**Author**: Peter M. Gruber,Jörg M. Wills

**Publisher:** North Holland

**ISBN:** 9780444895974

**Category:** Mathematics

**Page:** 765

**View:** 8336

Skip to content
# Free eBooks PDF

## Handbook of Convex Geometry

Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.
## Handbook of the Geometry of Banach Spaces

Handbook of the Geometry of Banach Spaces
## Handbook of Computational Geometry

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.
## Handbook of Discrete and Computational Geometry, Third Edition

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
## Handbook of Discrete and Computational Geometry, Third Edition

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
## Handbook of Discrete and Computational Geometry, Third Edition

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
## Handbook of Differential Geometry

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics
## Handbook of Analysis and Its Foundations

Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
## Handbook of the Geometry of Banach Spaces

The Handbook presents an overview of most aspects of modern Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.
## Computational Geometry

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.
## Convex and Discrete Geometry

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields.
## Means and Their Inequalities

Approach your problems from the right end It isn't !hat they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal 0/ Fa/her 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fie1ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "complete1y integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing c1assification schemes. They draw upon wide1y different sections of mathematics.
## Handbook of the Geometry of Banach Spaces

Encouraged by new perspectives in Banach space theory, the editors present this second volume that opens with an introductory essay that explains the basics of the theory. The rest of the chapters focus on specific directions of Banach space theory or its applications.
## Geometric Inequalities

A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.
## An Easy Path to Convex Analysis and Applications

Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical f
## An Introduction to the Geometry of Numbers

From the reviews: "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American Mathematical Monthly
## Handbook of Finsler geometry. 1 (2003)

There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook. The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M. Matsumoto. His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange Geometry) and J. Szilasi (Spray and Finsler Geometry). After studying either one of these, the reader will be able to understand the included survey articles on complex manifolds, holonomy, sprays and KCC-theory, symplectic structures, Legendre duality, Hodge theory and Gauss-Bonnet formulas. Finslerian diffusion theory is presented by its founders, P. Antonelli and T. Zastawniak. To help with calculations and conceptualizations, a CD-ROM containing the software package FINSLER, based on MAPLE, is included with the book.
## Convex Bodies: The Brunn–Minkowski Theory

A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
## Handbook of Semidefinite Programming

Semidefinite programming (SDP) is one of the most exciting and active research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. The Handbook of Semidefinite Programming offers an advanced and broad overview of the current state of the field. It contains nineteen chapters written by the leading experts on the subject. The chapters are organized in three parts: Theory, Algorithms, and Applications and Extensions.
## Geometry of Isotropic Convex Bodies

The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.

Just another PDF Download site

Mathematics

**Author**: Peter M. Gruber,Jörg M. Wills

**Publisher:** North Holland

**ISBN:** 9780444895974

**Category:** Mathematics

**Page:** 765

**View:** 8336

Mathematics

**Author**: N.A

**Publisher:** Elsevier

**ISBN:** 9780080533506

**Category:** Mathematics

**Page:** 870

**View:** 6288

Mathematics

**Author**: J.R. Sack,J. Urrutia

**Publisher:** Elsevier

**ISBN:** 9780080529684

**Category:** Mathematics

**Page:** 1075

**View:** 2895

Computers

**Author**: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

**Publisher:** CRC Press

**ISBN:** 1351645919

**Category:** Computers

**Page:** 1928

**View:** 2508

Computers

**Author**: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

**Publisher:** CRC Press

**ISBN:** 1351645919

**Category:** Computers

**Page:** 1928

**View:** 8172

Computers

**Author**: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

**Publisher:** CRC Press

**ISBN:** 1498711421

**Category:** Computers

**Page:** 1928

**View:** 6911

Mathematics

**Author**: Franki J.E. Dillen,Leopold C.A. Verstraelen

**Publisher:** Elsevier

**ISBN:** 9780080461205

**Category:** Mathematics

**Page:** 574

**View:** 6099

Mathematics

**Author**: Eric Schechter

**Publisher:** Academic Press

**ISBN:** 9780080532998

**Category:** Mathematics

**Page:** 883

**View:** 4723

Mathematics

**Author**: N.A

**Publisher:** Elsevier

**ISBN:** 9780080532806

**Category:** Mathematics

**Page:** 1016

**View:** 2126

Computers

*Algorithms and Applications*

**Author**: Mark de Berg

**Publisher:** Springer Science & Business Media

**ISBN:** 3540779736

**Category:** Computers

**Page:** 386

**View:** 4038

Mathematics

**Author**: Peter Gruber

**Publisher:** Springer Science & Business Media

**ISBN:** 3540711333

**Category:** Mathematics

**Page:** 580

**View:** 8079

Mathematics

**Author**: P.S. Bullen,Dragoslav S. Mitrinovic,M. Vasic

**Publisher:** Springer Science & Business Media

**ISBN:** 9401722269

**Category:** Mathematics

**Page:** 459

**View:** 5336

Mathematics

**Author**: William B. Johnson,Joram Lindenstrauss

**Publisher:** Elsevier

**ISBN:** 9780444513052

**Category:** Mathematics

**Page:** 1866

**View:** 7036

Mathematics

**Author**: Yurii D. Burago,Viktor A. Zalgaller

**Publisher:** Springer Science & Business Media

**ISBN:** 3662074419

**Category:** Mathematics

**Page:** 334

**View:** 4350

Mathematics

**Author**: Boris S. Mordukhovich,Nguyen Mau Nam

**Publisher:** Morgan & Claypool Publishers

**ISBN:** 1627052380

**Category:** Mathematics

**Page:** 218

**View:** 8668

Mathematics

**Author**: J.W.S. Cassels

**Publisher:** Springer Science & Business Media

**ISBN:** 3642620353

**Category:** Mathematics

**Page:** 345

**View:** 559

Mathematics

**Author**: Peter L. Antonelli

**Publisher:** Springer Science & Business Media

**ISBN:** 9781402015557

**Category:** Mathematics

**Page:** 1437

**View:** 6864

Mathematics

**Author**: Rolf Schneider

**Publisher:** Cambridge University Press

**ISBN:** 1107601010

**Category:** Mathematics

**Page:** 760

**View:** 3264

Business & Economics

*Theory, Algorithms, and Applications*

**Author**: Henry Wolkowicz,Romesh Saigal,Lieven Vandenberghe

**Publisher:** Springer Science & Business Media

**ISBN:** 1461543819

**Category:** Business & Economics

**Page:** 654

**View:** 9105

Mathematics

**Author**: Silouanos Brazitikos,Apostolos Giannopoulos,Petros Valettas,Beatrice-Helen Vritsiou

**Publisher:** American Mathematical Soc.

**ISBN:** 1470414562

**Category:** Mathematics

**Page:** 594

**View:** 2124