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SPIRES-BOOKS: FIND KEYWORD DISCRETE GROUPS *END*INIT* use /tmp/qspiwww.webspi1/2976.188 QRY 131.225.70.96 . find keyword discrete groups ( in books using www Cover
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Call number:9783319475127:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators: Groups, Geometry and Applications
Author(s):
Date:2017
Size:1 online resource (VIII, 239 p. 23 illus., 11 illus. in color p.)
Contents:Pseudo-Differential Operators on the Affine Group -- Pseudo-Differential Operators on Non-Isotropic Heisenberg Groups with Multi-Dimensional Center -- Curvatures of the Heisenberg Group -- Ellipticity with Global Projection Conditions
-- Multilinear Localization Operators Associated to Quaternion Fourier Transforms -- A Time-Frequency Relationship between the Langevin Equation and the Harmonic Oscillator -- Are There Quantum Operators and Wave Functions in Standard
Probability Theory -- A Class of Non-Markovian Pseudo-Differential Operators of Lévy Type -- On the Solvability of Some Systems of Integro-Differential Equations with Anomalous Diffusion -- Visualizing Discrete Complex-Valued
Time-Frequency Representations -- The Reassigned Spectrogram of the Stockwell transform -- Continuous Multi-Wavelet Transforms for Blind Signal Separation.
ISBN:9783319475127
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Operator theory , Partial differential equations , Information theory , Differential geometry , Probabilities , Mathematics , Operator Theory , Partial Differential Equations , Differential Geometry , Probability Theory and Stochastic Processes , Information and Communication, Circuits
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Call number:SPRINGER-2016-9783319270760:ONLINE Show nearby items on shelf
Title:Surfaces in Classical Geometries A Treatment by Moving Frames
Author(s): Gary R Jensen
Date:2016
Size:1 online resource (61 p.)
Note:10.1007/978-3-319-27076-0
Contents:1. Introduction -- 2. Lie Groups -- 3. Theory of Moving Frames -- 4. Euclidean Geometry -- 5. Spherical Geometry -- 6. Hyperbolic Geometry -- 7. Complex Structure -- 8. Minimal Immersions in Euclidean Space -- 9. Isothermic Immersions -- 10. The Bo nnet Problem -- 11. CMC 1 Surfaces in H3 -- 12. Möbius Geometry -- 13. Complex Structure and Möbius Geometry -- 14. Isothermic Immersions in Möbius Space -- 15. Lie Sphere Geometry -- Solutions to Select Problems -- References -- Index
ISBN:9783319270760
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Convex geometry , Discrete geometry , Differential geometry , Mathematics , Differential Geometry , Convex and Discrete Geometry
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Call number:SPRINGER-2016-9783319242989:ONLINE Show nearby items on shelf
Title:Recent Trends in Combinatorics
Author(s):
Date:2016
Size:1 online resource (14 p.)
Note:10.1007/978-3-319-24298-9
Contents:Section 1: Extremal and Probabilistic Combinatorics -- Problems Related to Graph Indices in Trees -- The edit distance in graphs: methods, results and generalizations -- Repetitions in graphs and sequences -- On Some Extremal Problems for Cycles in Graphs -- A survey of Turan problems for expansions -- Survey on matching, packing and Hamilton cycle problems on hypergraphs -- Rainbow Hamilton cycles in random graphs and hypergraphs -- Further applications of the Container Method -- Independent transv ersals and hypergraph matchings - an elementary approach -- Giant components in random graphs -- Infinite random graphs and properties of metrics -- Nordhaus-Gaddum Problems for Colin de Verdière Type Parameters, Variants of Tree-width, and Related Param eters -- Algebraic aspects of the normalized Laplacian -- Poset-free Families of Subsets.- Mathematics of causal sets -- Section 2: Additive and Analytic Combinatorics -- Lectures on Approximate groups and Hilbert's 5th Problem -- Character
sums and arithmetic combinatorics -- On sum-product problem -- Ajtai-Szemerédi Theorems over quasirandom groups -- Section 3: Enumerative and Geometric Combinatorics -- Moments of orthogonal polynomials and combinatorics -- The combinatorics of kno t invariants arising from the study of Macdonald polynomials -- Some algorithmic applications of partition functions in combinatorics -- Partition Analysis, Modular Functions, and Computer Algebra -- A survey of consecutive patterns in permutations -- Uni modality Problems in Ehrhart Theory -- Face enumeration on simplicial complexes -- Simplicial and Cellular Trees -- Parametric Polyhedra with at least k Lattice Points: Their Semigroup Structure and the k-Frobenius Problem.- Dynamical Algebraic Combinator ics and the Homomesy Phenomenon
ISBN:9783319242989
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:The IMA Volumes in Mathematics and its Applications: 159
Keywords: Mathematics , Dynamics , Ergodic theory , Functional analysis , Convex geometry , Discrete geometry , Combinatorics , Biomathematics , Mathematics , Combinatorics , Convex and Discrete Geometry , Dynamical Systems and Ergodic Theory , Functional Analysis , Genetics and Population Dynamics
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Call number:SPRINGER-2014-9783642553615:ONLINE Show nearby items on shelf
Title:Algebra, Geometry and Mathematical Physics [electronic resource] : AGMP, Mulhouse, France, October 2011
Author(s): Abdenacer Makhlouf
Eugen Paal
Sergei D Silvestrov
Alexander Stolin
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetriesand conservation laws and mathematical physics and applications, the book covers deformation theory and quantization Hom-algebras and n-ary algebraic structures Hopf algebra, integrable systems and related math structures jet theoryand Weil bundles Lie theory and applications non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures ofLie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry andapplications in physics and beyond. The book benefits a broad audience of researchers a nd advanced students
Contents:Part I Algebra
Part II Geometry
Part III Dynamical Symmetries and Conservation Laws
Part IV Mathematical Physics and Applications
ISBN:9783642553615
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v85
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry , Engineering mathematics
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Call number:SPRINGER-2014-9783319064475:ONLINE Show nearby items on shelf
Title:Regularity of Difference Equations on Banach Spaces [electronic resource]
Author(s): Ravi P Agarwal
Claudio Cuevas
Carlos Lizama
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevantresults. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research.This book is intended for graduate students and res earchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis
Contents:1.Discrete Semi groups and Cosine Operators
2. Maximal regularity and the method of Fourier Multipliers
3. First Order Linear Difference Equations
4. First Order Semi linear Difference Equations
5. Second Order Linear Difference Equations
6. Second Order Semi linear
7. Applications
ISBN:9783319064475
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional equations
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Call number:SPRINGER-2014-9781493907816:ONLINE Show nearby items on shelf
Title:Rigidity and Symmetry [electronic resource]
Author(s): Robert Connelly
Asia Ivi Weiss
Walter Whiteley
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry,algebra, and combinatorics . Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. Contributions present recent trends andadvances in discrete geometry, particularly in the the ory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry,group theory, classical geometry, hyperbolic geometry and topology. The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating thesurprising impact of symmetry. It will appeal to students at both the advanced undergraduate and grad uate levels, as well as postdocs, structural engineers, and chemists
Contents:Volumes of Polytopes in Spaces of Constant Curvature (N. Abrosimov, A. Mednykh)
Cubic Cayley Graphs and Snarks (H. Ademir, K. Kutnar, D. Marui)
Local, Dimensional and Universal Rigidities: A unified Gram Matrix Approach (A. Alfakih)
Geometric Constructions for Symmetric 6
Configurations (L.W. Berman)
On External Symmetry Groups of Regular Maps (M.D.E. Conder, Y.S. Kwon, J. ir)
Variance Groups and the Structure of Mixed Polytopes (G. Cunningham)
Mobility in Symmetry
Regular Bar
and
Joint Frameworks (P.W. Fowler, S.D. Guest, B. Schulze)
Generic Global Rigidity in C
ISBN:9781493907816
Series:eBooks
Series:SpringerLink
Series:Fields Institute Communications, 1069-5265 : v70
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Discrete groups , Topology
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Call number:SPRINGER-2013-9788847028418:ONLINE Show nearby items on shelf
Title:Geometric Properties for Parabolic and Elliptic PDE's [electronic resource]
Author(s): Rolando Magnanini
Shigeru Sakaguchi
Angelo Alvino
Date:2013
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understoodquite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad andwell-established research area, with contributions tha t often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name afew. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulatingfuture developments and perspectives in this very active area of research
Note:Springer eBooks
Contents:Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations
Elvise Berchio, A family of Hardy
Rellich type inequalities involving the L2
norm of the Hessian matrices
Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains
Lorenzo Brasco and Rolando Magnanini, The heart of a convex set
Giulio Ciraolo, A viscosity equation for minimizers of a class of very degenerate elliptic functionals
Adele Ferone, Kato's inequality in the half space: an alternative proof and relative i
ISBN:9788847028418
Series:e-books
Series:SpringerLink (Online service)
Series:Springer INdAM Series, 2281-518X : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Discrete groups , Global differential geometry , Mathematical optimization
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Call number:SPRINGER-2013-9783642393686:ONLINE Show nearby items on shelf
Title:Geometry of Continued Fractions [electronic resource]
Author(s): Oleg Karpenkov
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest inmultidimensional generalizati ons of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometricvision of continued fractions. It covers several appli cations to questions related tosuch areas asDiophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress inthe geometric theory of multidimensional continued fractions accompanied by current ly open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful forundergraduate or graduate courses
Note:Springer eBooks
Contents:Preface
Introduction
Part 1. Regular continued fractions: Chapter 1. Classical notions and definitions
Chapter 2. On integer geometry
Chapter 3. Geometry of regular continued fractions
Chapter 4. Complete invariant of integer angles
Chapter 5. Integer trigonometry for integer angles
Chapter 6. Integer angles of integer triangles
Chapter 7. Continued fractions and SL(2 Z) conjugacy classes. Elements of Gauss Reduction Theory. Markoff spectrum
Chapter 8. Lagrange theorem
Chapter 9. Gauss
Kuzmin statistics
Chapter 10. Geometric approximation aspects
Chapter 11
ISBN:9783642393686
Series:e-books
Series:SpringerLink (Online service)
Series:Algorithms and Computation in Mathematics, 1431-1550 : v26
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Discrete groups , Number theory
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Call number:SPRINGER-2013-9783642343643:ONLINE Show nearby items on shelf
Title:A Guide to the Classification Theorem for Compact Surfaces [electronic resource]
Author(s): Jean Gallier
Dianna Xu
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those withoutdetailed background know ledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy andformal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be awork-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincar characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learningwhere it is required, without interrupting the carefully planned structure of the core expositi on. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuineconfidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and val uable techniques available in algebraic topology
Note:Springer eBooks
Contents:The Classification Theorem: Informal Presentation
Surfaces
Simplices, Complexes, and Triangulations
The Fundamental Group, Orientability
Homology Groups
The Classification Theorem for Compact Surfaces
Viewing the Real Projective Plane in R3
Proof of Proposition 5.1
Topological Preliminaries
History of the Classification Theorem
Every Surface Can be Triangulated
Notes
ISBN:9783642343643
Series:e-books
Series:SpringerLink (Online service)
Series:Geometry and Computing, 1866-6795 : v9
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9783642333057:ONLINE Show nearby items on shelf
Title:Stochastic Geometry, Spatial Statistics and Random Fields [electronic resource] : Asymptotic Methods
Author(s): Evgeny Spodarev
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limittheorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers andresearchers interested in geometric probability and re lated subjects
Note:Springer eBooks
Contents:1 Foundations of stochastic geometry and theory of random sets
2 Introduction into integral geometry and stereology
3 Spatial point patterns models and statistics
4 Asymptotic methods in statistics of random point processes
5 Random tessellations and Cox processes
6 Asymptotic methods for random tessellations
7 Random polytopes
8 Limit theorems in discrete stochastic geometry
9 Introduction to random fields
10 Central limit theorems for weakly dependent random fields
11 Strong limit theorems for increments of random fields
12 Geometry of large random trees:
ISBN:9783642333057
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2068
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups , Distribution (Probability theory) , Mathematical statistics
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Call number:SPRINGER-2013-9783319002002:ONLINE Show nearby items on shelf
Title:Discrete Geometry and Optimization [electronic resource]
Author(s): Karoly Bezdek
Antoine Deza
Yinyu Ye
Date:2013
Publisher:Heidelberg : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplaybetween these subjects. Th e purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to furtherstimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas. The inspiring Fejes Tth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified thisapproach. While these fields have recently witnessed a lot of activity a nd successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial timealgorithm for linear optimization is one of the most important unsolved problems at the beginning o f the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections betweendifferent approaches, and features novel results and state-of-the-art surveys as well as open problems
Note:Springer eBooks
Contents:Preface
Discrete Geometry in Minkowski Spaces (Alonso, Martini, and Spirova)
Engineering Branch
and
Cut Algorithms for the Equicut Program (Anjos, Liers, Pardella, and Schmutzer)
An Approach to the Dodecahedral Conjecture Based on Bounds for Spherical Codes (Anstreicher)
On Minimal Tilings with Convex Cells Each Containing a Unit Ball (Bezdek)
On Volumes of Permutation Polytopes (Burggraf, De Loera, and Omar)
Monotone Paths in Planar Convex Subdivisions and Polytopes (Dumitrescu, Rote, and Toth)
Complexity of the Positive Semidefinite Matrix Completion Problem with a Rank
ISBN:9783319002002
Series:e-books
Series:SpringerLink (Online service)
Series:Fields Institute Communications, 1069-5265 : v69
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups
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Call number:SPRINGER-2013-9783034804875:ONLINE Show nearby items on shelf
Title:Arithmetic and Geometry Around Galois Theory [electronic resource]
Author(s): Pierre Dbes
Michel Emsalem
Matthieu Romagny
A. Muhammed Uluda
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This Lecture Notes volume isthe fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): Geometry and Arithmetic of Moduli Spacesof Coverings (2008) and Geome try and Arithmetic around Galois Theory (2009). The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern pointsof view on Galois theory and related moduli problems, us ing stacks, gerbes and groupoids. It contains lecture notes on tale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articlescomplete the collection
Note:Springer eBooks
Contents:Preface
J. Bertin: Algebraic stacks with a view toward moduli stacks of covers
M. Romagny: Models of curves
A. Cadoret: Galois categories:
M. Emsalem. Fundamental groupoid scheme
N. Borne: Extension of Galois groups by solvable groups, and application to fundamental groups of curves
M.A. Garuti: On the Galois closure for finite morphisms
J
C. Douai: Hasse Principle and Cohomology of Groups
Z. Wojtkowiak: Periods of mixed Tate motives, examples, l
adic side
L. Bary
Soroker and E. Paran: On totally ramified extensions of discrete valued fields
R
P. Holzapfel a
ISBN:9783034804875
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v304
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Field theory (Physics) , Group theory
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Call number:SPRINGER-2013-9783034804813:ONLINE Show nearby items on shelf
Title:Complex Kleinian Groups [electronic resource]
Author(s): Angel Cano
Juan Pablo Navarrete
Jos Seade
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph lays down the foundations of the theory of complex Kleinian groups, a newborn area of mathematics whose origin can be traced back to the work of Riemann, Poincar, Picard and many others. Kleinian groupsare, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions,there is a dichotomy: Should we look at conformal automorp hisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In thefirst case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition in the second, about an area of mathematics that is still in its infancy, and this is the focus ofstudy in this monograph. It brings together several important areas of mathematics, e.g. classical Kleini an group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds
Note:Springer eBooks
Contents:Preface
Introduction
Acknowledgments
1 A glance of the classical theory
2 Complex hyperbolic geometry
3 Complex Kleinian groups
4 Geometry and dynamics of automorphisms of P2C
5 Kleinian groups with a control group
6 The limit set in dimension two
7 On the dynamics of discrete subgroups of PU(n,1)
8 Projective orbifolds and dynamics in dimension two
9 Complex Schottky groups
10 Kleinian groups and twistor theory
Bibliography
Index.
ISBN:9783034804813
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v303
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Differentiable dynamical systems , Differential equations, partial
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Call number:SPRINGER-2013-9781461487814:ONLINE Show nearby items on shelf
Title:Ricci Flow for Shape Analysis and Surface Registration [electronic resource] : Theories, Algorithms and Applications
Author(s): Wei Zeng
Xianfeng David Gu
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Ricci Flow for Shape Analysis and Surface Registration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate calculus, readers can deduce all themajor theorems in surfac e Ricci flow by themselves. The authors adapttheRicci flow theory to practical computational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricciflow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network. Due to minimal pre-requisites, this bookis accessible toengineersand medicalexperts, including educators,researchers, students and industry engineerswhohave an interest insolvingreal problems related to shape analysis and surface registration.
Note:Springer eBooks
Contents:1. Introduction
2. Computational
3.Computational Geometry
4. Differential Geometry of Surface
5. Riemann Surface
6. Ricci Flow
7. Topological Algorithms
8. Harmonic Maps
9. Discrete Ricci Flow
10. Shape Analysis
11. Surface Diffeomorphism
12. Medical Imaging Applications
13. Computer Vision Applications
14. Computer Graphics Applications
15. Network Applications.
ISBN:9781461487814
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer vision , Computer science Mathematics , Geometry , Discrete groups
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Call number:SPRINGER-2013-9781461481188:ONLINE Show nearby items on shelf
Title:Lectures on Sphere Arrangements the Discrete Geometric Side [electronic resource]
Author(s): Kroly Bezdek
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph gives a short introduction to parts of modern discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate andearly graduate stude nts, as well as interested researchers. It contains 30 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for aone-semester advanced undergraduate or grad uate level course. The core of this book is based on three lectures given by the author at the Fields Institute during the thematic program on Discrete Geometry and Applications andcontains four basic topics. The first two deal with active areas that hav e been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection tonumber theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The thirdmajor topic can be found under the sections on ball-polyhedra that study the possibility of extending the theory of co nvex polytopes to the family of intersections of congruent balls. This section of the text is connected in many waysto the above-mentioned major topics as well as to some other important research areas such as that on coverings by planks (with close ties to geometric analysis). The fourth basic topic is discussed under covering balls by cylinders.
Note:Springer eBooks
Contents:1. Unit Sphere Packings
2. Proofs on Unit Sphere Packings
3. Contractions of Sphere Arrangements
4. Proofs on Contractions of Sphere Arrangements
5. Ball
Polyhedra and Spindle Convex Bodies
6. Proofs on Ball
Polyhedra and Spindle Convex Bodies
7. Coverings by Cylinders
8. Proofs on Coverings by Cylinders
9. Research Problems
an Overview
Glossary
References
ISBN:9781461481188
Series:e-books
Series:SpringerLink (Online service)
Series:Fields Institute Monographs, 1069-5273 : v32
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups
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Call number:SPRINGER-2013-9781461479727:ONLINE Show nearby items on shelf
Title:Harmonic Analysis on Symmetric SpacesEuclidean Space, the Sphere, and the Poincar Upper Half-Plane [electronic resource]
Author(s): Audrey Terras
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar upper half plane. This book is intended for beginning graduate students inmathematics or researchers in phy sics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, andengineering. Many corrections, new topics, and updates have be en incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T.Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question Can y ou hear the shape of a drum?, Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maasswaveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summationformula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon tr ansform, non-Euclidean geometry on the Poincar upper half plane H or unit disc andapplications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg tra ce formula and its applications in spectral theory as wellas number theory
Note:Springer eBooks
Contents:Chapter1 Flat Space. Fourier Analysis on R^m
1.1 Distributions or Generalized Functions
1.2 Fourier Integrals
1.3 Fourier Series and the Poisson Summation Formula
1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions
1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyls Criterion for Uniform Distribution
Chapter2 A Compact Symmetric Space
The Sphere
2.1 Fourier Analysis on the Sphere
2.2 O(3) and R^3. The Radon Transform
Chapter 3 The Poincar Upper Half
Plane
3.1 Hyperbolic Geometry
3.2 Harmonic Analysis on H
3.3 Fundamental Domains for
ISBN:9781461479727
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Topological Groups , Harmonic analysis , Fourier analysis , Functions of complex variables , Functions, special
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Call number:SPRINGER-2013-9781461472582:ONLINE Show nearby items on shelf
Title:The Mathematics of Paul Erds I [electronic resource]
Author(s): Ronald L Graham
Jaroslav Neetil
Steve Butler
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This is the most comprehensive survey of the mathematical life of the legendary Paul Erds (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erds'research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles aswell as key articles that survey some of the cornerst ones of Erds' work, each written by a leading world specialist in the field. A special chapter Early Days, rare photographs, and art related to Erds complement this strikingcollection. A unique contribution is the bibliography on Erds' publications: the m ost comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erds' birth, contains updates on many of the articlesfrom the two volumes of the first edition, several new articles from prominent mathematicians, a new introd uction, more biographical information about Paul Erds, and an updated list of publications. The first volume contains theunique chapter Early Days, which features personal memories of Paul Erds by a number of his colleagues. The other three chapters cover number theory, random methods, and geometry. All of these chapters are essentially updated,most notably the geometry chapter that covers the recent solution of the problem on the number of distinct distances in finite planar sets, which was the most popu lar of Erds' favorite geometry problems
Note:Springer eBooks
Contents:VOLUME I
Paul Erds Life and Work
Paul Erds Magic
Part I Early Days
Introduction
Some of My Favorite Problems and Results
3 Encounters with Paul Erds
4 Did Erds Save Western Civilization?
Integers Uniquely Represented by Certain Ternary Forms
Did Erds Save Western Civilization?
Encounters with Paul Erds
On Cubic Graphs of Girth at Least Five
Part II Number Theory
Introduction
Cross
disjoint Pairs of Clouds in the Interval Lattice
Classical Results on Primitive and Recent Results on Cross
Primitive Sequences
Dense Difference Sets a
ISBN:9781461472582
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups , Number theory , Distribution (Probability theory)
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Call number:SPRINGER-2013-9781461464068:ONLINE Show nearby items on shelf
Title:Asymptotic Geometric Analysis [electronic resource] : Proceedings of the Fall 2010 Fields Institute Thematic Program
Author(s): Monika Ludwig
Vitali D Milman
Vladimir Pestov
Nicole Tomczak-Jaegermann
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as thedimension tends to inf inity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in theFall of 2010 continued an established traditi on of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces *Concentration of measure and isoperimetric inequalities, optimal transport ation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Randommatrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working ina wide range of mathematical sciencesin particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science
Note:Springer eBooks
Contents:Preface
The Variance Conjecture on Some Polytopes (D. Alonso Gutirrez, J. Bastero)
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures (D. Bartosova)
On the Lyapounov Exponents of Schrodinger Operators Associated with the Standard Map (J. Bourgain)
Overgroups of the Automorphism Group of the Rado Graph (P. Cameron, C. Laflamme, M. Pouzet, S. Tarzi, R. Woodrow)
On a Stability Property of the Generalized Spherical Radon Transform (D. Faifman)
Banach Representations and Affine Compactification of Dynamical Systems (E. Glasner, M. Megrelishvili)
F
ISBN:9781461464068
Series:e-books
Series:SpringerLink (Online service)
Series:Fields Institute Communications, 1069-5265 : v68
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Functional analysis , Operator theory , Discrete groups , Distribution (Probability theory)
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Call number:SPRINGER-2013-9781461453925:ONLINE Show nearby items on shelf
Title:Interpolation and Sidon Sets for Compact Groups [electronic resource]
Author(s): Colin C Graham
Kathryn E Hare
Date:2013
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:Understanding special sets of integers was classically of interest to Hadamard, Zygmund and others, and continues to be of interest today. This book is a modern treatment of the subject of interpolation and Sidon sets. It is aunique book, aimed at bo th new and experienced researchers. In particular, this is the only book in Englishwhich featuresa complete treatment of the Pisier-Bourgain results on Sidon sets, many of which were originally in French, inhard to access publications. Applications of the P-B results, due to Pisier, Bourgain, Ramsey, and the authors are included.The book introduces the reader to a wealth of methods important in mathematics today: topological,probabilistic, algebraic, combinatoric and analytic. It prepares students to perf orm research in the area and provides both exercises and open problems. The book also provides direction to the literature for topics it does not fullycover. The book is self-contained, with appendices covering results that are required, but not necessari ly in the pre-requisite background of a student ready to choose an area for research in harmonic analysis
Note:Springer eBooks
Contents:Preface
Introduction
Hadamard Sets
$\epsilon$
Kronecker sets
Sidon sets: Introduction and decomposition properties
Characterizations of $I_0$ sets
Proportional characterizations of Sidon sets
Decompositions of $I_0$ sets
Sizes of thin sets
Sets of zero discrete harmonic density
Related results
Open problems
Appendices (Groups, Probability, Combinatoric results,...)
Bibliography
Author index
Subject index
Index of notation
ISBN:9781461453925
Series:e-books
Series:SpringerLink (Online service)
Series:CMS Books in Mathematics, Ouvrages de mathmatiques de la SMC, 1613-5237
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functional analysis
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Call number:SPRINGER-2013-9781461448976:ONLINE Show nearby items on shelf
Title:Recent Trends in Lorentzian Geometry [electronic resource]
Author(s): Miguel Snchez
MIguel Ortega
Alfonso Romero
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity,as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracteda renewed interest in this theoryfor many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energyphysics have been found, and further connection s with other geometries have been developed. Samplesof these fresh trends are presented in this volume, based on contributions from the VI International Meeting on LorentzianGeometry, held at the University of Granada, Spain, in September, 2011. Topics s uch as geodesics, maximal,trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations betweenLorentzian and Finslerian geometries, and applications to mathematical physics are included. This book wil l be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers inthe field
Note:Springer eBooks
ISBN:9781461448976
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v26
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups , Global differential geometry
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Call number:SPRINGER-2013-9781447148173:ONLINE Show nearby items on shelf
Title:Polyhedral and Algebraic Methods in Computational Geometry [electronic resource]
Author(s): Michael Joswig
Thorsten Theobald
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
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Note:Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementaryalgebraic geometry. The f irst part of the book studies classical problems and techniquesthat refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction ofVoronoi diagrams and Delone triangulations. The second p art of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Grbner bases and solving systems of polynomialequations. The theory is illustrated by applications in computer graphics, curve reconstr uction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry,optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineeringstudents who are interested in the applications of computational geometry
Note:Springer eBooks
Contents:Introduction and Overview
Geometric Fundamentals
Polytopes and Polyhedra
Linear Programming
Computation of Convex Hulls
Voronoi Diagrams
Delone Triangulations
Algebraic and Geometric Foundations
Grbner Bases and Buchbergers Algorithm
Solving Systems of Polynomial Equations Using Grbner Bases
Reconstruction of Curves
Plcker Coordinates and Lines in Space
Applications of Non
Linear Computational Geometry
Algebraic Structures
Separation Theorems
Algorithms and Complexity
Software
Notation
ISBN:9781447148173
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Algebra Data processing , Algorithms , Geometry , Discrete groups
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Call number:SPRINGER-2013-9781441979100:ONLINE Show nearby items on shelf
Title:A Course in Topological Combinatorics [electronic resource]
Author(s): Mark Longueville
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years withgrowing applications i n math, computer science, and other applied areas. Topological combinatorics is concerned with solutions to combinatorial problems by applying topological tools. In most cases these solutions are very elegant andthe connection between combinatorics and to pology often arises as an unexpected surprise. The textbook covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discretegeometry. The text contains a large number of figures that suppo rt the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given, and each chapter ends with a series of exercises. Theextensive appendix makes the book completely self-contained. The textbook is well sui ted for advanced undergraduate or beginning graduate mathematics students. Previous knowledge in topology or graph theory is helpful but notnecessary. The text may be used as a basis for a one- or two-semester course as well as a supplementary text for a topology or combinatorics class
Note:Springer eBooks
Contents:Preface
List of Symbols and Typical Notation
1 Fair
Division Problems
2 Graph
Coloring Problems
3 Evasiveness of Graph Properties
4 Embedding and Mapping Problems
A Basic Concepts from Graph Theory
B Crash Course in Topology
C Partially Ordered Sets, Order Complexes, and Their Topology
D Groups and Group Actions
E Some Results and Applications from Smith Theory
References
Index
ISBN:9781441979100
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Discrete groups
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Call number:SPRINGER-2012-9783642308055:ONLINE Show nearby items on shelf
Title:An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists [electronic resource]
Author(s): Hajime Ishimori
Tatsuo Kobayashi
Hiroshi Ohki
Hiroshi Okada
Yusuke Shimizu
Morimitsu Tanimoto
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics.While Abelian discrete sym metries are often imposed in order to control couplings for particle physics - in particular model building beyond the standard model - non-Abelian discrete symmetries have been applied to understand thethree-generation flavor structure in particular. Ind eed, non-Abelian discrete symmetries are considered to be the most attractive choice for the flavor sector: model builders have tried to derive experimental values of quark andlepton masses, and mixing angles by assuming non-Abelian discrete flavor symmet ries of quarks and leptons, yet, lepton mixing has already been intensively discussed in this context, as well. The possible origins of the non-Abeliandiscrete symmetry for flavors is another topic of interest, as they can arise from an underlying theory - e.g. the string theory or compactification via orbifolding thereby providing a possible bridge between the underlying theoryand the corresponding low-energy sector of particle physics. This text explicitly introduces and studies the group-theoretical a spects of many concrete groups and shows how to derive conjugacy classes, characters, representations,and tensor products for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest
Note:Springer eBooks
Contents:Introduction
Basics of Finite Groups
Subgroups and Decompositions of Multiplets
Anomalies
Non
Abelian Discrete Symmetry in Quark/Lepton Flavor Models
Useful Theorems
Representations of S4 in Different Bases
Representations of A4 in Different Bases
Representations of A5 in Different Bases
Representations of T1 in Different Bases
Other Smaller Groups
References
ISBN:9783642308055
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v858
Series:Physics and Astronomy (Springer-11651)
Keywords: Group theory , Mathematical physics , Quantum theory
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Call number:SPRINGER-2012-9783642298493:ONLINE Show nearby items on shelf
Title:Geometric Aspects of Functional Analysis [electronic resource] : Israel Seminar 20062010
Author(s): Bo'az Klartag
Shahar Mendelson
Vitali D Milman
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the generaltrends of Asymptotic Geome tric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convexbodies, inequalities involving volumes of such bo dies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensionalspaces and characterization of classical constructions in Geometry an d Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers
Note:Springer eBooks
Contents:The
Cosine Transform and Intertwining Integrals on Real Grassmannians
On Modules Over Valuations
On Multiplicative Maps of Continuous and Smooth Functions
Order Isomorphisms on Convex Functions in Windows
Finite Transitive Graph Embeddings into a Hyperbolic
Metric Space Must Stretch or Squeeze
Tightness of Fluctuations of First Passage Percolation on Some Large Graphs
Finitely Supported Measures on SL2(R) which are Absolutely Continuous at Infinity
Interpolations, Convexity and Geometric Inequalities
Hypercontractive Measures, Talagrand's Inequality, and Inuences
ISBN:9783642298493
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2050
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Discrete groups , Distribution (Probability theory)
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Call number:SPRINGER-2012-9783642278754:ONLINE Show nearby items on shelf
Title:Sparsity [electronic resource] : Graphs, Structures, and Algorithms
Author(s): Jaroslav Neetil
Patrice Ossona de Mendez
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authorsdevised an unifying clas sification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremalcombinatorial invariants. This study of sparse str uctures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphismpreservation,fixed parameter tractability and constraint satisfaction prob lems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Neetil is a professor atCharles University, Prague Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010
Note:Springer eBooks
Contents:Part I Presentation: 1. Introduction
2. A Few Problems
3. Commented Contents
Part II. The Theory: 4. Prolegomena
5. Measuring Sparsity
6. Classes and their Classification
7. Bounded Height Trees and Tree
Depth
8. Decomposition
9. Independence
10. First
Order Constraint Satisfaction Problems and Homomorphism Dualities
11. Restricted Homomorphism Dualities
12. Counting
13. Back to Classes
Part III Applications: 14. Classes with Bounded Expansion Examples
15. Property Testing, Hyperfiniteness and Separators
16. Algorithmic Applications
17. Other
ISBN:9783642278754
Series:e-books
Series:SpringerLink (Online service)
Series:Algorithms and Combinatorics, 0937-5511 : v28
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer software , Computational complexity , Combinatorics , Discrete groups , Logic, Symbolic and mathematical
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Call number:SPRINGER-2012-9783642154829:ONLINE Show nearby items on shelf
Title:Symmetries and Group Theory in Particle Physics [electronic resource] : An Introduction to Space-Time and Internal Symmetries
Author(s): Giovanni Costa
Gianluigi Fogli
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is anintroduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of theMinkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standardmodel of particle physics. This book, based on several courses given by th e authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge ofclassical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures
Note:Springer eBooks
Contents:Introduction to Lie Groups and their Representations
The Rotation Group
The Homogeneous Lorentz Group
The Poincare Transformation
One Particle and Two Particle States
Discrete Operations
Relativistic Equations
Unitary Symmetries
Gauge Symmetries
Rotation Matrices and Clebsch
Gordan Coeficients
Symmetric Goups and Identical Particles
Young Tableaux and Irreducible Representations ot he Unitary Groups
Solutions
Index
ISBN:9783642154829
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v823
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematical physics , Quantum theory
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Call number:SPRINGER-2012-9783034804059:ONLINE Show nearby items on shelf
Title:Associahedra, Tamari Lattices and Related Structures [electronic resource] : Tamari Memorial Festschrift
Author(s): Folkert Mller-Hoissen
Jean Marcel Pallo
Jim Stasheff
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. Thiswas the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematicalwork. Tamari lattices ca n be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure andapplied mathematics, such as algebra, combinator ics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari'scentennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers inmathematics and mathematical physics and are accompanied by high quality illustrations
Note:Springer eBooks
ISBN:9783034804059
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v299
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Discrete groups , Number theory , Algebraic topology
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Call number:SPRINGER-2012-9781461445593:ONLINE Show nearby items on shelf
Title:Bridging Mathematics, Statistics, Engineering and Technology [electronic resource] : Contributions from the Fall 2011 Seminar on Mathematical Sciences and Applications
Author(s): Bourama Toni
Keith Williamson
Nasser Ghariban
Dawit Haile
Zhifu Xie
Date:2012
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Springer eBooks
ISBN:9781461445593
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v24
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups
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Call number:SPRINGER-2012-9781461407768:ONLINE Show nearby items on shelf
Title:Representation Theory of Finite Groups [electronic resource] : An Introductory Approach
Author(s): Benjamin Steinberg
Date:2012
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Representation Theory of Finite Groups presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linearalgebra, group theory, a nd very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted.Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader. The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside'spq-theorem and the dimension theorem, permutation representations, indu ced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probabilityand statistics, a chapter on random walks on finite groups serves as an illustration to link finite stochastics and representation theory. Applications to the spectral theory of graphs are given to help the student appreciate theusefulness of the subject and the author provides motivation and a gentle style throughout the text. A number of exerci ses add greater dimension to the understanding of the subject and some aspects of a combinatorial nature are clearlyshown in diagrams. This text will engage a broad readership due to the significance of representation theory in diverse branches of mathema tics, engineering, and physics, to name a few. Its primary intended use is as a one semestertextbook for a third or fourth year undergraduate course or an introductory graduate course on group representation theory. The content can also be of use as a ref erence to researchers in all areas of mathematics, statistics, andseveral mathematical sciences
Note:Springer eBooks
ISBN:9781461407768
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2011-9783642220036:ONLINE Show nearby items on shelf
Title:Algebraic Topology of Finite Topological Spaces and Applications [electronic resource]
Author(s): Jonathan A Barmak
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makesfinite spaces a usefu l tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillens conjecture on the poset of p-subgroups ofa finite group and the Andrews-Curtis conjec ture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It isintended for topologists and combinatorialists, but it is also recom mended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology
Note:Springer eBooks
Contents:1 Preliminaries
2 Basic topological properties of finite spaces
3 Minimal finite models
4 Simple homotopy types and finite spaces
5 Strong homotopy types
6 Methods of reduction
7 h
regular complexes and quotients
8 Group actions and a conjecture of Quillen
9 Reduced lattices
10 Fixed points and the Lefschetz number
11 The Andrews
Curtis conjecture
ISBN:9783642220036
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2032
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Combinatorics , Discrete groups , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9783642172861:ONLINE Show nearby items on shelf
Title:Perspectives on Projective Geometry [electronic resource] : A Guided Tour Through Real and Complex Geometry
Author(s): Jrgen Richter-Gebert
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry.It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic andelliptic geometry or eve n relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications.In particular, itexplains how metric concepts may be best understood inprojective terms. One of the major themes that appears throughout this book is the beauty of the interplaybetweengeometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objectsand operations may be most elegantly expressed in algebraic terms, making it a va luable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the authors experience in implementinggeometric software and includes hundreds ofhigh-qualityillustrations
Note:Springer eBooks
Contents:1 Pappos's Theorem: Nine Proofs and Three Variations
2 Projective Planes
3 Homogeneous Coordinates
4 Lines and Cross
Ratios
5 Calculating with Points on Lines
6 Determinants
7 More on Bracket Algebra
8 Quadrilateral Sets and Liftings
9 Conics and Their Duals
10 Conics and Perspectivity
11 Calculating with Conics
12 Projective $d$
space
13 Diagram Techniques
14 Working with diagrams
15 Configurations, Theorems, and Bracket Expressions
16 Complex Numbers: A Primer
17 The Complex Projective Line
18 Euclidean Geometry
19 Euclidean Structures fr
ISBN:9783642172861
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algorithms , Visualization , Geometry , Discrete groups
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Call number:SPRINGER-2011-9783642111105:ONLINE Show nearby items on shelf
Title:Matroid Theory and its Applications [electronic resource]
Author(s): A Barlotti
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Lectures: T.H. Brylawski: The Tutte polynomial.- D.J.A. Welsh: Matroids and combinatorial optimisation.- Seminars: M. Barnabei, A. Brini, G.-C. Rota: Unintroduzione alla teoria delle funzioni di Mbius.- A. Brini: Someremarks on the critical problem.- J. Oxley: On 3-connected matroids and graphs.- R. Peele: The poset of subpartitions and Cayleys formula for the complexity of a complete graph.- A. Recski: Engineering applications of matroids.- T.Zaslavisky: Voltage-graphic matroids
Note:Springer eBooks
Contents:M. Barnabei, A. Brini, G
C. Rota: Unintroduzione alla teoria delle funzioni di Mbius
A. Brini: Some remarks on the critical problem
T.H. Brylawski: The Tutte polynomial
J. Oxley: On 3
connected matroids and graphs
R. Peele: The poset of subpartitions and Cayleys formula for the complexity of a complete graph
A. Recski: Engineering applications of matroids
D.J.A. Welsh: Matroids and combinatorial optimisation
T. Zaslavisky: Voltage
graphic matroids
ISBN:9783642111105
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v83
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups
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Call number:SPRINGER-2011-9781461411291:ONLINE Show nearby items on shelf
Title:The Kepler Conjecture [electronic resource] The Hales-Ferguson Proof
Author(s): Jeffrey C Lagarias
Date:2011
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing ofthree-dimensional Euclidean space by equal spheres is attained by the cannonball packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use ofcomputers. This book centers around six papers, prese nting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry. Further supporting materialis also presented: a follow-up paper of Hales et al (2010) revising the pr oof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales thatindicate his original approach to the conjecture. The editor's two introductory chapters situate th e conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature ofthis work. Thomas C. Hales, Mellon Professor of Mathematics at the University of Pittsburgh, began his efforts to solve th e Kepler conjecture before 1992. He is a pioneer in the use of computer proof techniques, and he continues workon a formal proof of the Kepler conjecture as the aim of the Flyspeck Project (F, P and K standing for Formal Proof of Kepler). Samuel P. Fergus on completed his doctorate in 1997 under the direction of Hales at the University ofMichigan. In 1995, Ferguson began to work with Hales and made significant contributions to the proof of the Kepler conjecture. His doctoral work established one crucial ca se of the proof, which appeared as a singly authored paper inthe detailed proof. Jeffrey C. Lagarias, Professor of Mathematics at the University of Michigan, Ann Arbor, was a co-guest editor, with G
Note:Springer eBooks
Contents:Preface
Part I, Introduction and Survey
1 The Kepler Conjecture and Its Proof, by J. C. Lagarias
2 Bounds for Local Density of Sphere Packings and the Kepler Conjecture, by J. C. Lagarias
Part II, Proof of the Kepler Conjecture
Guest Editor's Foreword
3 Historical Overview of the Kepler Conjecture, by T. C. Hales
4 A Formulation of the Kepler Conjecture, by T. C. Hales and S. P. Ferguson
5 Sphere Packings III. Extremal Cases, by T. C. Hales
6 Sphere Packings IV. Detailed Bounds, by T. C. Hales
7 Sphere Packings V. Pentahedral Prisms, by S. P. Ferguson
8 Sphere
ISBN:9781461411291
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups
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Call number:SPRINGER-2011-9780817680923:ONLINE Show nearby items on shelf
Title:Ramsey Theory [electronic resource] : Yesterday, Today, and Tomorrow
Author(s): Alexander Soifer
Date:2011
Edition:1
Publisher:Boston, MA : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
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Note:Ramsey theory is a relatively new, approximately 100 year-old direction of fascinating mathematical thought that touches on many classic fields of mathematics such as combinatorics, number theory, geometry, ergodic theory,topology, combinatorial geom etry, set theory, and measure theory. Ramsey theory possesses its own unifying ideas, and some of its results are among the most beautiful theorems of mathematics. The underlying theme of Ramsey theory canbe formulated as: any finite coloring of a large e nough system contains a monochromatic subsystem of higher degree of organization than the system itself, or as T.S. Motzkin famously put it, absolute disorder is impossible. RamseyTheory: Yesterday, Today, and Tomorrow explores the theorys history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys providehistorical background on the subject the last three address Euclidean Ramsey theory and related color ing problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal tograduate students and mathematicians alike. Contributors: J. Burkert, A. Dudek, R.L. Graham, A. Gyrfs, P.D. Johnson, Jr., S.P. Ra dziszowski, V. Rdl, J.H. Spencer, A. Soifer, E. Tressler
Note:Springer eBooks
Contents:How This Book Came into Being
Table of Contents
Ramsey Theory before Ramsey, Prehistory and Early History: An Essay in 13 Parts
Eighty Years of Ramsey R(3, k). . . and Counting!
Ramsey Numbers Involving Cycles
On the function of Erds and Rogers
Large Monochromatic Components in Edge Colorings of Graphs
Szlams Lemma: Mutant Offspring of a Euclidean Ramsey Problem: From 1973, with Numerous Applications
Open Problems in Euclidean Ramsey Theory
Chromatic Number of the Plane and Its Relatives, History, Problems and Results: An Essay in 11 Parts
Euclidean Distance
ISBN:9780817680923
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v285
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Combinatorics , Discrete groups
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Call number:SPRINGER-2010-9783764385149:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators and Symmetries [electronic resource] : Background Analysis and Advanced Topics
Author(s): Michael Ruzhansky
Ville Turunen
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups. Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim oftackling a number of import ant problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach byusing global symmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on thetorus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyz ed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups andhomogeneous spaces. The exposition of the book is self-contained and provides the reader with the backgro und material surrounding the theory and needed for working with pseudo-differential operators in different settings. Thebackground section of the book may be used for independent learning of different aspects of analysis and is complemented by numerous ex amples and exercises
Note:Springer eBooks
Contents:Preface
Introduction
Part I Foundations of Analysis
A Sets, Topology and Metrics
B Elementary Functional Analysis
C Measure Theory and Integration
D Algebras
Part II Commutative Symmetries
1 Fourier Analysis on Rn
2 Pseudo
differential Operators on Rn
3 Periodic and Discrete Analysis
4 Pseudo
differential Operators on Tn
5 Commutator Characterisation of Pseudo
differential Operators
Part III Representation Theory of Compact Groups
6 Groups
7 Topological Groups
8 Linear Lie Groups
9 Hopf Algebras
Part IV Non
commutative Symmetries
10 Pseu
ISBN:9783764385149
Series:e-books
Series:SpringerLink (Online service)
Series:Pseudo-Differential Operators, Theory and Applications : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Differential equations, partial
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Call number:SPRINGER-2010-9783642129711:ONLINE Show nearby items on shelf
Title:Triangulations [electronic resource] : Structures for Algorithms and Applications
Author(s): Jess A Loera
Jrg Rambau
Francisco Santos
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book studies the subdivisions and triangulations of polyhedral regions and point sets and presents the first comprehensivetreatment of the theory of secondary polytopes and related topics. A central theme of the book is the use of the rich structure of the space of triangulations to solve computational problems (e.g., counting the number of triangulationsor finding optimal triangulations with respect to various criteria), and to establish connections to applications in algebra, computer science, combinatorics, and optimization. With many examples and exercises, and with nearly fivehundred illustrations, the book gently guides readers through the prope rties of the spaces of triangulations of structured (e.g., cubes, cyclic polytopes, lattice polytopes) and pathological (e.g., disconnected spaces oftriangulations) situations using only elementary principles
Note:Springer eBooks
Contents:1 Triangulations in Mathematics
2 Configurations, Triangulations, Subdivisions, and Flips
3 Life in two Dimensions
4 A Tool Box
5 Regular Triangulations and Secondary Polytopes
6 Some Interesting Configurations
7 Some Interesting Triangulations
8 Algorithmic Issues
9 Further Topics
Bibliography
Index
ISBN:9783642129711
Series:e-books
Series:SpringerLink (Online service)
Series:Algorithms and Computation in Mathematics, 1431-1550 : v25
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Computer science Mathematics , Algorithms , Combinatorics , Discrete groups
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Call number:SPRINGER-2010-9783642118975:ONLINE Show nearby items on shelf
Title:New Paths Towards Quantum Gravity [electronic resource]
Author(s): Bernhelm Boo-Bavnbek
G Esposito
Matthias Lesch
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:Aside from the obvious statement that it should be a theory capable of unifying general relativity and quantum field theory, not much is known about the true nature of quantum gravity. New ideas - and there are many of them forthis is an exciting fie ld of research - often diverge to a degree where it seems impossible to decide in which of the many possible direction(s) the ongoing developments should be further sustained. The division of the book in two(overlapping) parts reflects the duality between the physical vision and the mathematical construction. The former is represented by tutorial reviews on non-commutative geometry, on space-time discretization and renormalization and ongauge field path integrals. The latter one by lectures on cohomology, on stochastic geometry and on mathematical tools for the effective action in quantum gravity. The book will benefit everyone working or entering the field of quantumgravity research
Note:Springer eBooks
Contents:Three Physics Visions
Notes on Quantum Gravity and Noncommutative Geometry
Quantum Gravity as Sum over Spacetimes
Lectures on Quantization of Gauge Systems
Novel Mathematical Tools
Mathematical Tools for Calculation of the Effective Action Effective Action in Quantum Gravity
Lectures on Cohomology, T
Duality, and Generalized Geometry
Stochastic Geometry and Quantum Gravity: Some Rigorous Results
Afterthoughts
Steps Towards Quantum Gravity and the Practice of Science: Will the Merger of Mathematics and Physics Work?
ISBN:9783642118975
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v807
Series:Physics and Astronomy (Springer-11651)
Keywords: Discrete groups
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Call number:SPRINGER-2010-9783642114434:ONLINE Show nearby items on shelf
Title:Reaction-Transport Systems [electronic resource] : Mesoscopic Foundations, Fronts, and Spatial Instabilities
Author(s): Werner Horsthemke
Sergei Fedotov
Vicenc Mendez
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simplyclassical diffusion ( Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport withinertia, described by persistent random walks an d hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particularreaction-diffusion systems are studied where the medium is in turn eit her spatially inhomogeneous, compositionally heterogeneous or spatially discrete. Applications span a vast range of interdisciplinary fields and the systemsconsidered can be as different as human or animal groups migrating under external influences, popul ation ecology and evolution, complex chemical reactions, or networks of biological cells. Several chapters treat these applications indetail
Note:Springer eBooks
Contents:Reaction Kinetics
Reactions and Transport: Diffusion Inertia, and Subdiffusion
Random Walks and Mesoscopic Reaction
Transport Equations
Reaction
Diffusion Fronts
Reaction
Transport Fronts Propagating into Unstable States
Reaction
Diffusion Fronts in Complex Structures
Ecological Applications
Biomedical Applications
Persistence and Extinction of Populations in Finite Domains
Turing Instabilities in Homogeneous Systems
Turing Instabilities in Reaction
Diffusion Systems With Temporally or Spatially Varying Parameters
Chemical and Biological Applications of Turing
ISBN:9783642114434
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Series in Synergetics, 0172-7389
Series:Physics and Astronomy (Springer-11651)
Keywords: Chemistry, Physical organic , Chemical engineering , Ecology , Genetics Mathematics
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Call number:SPRINGER-2010-9783642016424:ONLINE Show nearby items on shelf
Title:Profinite Groups [electronic resource]
Author(s): Luis Ribes
Pavel Zalesskii
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. The book is reasonably self-contained. Profinite groups are Galois groups. As such theyare of interest in alg ebraic number theory. Much of recent research on abstract infinite groups is related to profinite groups because residually finite groups are naturally embedded in a profinite group. In addition to basic factsabout general profinite groups, the book empha sizes free constructions (particularly free profinite groups and the structure of their subgroups). Homology and cohomology is described with a minimum of prerequisites. This second editioncontains three new appendices dealing with a new characterization of free profinite groups, presentations of pro-p groups and a new conceptually simpler approach to the proof of some classical subgroup theorems. Throughout the textthere are additions in the form of new results, improved proofs, typographical corrections , and an enlarged bibliography. The list of open questions has been updated comments and references have been added about those previously openproblems that have been solved after the first edition appeared
Note:Springer eBooks
Contents:Inverse and Direct Limits
Profinite Groups
Free Profinite Groups
Some Special Profinite Groups
Discrete and Profinite Modules
Homology and Cohomology of Profinite Groups
Cohomological Dimension
Normal Subgroups of Free Pro
C Groups
Free Constructions
Open Questions
Appendices (A
D)
Bibliography
Indices
ISBN:9783642016424
Series:e-books
Series:SpringerLink (Online service)
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics : v40
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Topological Groups , Number theory , Topology
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Call number:SPRINGER-2010-9783540709978:ONLINE Show nearby items on shelf
Title:Geometry Revealed [electronic resource] : A Jacob's Ladder to Modern Higher Geometry
Author(s): Marcel Berger
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating conceptfor the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools ofvarying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining theresults are elucidated. These are conceptual notions, each built above t he preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, thatangels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called elementary geometry is very much alive and at the very heart of thework of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concep ts to be created. The book is visually rich and inviting, so that readers may open it at random places andfind much pleasure throughout according their own intuitions and inclinations. Marcel Berger is the author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with anaffinity for geometry
Note:Springer eBooks
Contents:Points and lines in the plane
Circles and spheres
The sphere by itself: can we distribute points on it evenly?
Conics and quadrics
Plane curves
Smooth surfaces
Convexity and convex sets
Polygons, polyhedra, polytopes
Lattices, packings and tilings in the plane
Lattices and packings in higher dimensions
Geometry and dynamics I: billiards
Geometry and dynamics II: geodesic flow on a surface
ISBN:9783540709978
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Combinatorics , Geometry , Discrete groups , Global differential geometry , Mathematics_$xHistory
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Call number:SPRINGER-2010-9781441970237:ONLINE Show nearby items on shelf
Title:The Art of Proof [electronic resource] Basic Training for Deeper Mathematics
Author(s): Matthias Beck
Ross Geoghegan
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
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Note:The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interestingexamples, the student's p revious intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets.Methods, such as axiom, theorem and proof, ar e taught while discussing the mathematics rather than in abstract isolation. Some of the proofs are presented in detail, while others (some with hints) may be assigned to the student orpresented by the instructor. The authors recommend that the two parts of the book -- Discrete and Continuous -- be given equal attention. The book ends with short essays on further topics suitable for seminar-style presentation bysmall teams of students, either in class or in a mathematics club setting. These include: conti nuity, cryptography, groups, complex numbers, ordinal number, and generating functions
Note:Springer eBooks
Contents:Preface
Notes for the Student
Notes for Instructors
Part I: The Discrete
1 Integers
2 Natural Numbers and Induction
3 Some Points of Logic
4 Recursion
5 Underlying Notions in Set Theory
6 Equivalence Relations and Modular Arithmetic
7 Arithmetic in Base Ten
Part II: The Continuous
8 Real Numbers
9 Embedding Z in R
10. Limits and Other Consequences of Completeness
11 Rational and Irrational Numbers
12 Decimal Expansions
13 Cardinality
14 Final Remarks
Further Topics
A Continuity and Uniform Continuity
B Public
Key Cryptography
C
ISBN:9781441970237
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056 : v0
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2010-9780817649135:ONLINE Show nearby items on shelf
Title:Hyperbolic Manifolds and Discrete Groups [electronic resource]
Author(s): Michael Kapovich
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is onThurstons hyperbolization t heorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to thehyperbolization theorem as well as rich discussions on related t opics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich setof examples, numerous exercises, and an extensive bibliography and index, Hyperbolic M anifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairlyself-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem,this is an important book which had to be written some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolizationtheorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. -- -Zentralbatt MATH This book can act as source material for a postgraduatecourse and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide
Note:Springer eBooks
Contents:Preface
Three
dimensional Topology
Thurston Norm
Geometry of the Hyperbolic Space
Kleinian Groups
Teichmller Theory of Riemann Surfaces
Introduction to the Orbifold Theory
Complex Projective Structures
Sociology of Kleinian Groups
Ultralimits of Metric Spaces
Introduction to Group Actions on Trees
Laminations, Foliations and Trees
Rips Theory
Brooks' Theorem and Circle Packings
Pleated Surfaces and Ends of Hyperbolic Manifolds
Outline of the Proof of the Hyperbolization Theorem
Reduction to The Bounded Image Theorem
The Bounded Image Theorem
ISBN:9780817649135
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Geometry , Topology , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9780387789637:ONLINE Show nearby items on shelf
Title:Topics in Hyperplane Arrangements, Polytopes and Box-Splines [electronic resource]
Author(s): Corrado De Concini
Claudio Procesi
Date:2010
Edition:1
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Several mathematical areas that have been developed independently over the last 30 years are brought together revolving around the computation of the number of integral points in suitable families of polytopes. The problem isformulated here in terms of partition functions and multivariate splines. In its simplest form, the problem is to compute the number of ways a given nonnegative integer can be expressed as the sum of h fixed positive integers. Thisgoes back to ancient times and was investigated b y Euler, Sylvester among others in more recent times also in the higher dimensional case of vectors. The book treats several topics in a non-systematic way to show and compare a varietyof approaches to the subject. No book on the material is available in the existing literature. Key topics and features include: - Numerical analysis treatments relating this problem to the theory of box splines - Study of regularfunctions on hyperplane and toric arrangements via D-modules - Residue formulae for partition fu nctions and multivariate splines - Wonderful completion of the complement of hyperplane arrangements - Theory and properties of the Tuttepolynomial of a matroid and of zonotopes Graduate students as well as researchers in algebra, combinatorics and numeri cal analysis, will benefit from Topics in Hyperplane Arrangements, Polytopes, and Box Splines
Note:Springer eBooks
Contents:Introduction
I Preliminaries. 1 Polytopes. 2 Hyperplane Arrangements. 3 Fourier and Laplace Transforms. 4 Modules Over the Weyl Algebra. 5 Differential and Difference Equations. 6 Approximation Theory I
II The Differentiable Case. 7 Splines. 8 Rx as a D
Module. 9 The function Tx. 10 Cohomology. 11 Differential Equations
III The Discrete Case. 12 Partition Functions. 13 Toric Arrangements. 14 Cohomology of Toric Arrangements. 15 Difference Equations. 16 Applications. 17 Approximation Theory II
IV The Wonderful Model. 18 Minimal Models
ISBN:9780387789637
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Topological Groups , Differential Equations , Cell aggregation Mathematics
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Call number:SPRINGER-2009-9783540853329:ONLINE Show nearby items on shelf
Title:Generalized Lie Theory in Mathematics, Physics and Beyond [electronic resource]
Author(s): Sergei Silvestrov
Eugen Paal
Viktor Abramov
Alexander Stolin
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:The goal of this book is to extend the understanding of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics. This volume is devoted to theinterplay between severa l rapidly expanding research fields in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensionsof differential calculus and geometry, non-ass ociative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book will be a useful source ofinspiration for a broad spectrum of researchers and for research students , and includes contributions from several large research communities in modern mathematics and physics. This volume consists of 5 parts comprising 25 chapters,which were contributed by 32 researchers from 12 different countries. All contributions in the v olume have been refereed
Note:Springer eBooks
Contents:Non
Associative and Non
Commutative Structures for Physics
Moufang Transformations and Noether Currents
Weakly Nonassociative Algebras, Riccati and KP Hierarchies
Applications of Transvectants
Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics
A Rewriting Approach to Graph Invariants
Non
Commutative Deformations, Quantization, Homological Methods, and Representations
Graded q
Differential Algebra Approach to q
Connection
On Generalized N
Complexes Coming from Twisted Derivations
Remarks on Quantizations, Words and R
Matrices
Conn
ISBN:9783540853329
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Mathematical physics
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Call number:SPRINGER-2009-9783034600026:ONLINE Show nearby items on shelf
Title:Flag-transitive Steiner Designs [electronic resource]
Author(s): Michael Huber
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
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Note:The monograph provides the first full discussion of flag-transitive Steiner designs. This is a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines, likefinite or incidence ge ometry, group theory, combinatorics, coding theory, and cryptography. In a sufficiently self-contained and unified manner the classification of all flag-transitive Steiner designs is presented. This recent resultsettles interesting and challenging questio ns that have been object of research for more than 40 years. Its proof combines methods from finite group theory, incidence geometry, combinatorics, and number theory. The book contains abroad introduction to the topic, along with many illustrative exampl es. Moreover, a census of some of the most general results on highly symmetric Steiner designs is given in a survey chapter. The monograph is addressed to graduatestudents in mathematics and computer science as well as established researchers in design th eory, finite or incidence geometry, coding theory, cryptography, algebraic combinatorics, and more generally, discrete mathematics
Note:Springer eBooks
Contents:Preface
1. Incidence Structures and Steiner Designs
2. Permutation Groups and Group Actions
3. Number Theoretical Tools
4. Highly Symmetric Steiner Designs
5. A Census of Highly Symmetric Steiner Designs
6. The Classification of Flag
transitive Steiner Quadruple Systems
7. The Classification of Flag
transitive Steiner 3
Designs
8. The Classification of Flag
transitive Steiner 4
Designs
9. The Classification of Flag
transitive Steiner 5
Designs
10. The Non
Existence of Flag
transitive Steiner 6
Designs
References
Index
ISBN:9783034600026
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Discrete groups
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Call number:SPRINGER-2009-9781402096136:ONLINE Show nearby items on shelf
Title:Bilinear Control Systems [electronic resource] : Matrices in Action
Author(s): David Elliott
Date:2009
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
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Note:A control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. The study of bilinear control systems began in the 1960s and has since developed into afascinating field, vita l for the solution of many challenging practical control problems. Its methods and applications cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control in quantum physics and thestudy of Lie semigroups. The first half of th e book is based upon matrix analysis, introducing Lie algebras and the Campbell-Baker-Hausdorff Theorem. Individual chapters are dedicated to topics such as discrete-time systems,observability and realization, examples from science and engineering, linear ization of nonlinear systems, and input-output analysis. Written by one of the leading researchers in the field in a clear and comprehensible manner and ladenwith proofs, exercises and Mathematica scripts, this involving text will be a vital and thorough introduction to the subject for first-year graduate students of control theory. It will also be of great value to academics andresearchers with an interest in matrix analysis, Lie algebra, and semigroups
Note:Springer eBooks
Contents:1. Introduction
2. Lie Algebras, Lie Groups
3. Systems in Drift
4. Discrete Time Bilinear Systems
5. Systems with Outputs
6. Examples
7. Linearization
8. Input Structures
A. Matrix Algebra
B. Lie Algebras and Groups
C. Algebraic Geometry
D. Transitive Lie Algebras
References
Index
ISBN:9781402096136
Series:e-books
Series:SpringerLink (Online service)
Series:Applied Mathematical Sciences, 0066-5452 : v169
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra Data processing , Matrix theory , Topological Groups , Systems theory
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Call number:SPRINGER-2009-9780387894867:ONLINE Show nearby items on shelf
Title:Number Theory [electronic resource] : An Introduction to Mathematics
Author(s): W.A Coppel
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
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Note:Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope topics from analysis, modern algebra, and discrete mathematics are allincluded. The book is divi ded into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part Bcontains, for example, complete proofs of the HasseM inkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions. The prerequisitesfor this self-contained text are elements from linear algebra. Valuable refer ences for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or forself-study. From the reviews: This is a book which many mathematicians could enjoy browsing, and one whi ch a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparentlydisparate parts of mathematics. Canadian Mathematical Society As a source for information on the 'reach' of number theory into ot her areas of mathematics, it is an excellent work. Mathematical Association of America
Note:Springer eBooks
Contents:Preface
The Expanding Universe of Numbers
Divisibility
More on Divisibility
Continued Fractions and their Uses
Hadamards Determinant Problem
Hensels P
Adic Numbers
Notations
Axioms
The Arithmetic of Quadratic Forms
The Geometry of Numbers
The Number of Prime Numbers
A Character Study
Uniform Distribution and Ergodic Theory
Elliptic Functions
Connections with Number Theory
Notations
Axioms
Index
ISBN:9780387894867
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Number theory
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Call number:SPRINGER-2009-9780387873633:ONLINE Show nearby items on shelf
Title:Twentieth Anniversary Volume: [electronic resource] : Discrete & Computational Geometry
Author(s): Richard Pollack
Jnos Pach
Jacob E Goodman
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry, and presents a comprehensive picture of the current state of thefield. Formed during the pa st few decades by the merger of the classical discipline of combinatorial and discrete geometry with the new field of computational geometry that sprang up in the 1970s, discrete and computational geometrynow claims the allegiance of a sizeable number of mathematicians and computer scientists all over the world, whose most important work has been appearing since 1986 in the pages of the journal. The articles in this volume, a number ofwhich solve long-outstanding problems in the field, were chosen by the editors of DCG for the importance of their results, for the breadth of their scope, and to show the intimate connections that have arisen between discrete andcomputational geometry and other areas of both computer science and mathematics. Apart from the a rticles, the editors present an expanded preface, along with a set of photographs of groups and individuals who have played a major rolein the history of the field during the past twenty years. Contributors include: E. Ackerman P.K. Agarwal I. Aliev I. Br ny A. Barvinok S. Basu L.J. Billera J.-D. Boissonnat C. Borcea E. Boros K. Borys B. Braun K. Buchin O. Cheong D.Cohen-Steiner M. Damian K. Elbassioni R. Flatland T. Gerken J.E. Goodman X. Goaoc P. Gronchi V. Gurvich S. Har-Peled J. Hershberger A. Holmsen S.K. Hsiao A. Hubard J. Jernimo L. Khachiyan R. Klein C. Knauer S. Langerman J.-Y. Lee M.Longinetti E. Miller P. Morin U. Nagel E. Nevo P. Niyogi I. Novik J. ORourke J. Pach I. Pak M.J. Pelsmajer S. Petitjean F. Pfender R. Pinchasi R. Pollack J.S. Provan K. Przeslawski R.M. Richardson G. Rote M. Schaefer Y. Schreiber M.Sharir J.R. Shewchuk S. Smale B. Solomyak M. Soss D. tefankovic G. Vegter V.H. Vu S. Weinberger L. Wu D. Yost H. Yu T. Zell
Note:Springer eBooks
Contents:Preface
There are Not too Many Magic Configurations
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
Robus Shape Fitting via Peeling and Grating Coresets
Siegel's LEmaa and Sum
Distinct Sets
Slicing Convex Sets and Measures by a Hyperplane
A Centrally Symmetric Version of the Cyclic Polytope
On Projections of Semi
Algebraic Sets Defined by Few Quadratic Inequalities
Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres
Isotopic Implicit Surface Meshing
Line Transversals to Disjoint Balls
Generating all
ISBN:9780387873633
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computational complexity , Computer graphics , Geometry, algebraic , Computer science Mathematics , Discrete groups
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Call number:SPRINGER-2009-9780387763569:ONLINE Show nearby items on shelf
Title:Polytopes, Rings, and K-Theory [electronic resource]
Author(s): Joseph Gubeladze
Winfried Bruns
Date:2009
Edition:1
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, thealgebras derived from the m, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphismproblems and automorphism groups, homological prope rties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. Thismonograph has been written with a view towards graduate students and resear chers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, alsospecialists in lattice polytopes and related objects will find an up-to-date discussion of affine m onoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructiveapproach wherever possible. Winfried Bruns is Professor of Mathematics at Universitt Osnabrck. Joseph Gubeladze is Professor of Mathematics at San Francisco State University
Note:Springer eBooks
Contents:Preface
Polytopes, cones, and complexes
Affine monoids and their Hilbert bases
Multiples of lattice polytopes
Monoid algebras
Isomorphisms and automorphisms
Homological properties and Hilbert functions
Grbner bases, triangulations, and Koszul algebras
Projective modules over monoid rings
Bass
Whitehead groups of monoid rings
Varieties
References
Notation
Index
ISBN:9780387763569
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , K-theory , Discrete groups
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Call number:SPRINGER-2009-9780387094144:ONLINE Show nearby items on shelf
Title:Linear and Integer Programming vs Linear Integration and Counting [electronic resource] : A Duality Viewpoint
Author(s): Jean-Bernard Lasserre
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In this book the author analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, linear summation (or counting). The focus is on duality and the approach is rathernovel as it puts intege r programming in perspective with three associated problems, and permits one to define discrete analogues of well-known continuous duality concepts, and the rationale behind them. Also, the approach highlightsthe difference between the discrete and contin uous cases. Central in the analysis are the continuous and discrete Brion and Vergne's formulae for linear integration and counting. This approach provides some new insights on dualityconcepts for integer programs, and also permits to retrieve and shed ne w light on some well-known results. For instance, Gomory relaxations and the abstract superadditive dual of integer programs are re-interpreted in this algebraicapproach. This book will serve graduate students and researchers in applied mathematics, optim ization, operations research and computer science. Due to the substantial practical importance of some presented problems, researchers inother areas will also find this book useful
Note:Springer eBooks
Contents:Preface. Introduction
Part I. Linear Integration and Linear Programming. The Linear Integration Problem I. Comparing the Continuous Problems P and I
Part II. Linear Counting and Integer Programming
The Linear Counting Problem I(d). Relating the Discrete Problems P(d) and I(d) with P
Part III. Duality. Duality and Gomory Relaxations. Barvinoks Counting Algorithm and Gomory Relaxations. A Discrete Farkas Lemma. The Integer Hull of a Convex Rational Polytope. Duality and Superadditive Functions
Appendix: Legendre
Fenchel, Laplace, Cramer, and Z Transforms. References. Glossary
ISBN:9780387094144
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Series in Operations Research and Financial Engineering, 1431-8598
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computational complexity , Discrete groups , Mathematical optimization , Operations research
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