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Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to ha...
Stein Manifolds and Holomorphic Mappings
The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary.
XML and Web Technologies for Data Sciences with R
Web technologies are increasingly relevant to scientists working with data, for both accessing data and creating rich dynamic and interactive displays. The XML and JSON data formats are widely used in Web services, regular Web pages and JavaScript code, and visualization formats such as SVG and KML for Google Earth and Google Maps. In addition, scientists use HTTP and other network protocols to scrape data from Web pages, access REST and SOAP Web Services, and interact with NoSQL databases and text search applications. This book provides a practical hands-on introduction to these technologies, including high-level functions the authors have developed for data scientists. It describes strateg...
All India Civil List
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MIMO Wireless Networks
This book is unique in presenting channels, techniques and standards for the next generation of MIMO wireless networks. Through a unified framework, it emphasizes how propagation mechanisms impact the system performance under realistic power constraints. Combining a solid mathematical analysis with a physical and intuitive approach to space-time signal processing, the book progressively derives innovative designs for space-time coding and precoding as well as multi-user and multi-cell techniques, taking into consideration that MIMO channels are often far from ideal.Reflecting developments since the first edition was published, this book has been thoroughly revised, and now includes new secti...
Algebraic Cycles, Sheaves, Shtukas, and Moduli
Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.
Explorations in Complex and Riemannian Geometry
This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.
Analysis on Real and Complex Manifolds
Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincaré and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem. Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.
