known graduate course in microeconomics. Developed during the fifteen years that Rubinstein taught the course at Tel Aviv University, Princeton University, and New York University, these notes provide a critical assessment of models of rational economic agents, and are an invaluable supplement to any primary textbook in microeconomic theory. In this fully revised and expanded second edition, Rubinstein retains the striking originality and deep simplicity that characterize his famously engaging style of teaching. He presents these lecture notes with a precision that gets to the core of the material, and he places special emphasis on the interpretation of key concepts. Rubinstein brings this concise book thoroughly up to date, covering topics like modern choice theory and including dozens of original new problems. Written by one of the world's most respected and provocative economic theorists, this second edition of Lecture Notes in Microeconomic Theory is essential reading for students, teachers, and research economists. Fully revised, expanded, and updated Retains the engaging style and method of Rubinstein's well-known lectures Covers topics like modern choice theory Features numerous original new problems—including 21 new review problems Solutions manual (available only to teachers) can be found at: http://gametheory.tau.ac.il/microTheory/.
Author: John Erik Fornæss
Publisher: American Mathematical Soc.
ISBN: 9780821869499
Category : Mathematics
Languages : en
Pages : 264
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Book Description
Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornaess and Stensones look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex variables. The counterexamples cover a variety of important topics: the Levi problem, plurisubharmonic functions, Monge-Ampere equations, CR geometry, function theory, and the $\bar\partial$ equation. The book would be an excellent supplement to a graduate course on several complex variables.
Author: Gerd Faltings
Publisher: Princeton University Press
ISBN: 9780691025445
Category : Mathematics
Languages : en
Pages : 120
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Book Description
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Author: N. Bellomo
Publisher: World Scientific
ISBN: 9789810221669
Category : Science
Languages : en
Pages : 276
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Book Description
This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.
Author: Werner Ballmann
Publisher: Birkhäuser
ISBN: 3034892403
Category : Mathematics
Languages : en
Pages : 114
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Book Description
Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.
Author: Vančo Litovski
Publisher: Springer Nature
ISBN: 9819950953
Category : Technology & Engineering
Languages : en
Pages : 691
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Book Description
This book is mostly devoted to amplification of analogue signals. It covers different technologies (bipolar, MOS, and MES), and different frequency ranges but it always deals with small signals. Analogue signals processed in electronic system may have a wide variety of origins. Among them we have the signals coming from sensors (electro-mechanical, electro-magnetic, electro-chemical, electro-acoustic, electro-optical, etc.), the signals coming from antennas being produced by another electronic system or are simply cosmic produced, and signals that are generated within the electronic systems. The common property of most of the signals is their small amplitude. In many cases it is below a micro-volt. Since at the output of the system we most frequently need a high amplitude signal the main action undertaken in the electronic system before any further processing is to amplify.
Author:
Publisher:
ISBN:
Category : Graph theory
Languages : en
Pages : 394
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Book Description
Author: Jackson R. Herring
Publisher: World Scientific
ISBN: 9789971508272
Category : Science
Languages : en
Pages : 392
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Book Description
This book is a formal presentation of lectures given at the 1987 Summer School on Turbulence, held at the National Center for Atmospheric Research under the auspices of the Geophysical Turbulence Program. The lectures present in detail certain of the more challenging and interesting current turbulence research problems in engineering, meteorology, plasma physics, and mathematics. The lecturers-Uriel Frisch (Mathematics), Douglas Lilly (Meteorology), David Montgomery (Plasma Physics), and Hendrik Tennekes (Engineering) ? are distinguished for both their research contributions and their abilities to communicate these to students with enthusiasm. This book is distinguished by its simultaneous focus on the fundamentals of turbulent flows (in neutral and ionized fluids) and on a presentation of current research tools and topics in these fields.
Author: John Tappan Stoddard
Publisher:
ISBN:
Category : Chemistry
Languages : en
Pages : 148
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Book Description
