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This book gives an introduction to the field of Incidence Geometry by discussing the basic families of pointline geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a selfcontained introduction to strongly regular and distanceregular graphs. This book is essentially selfcontained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.
Mathematics.  Geometry.  Geometry, Projective.  Geometry, Modern.  Modern geometry  Projective geometry  Sphere  Geometry, Modern  Mathematics  Euclid's Elements
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This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of elementary Linear Algebra.
Mathematics.  Algebraic geometry.  Projective geometry.  Projective Geometry.  Algebraic Geometry.  Projective geometry  Algebraic geometry  Math  Geometry, algebraic.  Geometry  Geometry, Projective.  Geometry, Modern
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In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, andfor the irreducible casethe function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.
Topology.  Continuous groups.  Geometry, Projective.  Projective geometry  Geometry, Modern  Groups, Continuous  Differential equations  Group theory  Analysis situs  Position analysis  Rubbersheet geometry  Geometry  Polyhedra  Set theory  Algebras, Linear
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This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly selfcontained study of classical varieties over a finite field, related incidence structures and particular point sets in finite ndimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.
Geometry  Mathematics  Physical Sciences & Mathematics  Geometry, Projective.  Galois theory.  Projective geometry  Geometry, Modern  Equations, Theory of  Group theory  Number theory  Combinatorics.  Geometry, algebraic.  Projective Geometry.  Algebraic Geometry.  Algebraic geometry  Combinatorics  Algebra  Mathematical analysis  Projective geometry.  Algebraic geometry.
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This book introduces electric circuits with variable loads and voltage regulators. It allows to define invariant relationships for various parameters of regime and circuit sections and to prove the concepts characterizing these circuits. The book presents the fundamentals of electric circuits and develops circuit theorems. Generalized equivalent circuits are introduced. Projective geometry is used for the interpretation of changes of operating regime parameters. Expressions of normalized regime parameters and their changes are presented. Convenient formulas for the calculation of currents are given. Parallel voltage sources and the cascade connection of multiport networks are described. The twovalue voltage regulation characteristics of loads with limited power of voltage source is considered. This second edition is extended and contains additional chapters on circuits with nonlinear regulation curves, circuits with nonlinear load characteristics, concepts of powersource and powerload elements with twovalued characteristics, quasiresonant voltage converters with selflimitation of current as well as the similarity of characteristics of converters and electronic devices. This book is useful to engineers, researchers and graduate students who are interested in the basic electric circuit theory and the regulation and monitoring of power supply systems. .
Electrical Engineering  Electrical & Computer Engineering  Engineering & Applied Sciences  Electric circuit analysis  Geometry, Projective.  Methodology.  Projective geometry  Circuit analysis, Electric  Geometry, Modern  Electric circuits  Electric network analysis  Production of electric energy or.  Power Electronics, Electrical Machines and Networks.  Electronic Circuits and Devices.  Semiconductors.  Energy Systems.  Electrical engineering  Power electronics.  Electronic circuits.  Energy systems.  Crystalline semiconductors  Semiconductors  Semiconducting materials  Semiconductor devices  Crystals  Electronics  Solid state electronics  Electrontube circuits  Electron tubes  Electronics, Power  Electric power  Materials
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