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Call number: | SPRINGER-2016-9783319304519:ONLINE Show nearby items on shelf |
Title: | Symmetries in Graphs, Maps, and Polytopes 5th SIGMAP Workshop, West Malvern, UK, July 2014 |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (332 p.) |
Note: | 10.1007/978-3-319-30451-9 |
ISBN: | 9783319304519 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 159 |
Keywords: | Mathematics , Algebra , Field theory (Physics) , Topological groups , Lie groups , Graph theory , Mathematics , Graph Theory , Field Theory and Polynomials , Topological Groups, Lie Groups |
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Call number: | SPRINGER-2016-9783319281865:ONLINE Show nearby items on shelf |
Title: | Convexity and Discrete Geometry Including Graph Theory Mulhouse, France, September 2014 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (39 p.) |
Note: | 10.1007/978-3-319-28186-5 |
Contents: | Introduction -- PART I Research Articles. Marcus: Tudor Zamfirescu: from convex to magic -- Yuan: Acute Triangulations of Rectangles, with Angles Bounded Below -- Skupien: Multi-compositions in exponential counting of hypohamiltonian snarks -- Shabb ir & T. Zamfirescu: Hamiltonicity in k-tree-Halin graphs -- Schneider: Reflections of planar convex bodies -- Rouyer: Steinhaus conditions for convex polyhedra -- Riviere: About the Hausdorff dimension of the set of endpoints of convex surfaces -- Prunesc u: About a surprising computer program of Matthias Müller -- Oliveros, Martinez & Montejano: Extremal results on intersection graphs of boxes in R^d -- Massé, Euler & Lemarchand: On the connected spanning cubic subgraph problem -- Kincses: On the Helly dimension of Hanner polytopes -- Itoh & Ohtsuka: Classification of normal 2-polyhedra of positive constant curvature -- Heppes & Jeronimo-Castro: T(4) families ofϕ-disjoint ovals -- Fruchard & Magazinov: Fair partitioning by straight lines -- |
Filip & Petrusel: Fixed point theorems for multivalued Zamfrescu operators in convex Kasahara spaces -- Et-Taoui: Complex conference matrices, complex Hadamard matrices and complex equiangular tight frames -- Chevallier, Fruchard & Vilcu: Envelopes of α-sections -- Bokowski & al.: Selected open and solved problems in computational synthetic geometry -- Bau: Reductions of 3-connected quadrangulations of the sphere -- Barany & Por: Paths on the sphere without small angles -- PART II Open Problem Note s. Zamfirescu T.: Two problems on cages for discs -- Zamfirescu Carol T.: Seven problems on hypohamiltonian and almost hypohamiltonian graphs -- Vilcu & Zamfirescu: Six problems on the length of the cut locus -- Simoes-Pereira: Existence Problems for Matr oidal Families -- Funar: Cubical Pachner moves -- Eckhoff: Problems in Discrete Geometry -- Chevallier & Fruchard: What is the minimal cardinal of a family which shatters all d-subsets of a finite set? -- Baskoro: Some open problems of Ramsey | |
minimal graphs. | |
ISBN: | 9783319281865 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 148 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Convex geometry , Discrete geometry , Combinatorics , Graph theory , Mathematics , Convex and Discrete Geometry , Graph Theory , Combinatorics , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319052335:ONLINE Show nearby items on shelf |
Title: | Stochastic Analysis for Poisson Point Processes Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (346 p.) |
Note: | 10.1007/978-3-319-05233-5 |
Contents: | 1 Stochastic analysis for Poisson processes -- 2 Combinatorics of Poisson stochastic integrals with random integrands -- 3 Variational analysis of Poisson processes -- 4 Malliavin calculus for stochastic processes and random measures with independe nt increments -- 5 Introduction to stochastic geometry -- 6 The Malliavin-Stein method on the Poisson space -- 7 U-statistics in stochastic geometry -- 8 Poisson point process convergence and extreme values in stochastic geometry -- 9 U-statistics on the spherical Poisson space -- 10 Determinantal point processes |
ISBN: | 9783319052335 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics: 7 |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Polytopes , Probabilities , Combinatorics , Mathematics , Probability Theory and Stochastic Processes , Combinatorics , Polytopes , Applications of Mathematics |
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Call number: | SPRINGER-2014-9783319048703:ONLINE Show nearby items on shelf |
Title: | Combinatorial Algebraic Geometry [electronic resource] : Levico Terme, Italy 2013, Editors: Sandra Di Rocco, Bernd Sturmfels |
Author(s): |
Aldo Conca Sandra Di Rocco Jan Draisma June Huh Bernd Sturmfels Filippo Viviani |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions, and enumerative geometry. The aim of this volume is tointroduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varietiesendowed with a rich combinatorial structure. Rele vant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications |
Contents: | Koszul algebras, Koszul homology and syzygies |
Infinite | |
dimensional systems of polynomial equations with symmetry | |
Maximum Likelihood Geometry | |
Linear Toric fibrations and Cayley polytopes | |
Toroidal compactifications and tropicalizations of moduli spaces | |
ISBN: | 9783319048703 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2108 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Combinatorics |
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Call number: | SPRINGER-2014-9783319011837:ONLINE Show nearby items on shelf |
Title: | On the Device-Independent Approach to Quantum Physics [electronic resource] : Advances in Quantum Nonlocality and Multipartite Entanglement Detection |
Author(s): |
Jean-Daniel Bancal |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Quantum physics started in the 1920's with wave mechanics and the wave-particle duality. However, the last 20 years have seen a second quantum revolution, centered around non-locality and quantum correlations between measurementoutcomes. The associat ed key property, entanglement, is recognized today as the signature of quantumness. This second revolution opened the possibility of studying quantum correlations without any assumption on the internal functioningof the measurement apparata, the so-called Device-Independent Approach to Quantum Physics. This thesis explores this new approach using the powerful geometrical tool of polytopes. Emphasis is placed on the study of non-locality inthe case of three or more parties, where it is shown that a whole new variety of phenomena appear compared to the bipartite case. Genuine multiparty entanglement is also studied for the first time within the device-independentframework.Finally, these tools are used to answer a long-standing open question: could quantum non-locality be explained by influences that propagate from one party to the others faster than light, but that remain hidden so that onecannot use them to communicate faster than light? This would provide a way around Einstein's notion of action at a dis tance that would be compatible with relativity. However, the answer is shown to be negative, as such influences couldnot remain hidden |
Contents: | Advances in quantum nonlocality and multipartite entanglement Detection |
Nonlocality with three and more parties | |
Device | |
independent entanglement detection | |
Quantum information put into practice | |
Finite | |
speed hidden influences | |
ISBN: | 9783319011837 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5053 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory |
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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-2013-9783642333057: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-2013-9783034805728:ONLINE Show nearby items on shelf |
Title: | Offbeat Integral Geometry on Symmetric Spaces [electronic resource] |
Author(s): |
Valery V Volchkov Vitaly V Volchkov |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces ofarbitrary ranks as we ll as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for variousclasses of functions, far-reaching generalizatio ns of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful invarious fields of contemporary mathematics. The proofs given are mini mal in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historicalperspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and theHeisenberg group, integral equations, special functions, and transmutation operators theory |
Note: | Springer eBooks |
Contents: | Preface |
Part 1. Analysis on Symmetric Spaces. 1 Preliminaries | |
2 The Euclidean case | |
3 Symmetric spaces of the non | |
compact type | |
4 Analogies for compact two | |
point homogeneous Spaces | |
5 The phase space associated to the Heisenberg group | |
Part 2. Offbeat Integral Geometry | |
1 Functions with zero ball means on Euclidean space | |
2 Two | |
radii theorems in symmetric spaces | |
3 The problem of finding a function from its ball means | |
4 Sets with the Pompeiu property | |
5 Functions with zero integrals over polytopes | |
6 Ellipsoidal means | |
7 The Pompeiu property on a sphere | |
8 The Pompeiu | |
ISBN: | 9783034805728 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Integral Transforms , Functions, special , Global differential geometry |
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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-2013-9781461464068: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-2013-9781447148173: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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
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-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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
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-2011-9781441999610:ONLINE Show nearby items on shelf |
Title: | Geometric Methods and Applications [electronic resource] : For Computer Science and Engineering |
Author(s): |
Jean Gallier |
Date: | 2011 |
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 is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical,and applied books on c omputer graphics, computer vision, robotics, or machine learning. This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal componentanalysis, manifolds and Lie groups, quadratic optimi zation, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presentedin this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics. In this extensively updated second edition, more material on convex sets, Farkass lemma, quadraticoptimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now incl udes a presentation of PCA. The book is well illustrated and has chapter summaries and a large number of exercisesthroughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers. Reviews of first edition: Gallier's book will be a useful source for anyone interested in applications ofgeometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications. (MathematicalReviews, 2001) ...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry. (The Australian Mathematical Society, 200 1) |
Note: | Springer eBooks |
Contents: | Introduction |
Basics of Affine Geometry | |
Basic Properties of Convex Sets | |
Embedding an Affine Space in a Vector Space | |
Basics of Projective Geometry | |
Basics of Euclidean Geometry | |
Separating and Supporting Hyperplanes Polar Duality | |
Polytopes and Polyhedra | |
The CartanDieudonne Theorem | |
The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 | |
DirichletVoronoi Diagrams | |
Basics of Hermitian Geometry | |
Spectral Theorems | |
Singular Value Decomposition (SVD) and Polar Form | |
Applications of SVD and Pseudo | |
Inverses | |
Quadratic Optimization Problems | |
Schur | |
ISBN: | 9781441999610 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Texts in Applied Mathematics, 0939-2475 : v38 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Geometry , Mathematical optimization |
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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 |
Note: | Springer 2013 e-book collections |
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-2010-9783540709978: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-2010-9781441909992:ONLINE Show nearby items on shelf |
Title: | Nonlinear Computational Geometry [electronic resource] |
Author(s): |
Ioannis Z Emiris Frank Sottile Thorsten Theobald |
Date: | 2010 |
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: | An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design andmolecular biology, t ogether with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods fromalgebraic geometry with proven techniques fro m piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized underthe term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts inthis emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometricmodeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely th eoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of theIMA workshop |
Note: | Springer eBooks |
Contents: | Spectral Techniques to Explore Point Clouds in Euclidean Space, with Applications to Collective Coordinates in Structural Biology |
Rational Parametrizations, Intersection Theory, and Newton Polytopes | |
Some Discrete Properties of the Space of Line Transversals to Disjoint Balls | |
Algebraic Geometry and Kinematics | |
Rational Offset Surfaces and their Modeling Applications | |
A List of Challenges for Real Algebraic Plane Curve Visualization Software | |
A Subdivision Method for Arrangement Computation of Semi | |
Algebraic Curves | |
Invariant | |
Based Characterization of the Relative Position of Tw | |
ISBN: | 9781441909992 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | The IMA Volumes in Mathematics and its Applications, 0940-6573 : v151 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Computer science Mathematics , Geometry |
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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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
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-2009-9780817648039:ONLINE Show nearby items on shelf |
Title: | Stochastic Models, Information Theory, and Lie Groups, Volume 1 [electronic resource] : Classical Results and Geometric Methods |
Author(s): |
Gregory S Chirikjian |
Date: | 2009 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volumeset presents these topics in a unified setting, thereby building bridges betweenfields that are rarely stud ied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, andgroup-theoretic concepts in the modeling of physical ph enomena. Volume 1 establishes the geometric and statistical foundations required to understand the fundamentals of continuous-time stochastic processes, differential geometry, andthe probabilistic foundations of information theory. Volume 2 delves deeper into relationships between these topics, including stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statisticalanalysis, and error propagation on Lie groups. Key features and topics of Volume 1: * The author reviews stochastic processes and basic differential geometry in an accessible way for applied mathematicians, scientists, and engineers.* Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize ap plied stochastic processes or differential geometry. * The concept of Lie groups as continuous sets of symmetryoperations is introduced. * The FokkerPlanck Equation for diffusion processes in Euclidean space and on differentiable manifolds is derived in a way that can be understood by nonspecialists. * The concrete presentation style makesit easy for readers to obtain numerical solutions for their own problems the emphasis is on how to calculate quantities rather than how to prove theorems. * A self-conta ined appendix provides a comprehensive review of concepts fromlinear algebra, multivariate calculus, and systems of ordinary differential equations. Stochastic Models, Information Theory, and Li |
Note: | Springer eBooks |
Contents: | ANHA Series Preface |
Preface | |
Introduction | |
Gaussian Distributions and the Heat Equation | |
Probability and Information Theory | |
Stochastic Differential Equations | |
Geometry of Curves and Surfaces | |
Differential Forms | |
Polytopes and Manifolds | |
Stochastic Processes on Manifolds | |
Summary | |
Appendix: Review of Linear Algebra, Vector Calculus, and Systems Theory | |
Index | |
ISBN: | 9780817648039 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Harmonic analysis , Distribution (Probability theory) , Mathematical physics , Engineering mathematics |
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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-2008-9780387781334:ONLINE Show nearby items on shelf |
Title: | Software for Algebraic Geometry [electronic resource] |
Author(s): |
Michael Stillman Jan Verschelde Nobuki Takayama |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in boththeoretical advances and appli cations. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packagesevolve continuously, incorporating new mathematical a dvances, they both motivate and demand the creation of new mathematics and smarter algorithms. This volume reflects the workshop Software for Algebraic Geometry held in the weekfrom 23 to 27 October 2006, as the second workshop in the thematic year on App lications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit,ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the rea der a broad view of current trends in computational algebraic geometry through software development and applications |
Note: | Springer eBooks |
Contents: | Software for Numerical Algebraic Geometry: A Paradigm and Progress Towards its Implementation |
PHClab: A MATLAB/Octave Interface to PHCpack | |
Computing Grbner Fans and Tropical Varieties in Gfan | |
On a Conjecture for the Dimension of the Space of the Multiple Zeta Values | |
DEMiCs: A Software Package for Computing the Mixed Volume Via Dynamic Enumeration of all Mixed Cells | |
SYNAPS: A Library for Dedicated Applications in Symbolic Numeric Computing | |
Tropical Implicitization and Mixed Fiber Polytopes | |
Towards a Black | |
Box Solver for Finite Games: Computing All Equilibria With Gambit a | |
ISBN: | 9780387781334 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | The IMA Volumes in Mathematics and its Applications, 0940-6573 : v148 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Computer science , Numerical analysis |
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Call number: | SPRINGER-2007-9783540711339:ONLINE Show nearby items on shelf |
Title: | Convex and Discrete Geometry [electronic resource] |
Author(s): |
Peter M Gruber |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convexand discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers. It should also be of use to people working in otherareas of mathematics and in the applied fields |
Note: | Springer eBooks |
Contents: | Convex Functions |
Convex Bodies | |
Convex Polytopes | |
Geometry of Numbers and Aspects of Discrete Geometry | |
ISBN: | 9783540711339 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | A Series of Comprehensive Studies in Mathematics, 0072-7830 : v336 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Discrete groups |
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Call number: | SPRINGER-2007-9780387461120:ONLINE Show nearby items on shelf |
Title: | Computing the Continuous Discretely [electronic resource] : Integer-Point Enumeration in Polyhedra |
Author(s): |
Matthias Beck Sinai Robins |
Date: | 2007 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas indiscrete geometry, com binatorics, and number theory. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community. We encounter here a friendly invitationto the field of counting integer points in polytopes, also known as Ehrhart theory, and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magicsquares, Dedekind sums, computational geometry, and more. With 250 e xercises and open problems, the reader feels like an active participant, and the authors' engaging style encourages such participation. The many compelling picturesthat accompany the proofs and examples add to the inviting style. For teachers, this text i s ideally suited as a capstone course for undergraduate students or as a compelling text in discrete mathematical topics for beginning graduatestudents. For scientists, this text can be utilized as a quick tooling device, especially for those who want a s elf-contained, easy-to-read introduction to these topics |
Note: | Springer eBooks |
Contents: | Preface |
The Coin | |
Exchange Problem of Frobenius | |
A Gallery of Discrete Volumes | |
Counting Lattice Points in Polytopes: The Ehrhart Theory | |
Reciprocity | |
Face Numbers and the Dehn | |
Sommerville Relations in Ehrhartian Terms | |
Magic Squares | |
Finite Fourier Analysis | |
Dedekind Sums | |
The Decomposition of a Polytope into Its Cones | |
Euler | |
MacLaurin Summation in Rd | |
Solid Angles | |
A Discrete Version of Green's Theorem Using Elliptic Functions | |
Appendix A: Triangulations of Polytopes | |
Appendix B: Hints for Selected Exercises | |
References | |
Index | |
List of Symbols | |
ISBN: | 9780387461120 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Combinatorics , Discrete groups , Number theory |
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Call number: | SPRINGER-2006-9780817644512:ONLINE Show nearby items on shelf |
Title: | Selected Topics in Convex Geometry [electronic resource] |
Author(s): |
Maria Moszyska |
Date: | 2006 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The field of convex geometry has become a fertile subject of mathematical activity in the past few decades. This exposition, examining in detail those topics in convex geometry that are concerned with Euclidean space, is enrichedby numerous examples, illustrations, and exercises, with a good bibliography and index. The theory of intrinsic volumes for convex bodies, along with the Hadwiger characterization theorems, whose proofs are based on beautiful geometricideas such as the rounding theorems and t he Steiner formula, are treated in Part 1. In Part 2 the reader is given a survey on curvature and surface area measures and extensions of the class of convex bodies. Part 3 is devoted to theimportant class of star bodies and selectors for convex and star bodies, including a presentation of two famous problems of geometric tomography: the Shephard problem and the BusemannPetty problem. Selected Topics in Convex Geometryrequires of the reader only a basic knowledge of geometry, linear algebra, analysis, to pology, and measure theory. The book can be used in the classroom setting for graduates courses or seminars in convex geometry, geometric and convexcombinatorics, and convex analysis and optimization. Researchers in pure and applied areas will also benefi t from the book |
Note: | Springer eBooks |
Contents: | I |
Metric Spaces | |
Subsets of Euclidean Space | |
Basic Properties of Convex Sets | |
Transformations of the Space Kn of Compact Convex Sets | |
Rounding Theorems | |
Convex Polytopes | |
Functionals on the Space Kn. The Steiner Theorem | |
The Hadwiger Theorems | |
Applications of the Hadwiger Theorems | |
II | |
Curvature and Surface Area Measures | |
Sets with positive reach. Convexity ring | |
Selectors for Convex Bodies | |
Polarity | |
III | |
Star Sets. Star Bodies | |
Intersection Bodies | |
Selectors for Star Bodies | |
ISBN: | 9780817644512 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Global analysis (Mathematics) , Discrete groups , Topology |
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Call number: | SPRINGER-2005-9780387271057:ONLINE Show nearby items on shelf |
Title: | Using Algebraic Geometry [electronic resource] |
Author(s): |
David A Cox John Little Donal Oshea |
Date: | 2005 |
Edition: | Second Edition |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraicgeometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Grbnerbases and resultants. The book is written for nonsp ecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help tohave some previous exposure to Grbner bases. The book does not assume t he reader is familiar with more advanced concepts such as modules. For the new edition, the authors have added a unified discussion of how matrices can be used tospecify monomial orders a revised presentation of the Mora normal form algorithm two sections discussing the Grbner fan of an ideal and the Grbner Walk basis conversion algorithm and a new chapter on the theory of order domains,associated codes, and the Berlekamp-Massey-Sakata decoding algorithm. They have also updated the references, improved so me of the proofs, and corrected typographical errors. David Cox is Professor of Mathematics at Amherst College.John Little is Professor of Mathematics at College of the Holy Cross. Donal OShea is the Elizabeth T. Kennan Professor of Mathematics and Dean o f Faculty at Mt. Holyoke College. These authors also co-wrote the immensely successfulbook, Ideals, Varieties, and Algorithms |
Note: | Springer eBooks |
Contents: | Solving Polynomial Equations |
Resultants | |
Computation in Local Rings | |
Modules | |
Free Resolutions | |
Polytopes, Resultants, and Equations | |
Polyhedral Regions and Polynomials | |
Algebraic Coding Theory | |
The Berlekamp | |
Massey | |
Sakata Decoding Algorithm | |
ISBN: | 9780387271057 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v185 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra Data processing , Geometry, algebraic , Algorithms |
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Call number: | SPRINGER-2004-9783322803030:ONLINE Show nearby items on shelf |
Title: | Geometric Graphs and Arrangements Some Chapters from Combinatorial Geometry |
Author(s): |
Stefan Felsner |
Date: | 2004 |
Size: | 1 online resource (170 p.) |
Note: | 10.1007/978-3-322-80303-0 |
Contents: | 1 Geometric Graphs: Turán Problems -- 1.1 What is a Geometric Graph? -- 1.2 Fundamental Concepts in Graph Theory -- 1.3 Planar Graphs -- 1.4 Outerplanar Graphs and Convex Geometric Graphs -- 1.5 Geometric Graphs without (k + |
1)-Pairwise Disjoint Edges -- 1.6 Geometric Graphs without Parallel Edges -- 1.7 Notes and References -- 2 Schnyder Woods or How to Draw a Planar Graph? -- 2.1 Schnyder Labelings and Woods -- 2.2 Regions and Coordinates -- 2.3 Geodesic | |
Embeddings of Planar Graphs -- 2.4 Dual Schnyder Woods -- 2.5 Order Dimension of 3-Polytopes -- 2.6 Existence of Schnyder Labelings -- 2.7 Notes and References -- 3 Topological Graphs: Crossing Lemma and Applications -- 3.1 Crossing | |
Numbers -- 3.2 Bounds for the Crossing Number -- 3.3 Improving the Crossing Constant -- 3.4 Crossing Numbers and Incidence Problems -- 3.5 Notes and References -- 4 k-Sets and k-Facets -- 4.1 k-Sets in the Plane -- 4.2 Beyond the Plane | |
-- 4.3 The Rectilinear Crossing Number of Kn -- 4.4 Notes and References -- 5 Combinatorial Problems for Sets of Points and Lines -- 5.1 Arrangements, Planes, Duality -- 5.2 Sylvester’s Problem -- 5.3 How many Lines are Spanned by n | |
Points? -- 5.4 Triangles in Arrangements -- 5.5 Notes and References -- 6 Combinatorial Representations of Arrangements of Pseudolines -- 6.1 Marked Arrangements and Sweeps -- 6.2 Allowable Sequences and Wiring Diagrams -- 6.3 Local | |
Sequences -- 6.4 Zonotopal Tilings -- 6.5 Triangle Signs -- 6.6 Signotopes and their Orders -- 6.7 Notes and References -- 7 Triangulations and Flips -- 7.1 Degrees in the Flip-Graph -- 7.2 Delaunay Triangulations -- 7.3 Regular | |
Triangulations and Secondary Polytopes -- 7.4 The Associahedron and Catalan families -- 7.5 The Diameter of Gn and Hyperbolic Geometry -- 7.6 Notes and References -- 8 Rigidity and Pseudotriangulations -- 8.1 Rigidity, Motion and | |
Stress -- 8.2 Pseudotriangles and Pseudotriangulations -- 8.3 Expansive Motions -- 8.4 The Polyhedron of of Pointed Pseudotriangulations -- 8.5 Expansive Motions and Straightening Linkages -- 8.6 Notes and References | |
ISBN: | 9783322803030 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algebra , Geometry , Mathematics , Geometry , Algebra |
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Call number: | SPRINGER-2003-9783540364283:ONLINE Show nearby items on shelf |
Title: | Geometric Aspects of Functional Analysis Israel Seminar 2001-2002 |
Author(s): | |
Date: | 2003 |
Size: | 1 online resource (432 p.) |
Note: | 10.1007/b10415 |
Contents: | Preface -- F. Barthe, M. Csörnyei and A. Naor: A Note on Simultaneous Polar and Cartesian Decomposition -- A. Barvinok: Approximating a Norm by a Polynomial -- S.G. Bobkov: Concentration of Distributions of the Weighted Sums with |
Bernoullian Coefficients -- S.G. Bobkov: Spectral Gap and Concentration for Some Spherically Symmetric Probability Measures -- S.G. Bobkov and A. Koldobsky: On the Central Limit Property of Convex Bodies -- S.G. Bobkov and F.L. | |
Nazarov: On Convex Bodies and Log-Concave Probability Measures with Unconditional Basis -- J. Bourgain: Random Lattice Schrödinger Operators with Decaying Potential: Some Higher Dimensional Phenomena -- J. Bourgain: On Long-Time | |
Behaviour of Solutions of Linear Schrödinger Equations with Smooth Time-Dependent Potential -- J. Bourgain: On the Isotropy-Constant Problem for 'PSI-2'-Bodies -- E.D. Gluskin: On the Sum of Intervals -- E. Gluskin and V. Milman: Note | |
on the Geometric-Arithmetic Mean Inequality -- O. Guédon and A. Zvavitch: Supremum of a Process in Terms of Trees -- O. Maleva: Point Preimages under Ball Non-Collapsing Mappings -- V. Milman and R. Wagner: Some Remarks on a Lemma of | |
Ran Raz -- F. Nazarov: On the Maximal Perimeter of a Convex Set in R^n with Respect to a Gaussian Measure -- K. Oleszkiewicz: On p-Pseudostable Random Variables, Rosenthal Spaces and l_p^n Ball Slicing -- G. Paouris: Psi_2-Estimates | |
for Linear Functionals on Zonoids -- G. Schechtman, N. Tomczak-Jaegermann and R. Vershynin: Maximal l_p^n-Structures in Spaces with Extremal Parameters -- C. Schütt and E. Werner: Polytopes with Vertices Chosen Randomly from the | |
Boundary of a Convex Body -- Seminar Talks (with Related Workshop and Conference Talks) | |
ISBN: | 9783540364283 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1807 |
Keywords: | Mathematics , Functional analysis , Convex geometry , Discrete geometry , Probabilities , Mathematics , Functional Analysis , Convex and Discrete Geometry , Probability Theory and Stochastic Processes |
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Call number: | SPRINGER-2003-9781461300199:ONLINE Show nearby items on shelf |
Title: | Convex Polytopes |
Author(s): |
Branko Grünbaum |
Date: | 2003 |
Edition: | Second Edition |
Size: | 1 online resource (471 p.) |
Note: | 10.1007/978-1-4613-0019-9 |
Contents: | 1 Notation and prerequisites -- 1.1 Algebra -- 1.2 Topology -- 1.3 Additional notes and comments -- 2 Convex sets -- 2.1 Definition and elementary properties -- 2.2 Support and separation -- 2.3 Convex hulls -- 2.4 Extreme and exposed |
points faces and poonems -- 2.5 Unbounded convex sets -- 2.6 Polyhedral sets -- 2.7 Remarks -- 2.8 Additional notes and comments -- 3 Polytopes -- 3.1 Definition and fundamental properties -- 3.2 Combinatorial types of polytopes | |
complexes -- 3.3 Diagrams and Schlegel diagrams -- 3.4 Duality of polytopes -- 3.5 Remarks -- 3.6 Additional notes and comments -- 4 Examples -- 4.1 The d-simplex -- 4.2 Pyramids -- 4.3 Bipyramids -- 4.4 Prisms -- 4.5 Simplicial and | |
simple polytopes -- 4.6 Cubical polytopes -- 4.7 Cyclic polytopes -- 4.8 Exercises -- 4.9 Additional notes and comments -- 5 Fundamental properties and constructions -- 5.1 Representations of polytopes as sections or projections -- 5.2 | |
The inductive construction of polytopes -- 5.3 Lower semicontinuity of the functions fk(P) -- 5.4 Gale-transforms and Gale-diagrams -- 5.5 Existence of combinatorial types -- 5.6 Additional notes and comments -- 6 Polytopes with few | |
vertices -- 6.1 d-Polytopes with d + 2 vertices -- 6.2 d-Polytopes with d + 3 vertices -- 6.3 Gale diagrams of polytopes with few vertices -- 6.4 Centrally symmetric polytopes -- 6.5 Exercises -- 6.6 Remarks -- 6.7 Additional notes and | |
comments -- 7 Neighborly polytopes -- 7.1 Definition and general properties -- 7.2 % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % | |
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadG % aGmUaaaeacaYOaiaiJigdaaeacaYOaiaiJikdaaaacbiGaiaiJ-rga % | |
aiaawUfacaGLDbaaaaa!40CC! $$ \left[ {\frac{1} {2}d} \right] $$-Neighborly d-polytopes -- 7.3 Exercises -- 7.4 Remarks -- 7.5 Additional notes and comments -- 8 Euler’s relation -- 8.1 Euler’s theorem -- 8.2 Proof of Euler’s theorem -- | |
8.3 A generalization of Euler’s relation -- 8.4 The Euler characteristic of complexes -- 8.5 Exercises -- 8.6 Remarks -- 8.7 Additional notes and comments -- 9 Analogues of Euler’s relation -- 9.1 The incidence equation -- 9.2 The | |
Dehn-Sommerville equations -- 9.3 Quasi-simplicial polytopes -- 9.4 Cubical polytopes -- 9.5 Solutions of the Dehn-Sommerville equations -- 9.6 The f-vectors of neighborly d-polytopes -- 9.7 Exercises -- 9.8 Remarks -- 9.9 Additional | |
notes and comments -- 10 Extremal problems concerning numbers of faces -- 10.1 Upper bounds for fi, i ? 1, in terms of fo -- 10.2 Lower bounds for fi, i ? 1, in terms of fo -- 10.3 The sets f(P3) and f(PS3) -- 10.4 The set fP4) -- 10.5 | |
Exercises -- 10.6 Additional notes and comments -- 11 Properties of boundary complexes -- 11.1 Skeletons of simplices contained in ?(P) -- 11.2 A proof of the van Kampen-Flores theorem -- 11.3 d-Connectedness of the graphs of | |
d-polytopes -- 11.4 Degree of total separability -- 11.5 d-Diagrams -- 11.6 Additional notes and comments -- 12 k-Equivalence of polytopes -- 12.1 k-Equivalence and ambiguity -- 12.2 Dimensional ambiguity -- 12.3 Strong and weak | |
ambiguity -- 12.4 Additional notes and comments -- 13 3-Polytopes -- 13.1 Steinitz’s theorem -- 13.2 Consequences and analogues of Steinitz’s theorem -- 13.3 Eberhard’s theorem -- 13.4 Additional results on 3-realizable sequences -- | |
13.5 3-Polytopes with circumspheres and circumcircles -- 13.6 Remarks -- 13.7 Additional notes and comments -- 14 Angle-sums relations the Steiner point -- 14.1 Gram’s relation for angle-sums -- 14.2 Angle-sums relations for simplicial | |
polytopes -- 14.3 The Steiner point of a polytope (by G. C. Shephard) -- 14.4 Remarks -- 14.5 Additional notes and comments -- 15 Addition and decomposition of polytopes -- 15.1 Vector addition -- 15.2 Approximation of polytopes by | |
vector sums -- 15.3 Blaschke addition -- 15.4 Remarks -- 15.5 Additional notes and comments -- 16 Diameters of polytopes (by Victor Klee) -- 16.1 Extremal diameters of d-polytopes -- 16.2 The functions ? and ?b -- 16.3 Wv Paths -- 16.4 | |
Additional notes and comments -- 17 Long paths and circuits on polytopes -- 17.1 Hamiltonian paths and circuits -- 17.2 Extremal path-lengths of polytopes -- 17.3 Heights of polytopes -- 17.4 Circuit codes -- 17.5 Additional notes and | |
comments -- 18 Arrangements of hyperplanes -- 18.1 d-Arrangements -- 18.2 2-Arrangements -- 18.3 Generalizations -- 18.4 Additional notes and comments -- 19 Concluding remarks -- 19.1 Regular polytopes and related notions -- 19.2 | |
k-Content of polytopes -- 19.3 Antipodality and related notions -- 19.4 Additional notes and comments -- Tables -- Addendum -- Errata for the 1967 edition -- Additional Bibliography -- Index of Terms -- Index of Symbols | |
ISBN: | 9781461300199 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 221 |
Keywords: | Mathematics , Convex geometry , Discrete geometry , Mathematics , Convex and Discrete Geometry |
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Call number: | SPRINGER-2003-9781461220664:ONLINE Show nearby items on shelf |
Title: | Coxeter Matroids |
Author(s): |
Alexandre V Borovik |
Date: | 2003 |
Size: | 1 online resource (266 p.) |
Note: | 10.1007/978-1-4612-2066-4 |
Contents: | 1 Matroids and Flag Matroids -- 1.1 Matroids -- 1.2 Representable matroids -- 1.3 Maximality Property -- 1.4 Increasing Exchange Property -- 1.5 Sufficient systems of exchanges -- 1.6 Matroids as maps -- 1.7 Flag matroids -- 1.8 Flag |
matroids as maps -- 1.9 Exchange properties for flag matroids -- 1.10 Root system -- 1.11 Polytopes associated with flag matroids -- 1.12 Properties of matroid polytopes -- 1.13 Minkowski sums -- 1.14 Exercises for Chapter 1 -- 2 | |
Matroids and Semimodular Lattices -- 2.1 Lattices as generalizations of projective geometry -- 2.2 Semimodular lattices -- 2.3 Jordan—Hölder permutation -- 2.4 Geometric lattices -- 2.5 Representations of matroids -- 2.6 Representation | |
of flag matroids -- 2.7 Every flag matroid is representable -- 2.8 Exercises for Chapter 2 -- 3 Symplectic Matroids -- 3.1 Definition of symplectic matroids -- 3.2 Root systems of type Cn -- 3.3 Polytopes associated with symplectic | |
matroids -- 3.4 Representable symplectic matroids -- 3.5 Homogeneous symplectic matroids -- 3.6 Symplectic flag matroids -- 3.7 Greedy Algorithm -- 3.8 Independent sets -- 3.9 Symplectic matroid constructions -- 3.10 Orthogonal | |
matroids -- 3.11 Open problems -- 3.12 Exercises for Chapter 3 -- 4 Lagrangian Matroids -- 4.1 Lagrangian matroids -- 4.2 Circuits and strong exchange -- 4.3 Maps on orientable surfaces -- 4.4 Exercises for Chapter 4 -- 5 Reflection | |
Groups and Coxeter Groups -- 5.1 Hyperplane arrangements -- 5.2 Polyhedra and polytopes -- 5.3 Mirrors and reflections -- 5.4 Root systems -- 5.5 Isotropy groups -- 5.6 Parabolic subgroups -- 5.7 Coxeter complex -- 5.8 Labeling of the | |
Coxeter complex -- 5.9 Galleries -- 5.10 Generators and relations -- 5.11 Convexity -- 5.12 Residues -- 5.13 Foldings -- 5.14 Bruhat order -- 5.15 Splitting the Bruhat order -- 5.16 Generalized permutahedra -- 5.17 Symmetric group as a | |
Coxeter group -- 5.18 Exercises for Chapter 5 -- 6 Coxeter Matroids -- 6.1 Coxeter matroids -- 6.2 Root systems -- 6.3 The Gelfand—Serganova Theorem -- 6.4 Coxeter matroids and polytopes -- 6.5 Examples -- 6.6 W-matroids -- 6.7 | |
Characterization of matroid maps -- 6.8 Adjacency in matroid polytopes -- 6.9 Combinatorial adjacency -- 6.10 The matroid polytope -- 6.11 Exchange groups of Coxeter matroids -- 6.12 Flag matroids and concordance -- 6.13 Combinatorial | |
flag variety -- 6.14 Shellable simplicial complexes -- 6.15 Shellability of the combinatorial flag variety -- 6.16 Open problems -- 6.17 Exercises for Chapter 6 -- 7 Buildings -- 7.1 Gaussian decomposition -- 7.2 BN-pairs -- 7.3 | |
Deletion Property -- 7.4 Deletion property and Coxeter groups -- 7.5 Reflection representation of W -- 7.6 Classification of finite Coxeter groups -- 7.7 Chamber systems -- 7.8 W-metric -- 7.9 Buildings -- 7.10 Representing Coxeter | |
matroids in buildings -- 7.11 Vector-space representations and building representations -- 7.12 Residues in buildings -- 7.13 Buildings of type An-1 = Symn -- 7.14 Combinatorial flag varieties, revisited -- 7.15 Open Problems -- 7.16 | |
Exercises for Chapter 7 -- References | |
ISBN: | 9781461220664 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics : 216 |
Keywords: | Mathematics , Algebra , Algebraic geometry , Combinatorics , Mathematics , Algebraic Geometry , Mathematics, general , Algebra , Combinatorics |
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Call number: | SPRINGER-2002-9781461300397:ONLINE Show nearby items on shelf |
Title: | Lectures on Discrete Geometry |
Author(s): | |
Date: | 2002 |
Size: | 1 online resource (486 p.) |
Note: | 10.1007/978-1-4613-0039-7 |
Contents: | 1 Convexity -- 1.1 Linear and Affine Subspaces, General Position -- 1.2 Convex Sets, Convex Combinations, Separation -- 1.3 Radon’s Lemma and Helly’s Theorem -- 1.4 Centerpoint and Harn Sandwich -- 2 Lattices and Minkowski’s Theorem |
-- 2.1 Minkowski’s Theorem -- 2.2 General Lattices -- 2.3 An Application in Number Theory -- 3 Convex Independent Subsets -- 3.1 The Erd?s-Szekeres Theorem -- 3.2 Horton Sets -- 4 Incidence Problems -- 4.1 Formulation -- 4.2 Lower | |
Bounds: Incidences and Unit Distances -- 4.3 Point-Line Incidences via Crossing Numbers -- 4.4 Distinct Distances via Crossing Numbers -- 4.5 Point-Line Incidences via Cuttings -- 4.6 A Weaker Cutting Lemma -- 4.7 The Cutting Lemma: A | |
Tight Bound -- 5 Convex Polytopes -- 5.1 Geometric Duality -- 5.2 H-Polytopes and V-Polytopes -- 5.3 Faces of a Convex Polytope -- 5.4 Many Faces: The Cyclic Polytopes -- 5.5 The Upper Bound Theorem -- 5.6 The Gale Transform -- 5.7 | |
Voronoi Diagrams -- 6 Number of Faces in Arrangements -- 6.1 Arrangements of Hyperplanes -- 6.2 Arrangements of Other Geometric Objects -- 6.3 Number of Vertices of Level at Most k -- 6.4 The Zone Theorem -- 6.5 The Cutting Lemma | |
Revisited -- 7 Lower Envelopes -- 7.1 Segments and Davenport-Schinzel Sequences -- 7.2 Segments: Superlinear Complexity of the Lower Envelope -- 7.3 More on Davenport-Schinzel Sequences -- 7.4 Towards the Tight Upper Bound for Segments | |
-- 7.5 Up to Higher Dimension: Triangles in Space -- 7.6 Curves in the Plane -- 7.7 Algebraic Surface Patches -- 8 Intersection Patterns of Convex Sets -- 8.1 The Fractional Helly Theorem -- 8.2 The Colorful Carathéodory Theorem -- 8.3 | |
Tverberg’s Theorem -- 9 Geometric Selection Theorems -- 9.1 A Point in Many Simplices: The First Selection Lemma -- 9.2 The Second Selection Lemma -- 9.3 Order Types and the Same-Type Lemma -- 9.4 A Hypergraph Regularity Lemma -- 9.5 A | |
Positive-Fraction Selection Lemma -- 10 Transversals and Epsilon Nets -- 10.1 General Preliminaries: Transversals and Matchings -- 10.2 Epsilon Nets and VC-Dimension -- 10.3 Bounding the VC-Dimension and Applications -- 10.4 Weak | |
Epsilon Nets for Convex Sets -- 10.5 The Hadwiger-Debrunner (p, q)-Problem -- 10.6 A (p, q)-Theorem for Hyperplane Transversals -- 11 Attempts to Count k-Sets -- 11.1 Definitions and First Estimates -- 11.2 Sets with Many Halving Edges | |
-- 11.3 The Lovász Lemma and Upper Bounds in All Dimensions -- 11.4 A Better Upper Bound in the Plane -- 12 Two Applications of High-Dimensional Polytopes -- 12.1 The Weak Perfect Graph Conjecture -- 12.2 The Brunn-Minkowski Inequality | |
-- 12.3 Sorting Partially Ordered Sets -- 13 Volumes in High Dimension -- 13.1 Volumes, Paradoxes of High Dimension, and Nets -- 13.2 Hardness of Volume Approximation -- 13.3 Constructing Polytopes of Large Volume -- 13.4 Approximating | |
Convex Bodies by Ellipsoids -- 14 Measure Concentration and Almost Spherical Sections -- 14.1 Measure Concentration on the Sphere -- 14.2 Isoperimetric Inequalities and More on Concentration -- 14.3 Concentration of Lipschitz Functions | |
-- 14.4 Almost Spherical Sections: The First Steps -- 14.5 Many Faces of Symmetric Polytopes -- 14.6 Dvoretzky’s Theorem -- 15 Embedding Finite Metric Spaces into Normed Spaces -- 15.1 Introduction: Approximate Embeddings -- 15.2 The | |
Johnson-Lindenstrauss Flattening Lemma -- 15.3 Lower Bounds By Counting -- 15.4 A Lower Bound for the Hamming Cube -- 15.5 A Tight Lower Bound via Expanders -- 15.6 Upper Bounds for ??-Embeddings -- 15.7 Upper Bounds for Euclidean | |
Embeddings -- What Was It About? An Informal Summary -- Hints to Selected Exercises | |
ISBN: | 9781461300397 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 212 |
Keywords: | Mathematics , Geometry , Convex geometry , Discrete geometry , Mathematics , Geometry , Convex and Discrete Geometry |
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Call number: | SPRINGER-2001-9781447102434:ONLINE Show nearby items on shelf |
Title: | Symmetries |
Author(s): |
D. L Johnson |
Date: | 2001 |
Size: | 1 online resource (198 p.) |
Note: | 10.1007/978-1-4471-0243-4 |
Contents: | 1 Metric Spaces and their Groups -- 1.1 Metric Spaces -- 1.2 Isometries -- 1.3 Isometries of the Real Line -- 1.4 Matters Arising -- 1.5 Symmetry Groups -- 2 Isometries of the Plane -- 2.1 Congruent Triangles -- 2.2 Isometries of |
Different Types -- 2.3 The Normal Form Theorem -- 2.4 Conjugation of Isometries -- 3 Some Basic Group Theory -- 3.1 Groups -- 3.2 Subgroups -- 3.3 Factor Groups -- 3.4 Semidirect Products -- 4 Products of Reflections -- 4.1 The Product | |
of Two Reflections -- 4.2 Three Reflections -- 4.3 Four or More -- 5 Generators and Relations -- 5.1 Examples -- 5.2 Semidirect Products Again -- 5.3 Change of Presentation -- 5.4 Triangle Groups -- 5.5 Abelian Groups -- 6 Discrete | |
Subgroups of the Euclidean Group -- 6.1 Leonardo’s Theorem -- 6.2 A Trichotomy -- 6.3 Friezes and Their Groups -- 6.4 The Classification -- 7 Plane Crystallographic Groups: OP Case -- 7.1 The Crystallographic Restriction -- 7.2 The | |
Parameter n -- 7.3 The Choice of b -- 7.4 Conclusion -- 8 Plane Crystallographic Groups: OR Case -- 8.1 A Useful Dichotomy -- 8.2 The Case n = 1 -- 8.3 The Case n = 2 -- 8.4 The Case n = 4 -- 8.5 The Case n = 3 -- 8.6 The Case n = 6 -- | |
9 Tessellations of the Plane -- 9.1 Regular Tessellations -- 9.2 Descendants of (4, 4) -- 9.3 Bricks -- 9.4 Split Bricks -- 9.5 Descendants of (3, 6) -- 10 Tessellations of the Sphere -- 10.1 Spherical Geometry -- 10.2 The Spherical | |
Excess -- 10.3 Tessellations of the Sphere -- 10.4 The Platonic Solids -- 10.5 Symmetry Groups -- 11 Triangle Groups -- 11.1 The Euclidean Case -- 11.2 The Elliptic Case -- 11.3 The Hyperbolic Case -- 11.4 Coxeter Groups -- 12 Regular | |
Polytopes -- 12.1 The Standard Examples -- 12.2 The Exceptional Types in Dimension Four -- 12.3 Three Concepts and a Theorem -- 12.4 Schläfli’s Theorem -- Solutions -- Guide to the Literature -- Index of Notation | |
ISBN: | 9781447102434 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Group theory , Algebra , Ordered algebraic structures , Geometry , Mathematics , Geometry , Group Theory and Generalizations , Order, Lattices, Ordered Algebraic Structures |
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Call number: | SPRINGER-2000-9783034884389:ONLINE Show nearby items on shelf |
Title: | Polytopes — Combinatorics and Computation |
Author(s): | |
Date: | 2000 |
Size: | 1 online resource (225 p.) |
Note: | 10.1007/978-3-0348-8438-9 |
Contents: | Lectures on 0/l-Polytopes -- polymake: A Framework for Analyzing Convex Polytopes -- Flag Numbers and FLAGTOOL -- A Census of Flag-vectors of 4-Polytopes -- Extremal Properties of 0/1-Polytopes of Dimension 5 -- Exact Volume |
Computation for Polytopes: A Practical Study -- Reconstructing a Simple Polytope from its Graph -- Reconstructing a Non-simple Polytope from its Graph -- A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm -- | |
The Complexity of Yamnitsky and Levin’s Simplices Method | |
ISBN: | 9783034884389 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | DMV Seminar : 29 |
Keywords: | Mathematics , Geometry , Mathematics , Geometry |
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Call number: | SPRINGER-1998-9781475769111:ONLINE Show nearby items on shelf |
Title: | Using Algebraic Geometry |
Author(s): |
David Cox |
Date: | 1998 |
Size: | 1 online resource (503 p.) |
Note: | 10.1007/978-1-4757-6911-1 |
Contents: | 1. Introduction -- 2. Solving Polynomial Equations -- 3. Resultants -- 4. Computation in Local Rings -- 5. Modules -- 6. Free Resolutions -- 7. Polytopes, Resultants, and Equations -- 8. Integer Programming, Combinatorics, and Splines |
-- 9. Algebraic Coding Theory -- References | |
ISBN: | 9781475769111 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 185 |
Keywords: | Mathematics , Algebraic geometry , Combinatorics , Mathematics , Algebraic Geometry , Combinatorics |
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Call number: | SPRINGER-1997-9783642042959:ONLINE Show nearby items on shelf |
Title: | Geometry of Cuts and Metrics |
Author(s): |
Michel Marie Deza |
Date: | 1997 |
Size: | 1 online resource (588 p.) |
Note: | 10.1007/978-3-642-04295-9 |
Contents: | Outline of the Book -- I.Measure Aspects: El-Embeddability and Probability -- Preliminaries on Distances -- The Cut Cone and #x2113-Metrics -- The Correlation Cone and {0. 1}-Covariances -- Conditions for -Embeddability -- Operations |
-- -Metrics from Lattices, Semigroups and Normed Spaces -- Metric Transforms of -Spaces -- Lipschitz Embeddings -- Dimensionality Questions for -Embeddings -- Examples of the Use of the -Metric -- Basic Definitions -- I1.Hypermetric | |
Spaces: an Approach via Geometry of Numbers -- Preliminaries on Lattices -- Hypermetrics and Delaunay Polytopes -- Delaunay Polytopes: Rank and Hypermetric Faces -- Extreme Delaunay Polytopes -- Hypermetric Graphs -- I11.Isometric | |
Embeddings of Graphs -- Preliminaries on Graphs -- Isometric Embeddings of Graphs into Hypercubes -- Isometric Embeddings of Graphs into Cartesian Products -- -Graphs -- IV.Hypercube Embeddings and Designs -- Rigidity of the | |
Equidistant Metric -- Hypercube Embeddings of the Equidistant Metric -- Recognition of Hypercube Embeddable Metrics -- Cut Lattices, Quasi -Distances and Hilbert Bases -- V.Facets of the Cut Cone and Polytope -- Operations on Valid | |
Inequalities and Facets -- Triangle Inequalities -- Hypermetric Inequalities -- Clique-Web Inequalities -- Other Valid Inequalities and Facets -- Geometric Properties | |
ISBN: | 9783642042959 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Algorithms and Combinatorics: 15 |
Keywords: | Mathematics , Geometry , Convex geometry , Discrete geometry , Number theory , Discrete mathematics , Combinatorics , Graph theory , Mathematics , Discrete Mathematics , Geometry , Graph Theory , Combinatorics , Convex and Discrete Geometry , Number Theory |
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Call number: | SPRINGER-1996-9783540496403:ONLINE Show nearby items on shelf |
Title: | Realization Spaces of Polytopes |
Author(s): |
Jürgen Richter-Gebert |
Date: | 1996 |
Size: | 1 online resource (188 p.) |
Note: | 10.1007/BFb0093761 |
Contents: | The objects and the tools -- The universality theorem -- Applications of university -- Three-dimensional polytopes -- Alternative construction techniques -- Problems |
ISBN: | 9783540496403 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1643 |
Keywords: | Mathematics , Algebraic geometry , Convex geometry , Discrete geometry , Combinatorics , Mathematics , Convex and Discrete Geometry , Combinatorics , Algebraic Geometry |
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Call number: | SPRINGER-1996-9781461240440:ONLINE Show nearby items on shelf |
Title: | Combinatorial Convexity and Algebraic Geometry |
Author(s): |
Günter Ewald |
Date: | 1996 |
Size: | 1 online resource (374 p.) |
Note: | 10.1007/978-1-4612-4044-0 |
Contents: | 1 Combinatorial Convexity -- I. Convex Bodies -- II. Combinatorial theory of polytopes and polyhedral sets -- III. Polyhedral spheres -- IV. Minkowski sum and mixed volume -- V. Lattice polytopes and fans -- 2 Algebraic Geometry -- |
VI. Toric varieties -- VII. Sheaves and projective toric varieties -- VIII. Cohomology of toric varieties -- Appendix Comments, historical notes, further exercises, research problems, suggestions for further reading -- References -- | |
List of Symbols | |
ISBN: | 9781461240440 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 168 |
Keywords: | Mathematics , Algebraic geometry , Combinatorics , Mathematics , Combinatorics , Algebraic Geometry |
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Call number: | SPRINGER-1995-9781461384311:ONLINE Show nearby items on shelf |
Title: | Lectures on Polytopes Updated Seventh Printing of the First Edition |
Author(s): |
Günter M Ziegler |
Date: | 1995 |
Size: | 1 online resource (300 p.) |
Note: | 10.1007/978-1-4613-8431-1 |
Contents: | and Examples -- Polytopes, Polyhedra, and Cones -- Faces of Polytopes -- Graphs of Polytopes -- Steinitz’ Theorem for 3-Polytopes -- Schlegel Diagrams for 4-Polytopes -- Duality, Gale Diagrams, and Applications -- Fans, Arrangements, |
Zonotopes, and Tilings -- Shellability and the Upper Bound Theorem -- Fiber Polytopes, and Beyond -- Fiber Polytopes, and Beyond | |
ISBN: | 9781461384311 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 152 |
Keywords: | Mathematics , Geometry , Mathematics , Geometry |
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Call number: | SPRINGER-1995-9781461335542:ONLINE Show nearby items on shelf |
Title: | Combinatorics Advances |
Author(s): | |
Date: | 1995 |
Size: | 1 online resource (328 p.) |
Note: | 10.1007/978-1-4613-3554-2 |
Contents: | 1 On a Conjecture of A. Hartman -- 1 Notations and Preliminaries -- 2 The Structure of Trades -- 3 Block Size 3 and Strength 2 -- 4 A Possible Approach to the Problem -- 5 The Case of Strength 2 -- 6 Some Examples -- 7 Concluding |
Remarks -- 2 Some Problems in Total Graph Theory -- 1 Introduction and Preliminaries -- 2 Total Ramsey Numbers -- 3 Vertex Reconstructibility of Total Graphs -- 4 Edge Reconstructibility of Total Graphs -- 5 The Spectrum of Total | |
Graphs -- 6 Groups, and Polynomials of Graphs -- 7 Relationships Between some Parameters of G and those of T(G) -- 8 Some Generalizations and Applications -- 9 Upper Bounds for x? (G) -- 10 Remarks -- 3 Construction Techniques for | |
Mutually Orthogonal Latin Squares -- 1 Background -- 2 History and Small Orders -- 3 Pairwise balanced designs and Greig’s line-flip -- 4 Difference matrices: some direct constructions -- 5 A variant of Wilson’s theorem -- 6 Concluding | |
remarks -- 4 The Spectrum of R-Orthogonal Latin Squares -- 1 Latin squares and r-orthogonality -- 2 Some basic constructions -- 3 Small sides -- 4 A GDD construction -- 5 Intermediate sides -- 5 General Theory of Translation Invariant | |
Systems -- 1 Introduction -- 2 The Model -- 3 A Residuated Semigroup -- 4 Some Basic Questions -- 6 Some Mathematical Problems Arising in Molecular Bioinformatics: The Concept of Bioinformatics -- 1 Introduction -- 2 The concept of | |
sequence space -- 3 The geometry of sequence space -- 4 Cluster analysis -- 5 Split decomposition -- 6 Concluding remark -- 7 An Algorithmic Approach to Tilings -- 8 A New Connection Between Convex Geometry and Threshold Logic -- 1 | |
Introduction -- 2 Algorithmic Enumeration of Nonisomorphic Cut-Complexes and a Generation of Convex Polytopes -- 3 Geometric Properties -- 9 The Unity of Combinatorics -- 1 Introduction -- 2 Langford’s Problem -- 3 Skolem’s Problem -- | |
4 Beatty Sequences -- 5 Penrose Pieces -- 6 Wythoff’s Game -- 7 Triples satisfying x + y = z -- 8 Triples satisfying x + y = 2z -- 9 Coil diagrams -- 10 Squaring the square -- 11 Packing or covering the complete graph -- 12 Hanani’s | |
cyclic Steiner systems -- 13 Perfect difference sets -- 14 Projective planes -- 15 Affine geometries -- 16 Magic squares -- 17 Kirkman’s schoolgirls problem -- 18 Heawood’s map on the torus -- 19 The toroidal thickness of the complete | |
graph -- 20 Nim addition -- 21 Incidence matrices -- 22 Zarankiewicz’s problem -- 23 Error-correcting codes -- 24 Hadamard matrices -- 25 Cyclic Hadamard matrices -- 26 Factoring with quadratic forms -- 27 Projective geometries -- 28 | |
Sphere packing -- 29 Mock Turtles -- 10 Unsolved Problems in Combinatorial Games -- 11 (F, 2)—Rotational Steiner Triple Systems -- 1 Introduction -- 2 Skolem Sequences -- 3 Constructions -- 4 Main Results -- 12 A Simple Polynomial Time | |
Algorithm for a Convex Hull Problem Equivalent to Linear Programming -- 1 Introduction -- 2 The Algorithm -- 13 A Linear—Time Algorithm for Minimum Cost Flow on Undirected One—Trees -- 1 Introduction -- 2 The Algorithm -- 14 An | |
Asymptotic Existence Result for Orthogonal Designs -- 1 Introduction -- 2 Basic Results -- 3 Main Results -- 15 Decomposition of Complete Tripartite Graphs Into 5-Cycles -- 1 Introduction -- 2 Necessary Conditions -- 3 An Application | |
-- 4 Sufficiency of Conditions -- 5 Searching for a decomposition in other cases -- 16 The Nsm of a Graph -- 1 The New Stability Measure of a Graph (NSM) -- 2 NSM and Operations on Graphs -- 3 Hamilton Properties of NSM -- 17 | |
Zero-Knowledge Proofs For Independent Set and Dominating Set Problems -- 1 Introduction -- 2 A Zero-Knowledge Proof for Independent set problem -- 3 A Zero-Knowledge Proof for Dominating set problem -- 18 Exploring the Spectrum of | |
Values of Permanents by Simulated Annealing -- 1 The Permanent -- 2 Upper Bounds and Lower Bounds for the Permanent -- 3 Simulated Annealing -- 4 The Metropolis Algorithm -- 5 Results and Conclusions -- 19 Vector—Weighted Matchings -- | |
1 Introduction -- 2 Preliminaries -- 3 Preference Matchings -- 4 Preference Poly topes -- 5 The Set of Efficient Solutions -- 20 Directed Quadruple Designs -- 1 Introduction -- 2 Existence of 3-(v, 4, l)DDs -- 3 On the Existence of | |
3-(v, 4, 2)DDs -- 4 Some Small Cases (for ? = 2) -- 21 Bounding Two-Terminal Network Reliability Via Surface Duality -- 1 Introduction -- 2 Definitions -- 3 Results -- 4 Implementation -- 5 Examples -- 22 Defining Sets for Block | |
Designs: An Update -- 1 Introduction -- 2 Some Theoretical Results -- 3 Finding Smallest Defining Sets in Small Designs -- 4 Defining Sets in Some Infinite Classes of Designs -- 23 Open Problems at the Combinatorics Workshop of Aimc25 | |
(Tehran, 1994) | |
ISBN: | 9781461335542 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 329 |
Keywords: | Mathematics , Computer science , Number theory , Combinatorics , Mathematics , Combinatorics , Discrete Mathematics in Computer Science , Number Theory |
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Call number: | SPRINGER-1994-9789401109246:ONLINE Show nearby items on shelf |
Title: | Polytopes: Abstract, Convex and Computational |
Author(s): | |
Date: | 1994 |
Size: | 1 online resource (507 p.) |
Note: | 10.1007/978-94-011-0924-6 |
Contents: | Abstract -- Recent results on Coxeter groups -- The evolution of Coxeter-Dynkin diagrams -- Polyhedra with hollow faces -- A hierarchical classification of Euclidean polytopes with regularity properties, -- Modern developments in |
regular polytopes -- Classification of locally toroidal regular polytopes -- Convex -- Face numbers and subdivisions of convex polytopes -- Approximation by convex polytopes -- Some aspects of the combinatorial theory of convex | |
polytopes -- On volumes of non-Euclidean polytopes -- Manifolds in the skeletons of convex polytopes,tightness, and generalized Heawood inequalities -- Generalized stress and motions -- Polytopes and Brunn-Minkowski theory -- A survey | |
of Eulerian posets -- Computational -- On recent progress in computational synthetic geometry -- The ridge graph of the metric polytope and some relatives -- On the complexity of some basic problems in Computational Convexity: II. | |
Volume and mixed volumes -- The diameter of polytopes and related applications -- Problems -- Contributed problems -- Three problems about 4-polytopes | |
ISBN: | 9789401109246 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | NATO ASI Series, Series C: Mathematical and Physical Sciences: 440 |
Keywords: | Mathematics , Numerical analysis , Computer science , Group theory , Geometry , Convex geometry , Discrete geometry , Mathematics , Geometry , Convex and Discrete Geometry , Numeric Computing , Discrete Mathematics in Computer Science , Group Theory and Generalizations |
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Call number: | SPRINGER-1994-9780817647711:ONLINE Show nearby items on shelf |
Title: | Discriminants, Resultants, and Multidimensional Determinants |
Author(s): |
Israel M Gelfand |
Date: | 1994 |
Size: | 1 online resource (523 p.) |
Note: | 10.1007/978-0-8176-4771-1 |
Contents: | General Discriminants and Resultants -- Projective Dual Varieties and General Discriminants -- The Cayley Method for Studying Discriminants -- Associated Varieties and General Resultants -- Chow Varieties -- A-Discriminants and |
A-Resultants -- Toric Varieties -- Newton Polytopes and Chow Polytopes -- Triangulations and Secondary Polytopes -- A-Resultants and Chow Polytopes of Toric Varieties -- A-Discriminants -- Principal A-Determinants -- Regular | |
A-Determinants and A-Discriminants -- Classical Discriminants and Resultants -- Discriminants and Resultants for Polynomials in One Variable -- Discriminants and Resultants for Forms in Several Variables -- Hyperdeterminants | |
ISBN: | 9780817647711 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algebra , Algebraic geometry , Commutative algebra , Commutative rings , Matrix theory , Mathematics , Algebra , General Algebraic Systems , Commutative Rings and Algebras , Linear and Multilinear Algebras, Matrix Theory , Algebraic Geometry |
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Call number: | SPRINGER-1993-9783642580437:ONLINE Show nearby items on shelf |
Title: | New Trends in Discrete and Computational Geometry |
Author(s): | |
Date: | 1993 |
Size: | 1 online resource (340 p.) |
Note: | 10.1007/978-3-642-58043-7 |
Contents: | I. Combinatorics and Algorithms of Arrangements -- 1. Introduction -- 2. Arrangements of Curves in the Plane -- 3. Lower Envelopes and Davenport-Schinzel Sequences -- 4. Faces in Arrangements -- 5. Arrangements in Higher Dimensions -- |
6. Summary -- References -- II. Backwards Analysis of Randomized Geometric Algorithms -- 1. Introduction -- 2. Delaunay Triangulations of Convex Polygons -- 3. Intersecting Line Segments -- 4. Constructing Planar Convex Hulls -- 5. | |
Backwards Analysis of QUICKSORT -- 6. A Bad Example -- 7. Linear Programming for Small Dimension -- 8. Welzl’s Minidisk Algorithm -- 9. Clarkson’s Backwards Analysis of the Conflict Graph Based on the Convex Hull Algorithm -- 10. Odds | |
and Ends -- References -- III. Epsilon-Nets and Computational Geometry -- 1. Range Spaces and ?-Nets -- 2. Geometric Range Spaces -- 3. A Sample of Applications -- 4. Removing Logarithms -- 5. Removing the Randomization -- References | |
-- IV. Complexity of Polytope Volume Computation -- 1. Jumps of the Derivatives -- 2. Exact Volume Computation is Hard -- 3. Volume Approximation -- References -- V. Allowable Sequences and Order Types in Discrete and Computational | |
Geometry -- 1. Introduction -- 2. Combinatorial Types of Configurations in the Plane and Allowable Sequences -- 3. Arrangements of Lines and Pseudolines -- 4. Applications of Allowable Sequences -- 5. Order Types of Points in Rd and | |
“Geometric Sorting” -- 6. The Number of Order Types in Rd -- 7. Isotopy and Realizability Questions -- 8. Lattice Realization of Order Types and the Problem of Robustness in Computational Geometry -- References -- VI. Hyperplane | |
Approximation and Related Topics -- 1. Introduction -- 2. MINSUM Problem: Orthogonal L1-Fit -- 3. MINSUM Problem: Vertical L1-Fit -- 4. MINMAX Problem: Orthogonal L?-Fit -- 5. MINMAX Problem: Vertical L?-Fit -- 6. Related Issues -- | |
References -- VII. Geometric Transversal Theory -- 1. Introduction -- 2. Hadwiger-Type Theorems -- 3. The Combinatorial Complexity of the Space of Transversals -- 4. Translates of a Convex Set -- 5. Transversal Algorithms -- 6. Other | |
Directions -- References -- VIII. Hadwiger-Levi’s Covering Problem Revisited -- 0. Introduction -- 1. On I0(K) and I?(K) -- 2. On Il(K) and k-fold Illumination -- 3. Some Simple Remarks on H(B) -- 4. On Convex Bodies with Finitely Many | |
Corner Points -- 5. Solution of Hadwiger-Levi’s Covering Problem for Convex Polyhedra with Affine Symmetry -- References -- IX. Geometric and Combinatorial Applications of Borsuk’s Theorem -- 1. Introduction -- 2. Van Kampen-Flores | |
Type Results -- 3. The Ham-Sandwich Theorem -- 4. Centrally Symmetric Polytopes -- 5. Kneser’s Conjecture -- 6. Sphere Coverings -- References -- X. Recent Results in the Theory of Packing and Covering -- 1. Introduction -- 2. | |
Preliminaries and Basic Concepts -- 3. A Review of Some Classical Results in the Plane -- 4. Economical Packing in and Covering of the Plane -- 5. Multiple Packing and Covering -- 6. Some Computational Aspects of Packing and Covering | |
-- 7. Restrictions on the Number of Neighbors in a Packing -- 8. Selected Topics in 3 Dimensions -- References -- XI. Recent Developments in Combinatorial Geometry -- 1. The Distribution of Distances -- 2. Graph Dimensions -- 3. | |
Geometric Graphs -- 4. Arrangements of Lines in Space -- References -- XII. Set Theoretic Constructions in Euclidean Spaces -- 0. Introduction -- 1. Simple Transfinite Constructions -- 2. Closed Sets or Better Well-Orderings -- 3. | |
Extending the Coloring More Carefully -- 4. The Use of the Continuum Hypothesis -- 5. The Infinite Dimensional Case -- 6. Large Paradoxical Sets in Another Sense -- References -- Author Index | |
ISBN: | 9783642580437 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Algorithms and Combinatorics: 10 |
Keywords: | Mathematics , Chemometrics , Geometry , Combinatorics , Computational intelligence , Economic theory , Mathematics , Combinatorics , Geometry , Economic Theory/Quantitative Economics/Mathematical Methods , Math. Applications in Chemistry , Computational Intelligence |
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Call number: | SPRINGER-1991-9781461209638:ONLINE Show nearby items on shelf |
Title: | Unsolved Problems in Geometry Unsolved Problems in Intuitive Mathematics |
Author(s): |
Hallard T Croft |
Date: | 1991 |
Size: | 1 online resource (199 p.) |
Note: | 10.1007/978-1-4612-0963-8 |
Contents: | Notation and Definitions -- A. Convexity -- B. Polygons, Polyhedra, and Polytopes -- C. Tiling and Dissection -- D. Packing and Covering -- E. Combinatorial Geometry -- F. Finite Sets of Points -- G. General Geometric Problems -- |
Index of Authors Cited -- General Index | |
ISBN: | 9781461209638 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Problem Books in Mathematics: 2 |
Keywords: | Mathematics , Geometry , Mathematics , Geometry |
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Call number: | SPRINGER-1990-9783642469084:ONLINE Show nearby items on shelf |
Title: | Topics in Combinatorics and Graph Theory Essays in Honour of Gerhard Ringel |
Author(s): | |
Date: | 1990 |
Size: | 1 online resource (792 p.) |
Note: | 10.1007/978-3-642-46908-4 |
Contents: | On the Problem of Relative Components of Minimal Graphs -- Irregular Assignments and Two Problems á la Ringel -- A Recursive Bound for the Number of Complete K-Subgraphs of a Graph -- One-Factorizations of Tensor Products of Graphs -- |
Non-Commutative Geometry and Graphs -- The Complexity of the Graph Embedding Problem -- Helly Theorems for Dismantlable Graphs and Pseudo-Modular Graphs -- On the Level-Oriented Two-Dimensional Packing with Rotation of the Rectangles | |
-- On Planar Tilings with Finitely Many Sorts of Tiles -- Examples of Space-Tiling Polyhedra Related to Hilbert’s Problem 18, Question 2 -- The Historical Background to Gerhard Ringel’s Work -- Around Three Lemmas in Hamiltonian Graph | |
Theory -- A Note on Metric Properties of Infinite Graphs -- Automotphism Groups of Directed Cayley Graphs -- Triangular Embeddings of Tensor Products of Graphs -- Computing Light Edges in Planar Graphs -- On the Domination Problem for | |
Bipartite Graphs -- Polyhedral Maps with Few Edges -- Aut Gm,n for the Hasse Graph Gm,n of the Subword Poset Bm,n of an m-Ary Cyclic Word of Length n -- Status of Graceful Tree Conjecture in 1989 -- Embedded Graphs, Facial Colorings, | |
and Double Cycle Covers -- On Peripheral Vertices in Graphs -- The Vertex-Degrees of Steiner Minimal Trees in Minkowski Planes -- Unfolding Weighted Concensus Orders into Consistent Numerical Scales -- Forbidden Ordered Subgraphs -- On | |
Normal Tournaments with the Least Number of 3-Cycles -- Two-Irregular Graphs -- Cell Complexes and Lower Bounds in Computational Geometry -- Characterizing Directed Postman Tours -- Some Properties of “Almost All” Functions from pk -- | |
Composition of Facets of the Clique Partitioning Polytope -- Optimal Edge-Numbering of Binary Trees -- On Independent Vertices and Edges of a Graph -- The Outerthickness & Outercoarseness of Graphs I. the Complete Graph & the n-Cube -- | |
On Some Graphic Aspects of Addition Theorems -- On the Circumference of Regular Polyhedral Graphs -- Longest Cycles in Circulant Graphs -- Spanning Trees of the Complete Bipartite Graph -- A Combinatorial Theorem Which is Related to | |
the Invariance of the Separating Set for the Plane -- On Certain Trees in Hypercubes -- Extending Hall’s Theorem -- On the Coupling Condition and Hamiltonicity -- Transversals and Matroids -- Classification and Construction of Geodetic | |
Block with Diameter Two -- Graph Distances and Similarity -- Witt Rings and Semiorderings of Planar Ternary Rings -- Linear Inequalities Describing the Class of Intersecting Sperner Families of Subsets, I -- Integral Drawings of the | |
Complete Graph K6 -- On Certain Binomial Sums -- Colouring of Spider Graphs -- A Las-Vergnas Type Theorem for Trees -- Quick Gossiping by Multi-Telegraphs -- Numberings on Graphs Having Small Edge Weights -- On Vertexminimal Graphs | |
with Radius r and Connectivity 2m -- Embedding Schemes and the Jordan Curve Theorem -- Subgraph Packing — A Survey -- On the Radius of Random Subgraphs of the n-Cube -- A Result in Combinatorial Matroid Theory -- On Graphs Embeqdable | |
with Short Faces -- On Cyclic Representations of Triples by Pairs -- On the Steiner Periphery and Steiner Eccentricity of a Graph -- Cycles Containing Three Consecutive Edges in 2k-Edge-Connected Graphs -- Graph Distance and Euclidean | |
Distance on the Grid -- About the Complexity of Some Homomorphism Problems on Graphs -- On an Inequality of Sperner -- Counting Perfect Matchings in Lattice Graphs -- Genus — Minimal Edges and Kuratowski Subgraphs of a Graph -- From | |
Tree Path-Factors and Doubly Exponential Sequences to a Binomial Inequality -- A Characterization of Point-Colour-Symmetric Hypergraphs -- A Linear Algorithm for the Pathwidth of Trees -- The Time Travelling Problem -- An Aperiodic | |
Triple of Prototiles -- Representation of Graphs by Integers -- Special Systems of Linear Equations and Graphs of Convex Polytopes -- On 2-Embeddable Graphs -- On an Application of the Boolean Differential Calculus to Digital System | |
Theory -- Equtareal Sets in Rd -- On the Piaget Graph -- On a Characterization of Closure Operators by Identities on Semigroups -- Symmetries of Group-Triangulations -- Experimental Mathematics — Tesselations of Convex Polygons in a | |
Hexagonal Lattice -- Domination in Cubic Graphs -- A Generalization of the Bodendiek Conjecture About Graceful Graphs -- A Sparse callai-Witt Theorem -- Edges with at Most One Crossing in Drawings of the Complete Graph -- Long Cycles | |
in Graphs with Moderate Connectivity -- Independent Covers in Plane Graphs -- List of Contributors | |
ISBN: | 9783642469084 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Operations research , Decision making , Combinatorics , Mathematics , Combinatorics , Operation Research/Decision Theory |
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Call number: | SPRINGER-1989-9783642834349:ONLINE Show nearby items on shelf |
Title: | Beyond the Crystalline State An Emerging Perspective |
Author(s): |
Ganesan Venkataraman |
Date: | 1989 |
Size: | 1 online resource (207 p.) |
Note: | 10.1007/978-3-642-83434-9 |
Contents: | 1. Introduction -- 2. Variety in Structures -- 2.1 Crystals -- 2.2 Incommensurate and Long-Period Structures -- 2.3 Quasicrystals -- 2.4 Liquid Crystals -- 2.5 Glass -- 2.6 Systems with Quasi Long-Range Order -- 2.7 Overview -- 3. |
Order Out of Disorder -- 3.1 Landau Theory -- 3.2 Conjugate Field -- 3.3 Symmetry Breaking: Further Aspects -- 3.4 Goldstone Modes -- 3.5 Generalized Rigidity -- 3.6 Quasi LRO -- 3.7 Overview -- 4. Defects and Topology -- 4.1 Basic | |
Strategy -- 4.2 Some Basic Concepts of Topology -- 4.3 Continuous Groups and Topological Spaces -- 4.4 The First or the Fundamental Homotopy Group and Defects -- 4.5 Some Examples -- 4.6 Stability -- 4.7 Combination of Defects -- 4.8 | |
Other Homotopy Groups -- 4.9 Ordered Media with Broken Translational Symmetry -- 4.10 Summary -- 5. Structures by Projection -- 5.1 Concerning Tilings -- 5.2 Regular Polytopes -- 5.3 Amorphous Structures from Mappings of Polytopes -- | |
5.4 Line Defects in Amorphous Structures -- 5.5 Disclinations and Frank-Kasper Chains -- 5.6 Mapping from S3 to E3 -- 5.7 Defects and Star Mapping -- 5.8 Mapping by Disclination Procedure -- 5.9 Decoration -- 5.10 Defects in the CRN -- | |
5.11 Amorphous Structures by Projection of Hyperbolic Tilings -- 5.12 Polymers and Polytopes -- 5.13 Quasicrystals by the Projection Method -- 5.14 Generalization -- 5.15 Some Comments on the Projection Method -- 5.16 Miller Indices | |
for Quasicrystals -- 5.17 Diffraction Patterns of Quasicrystals -- 5.18 Incommensurate Crystals -- 5.19 Summary -- 6. Beyond Simple Geometry -- 6.1 Some Basics -- 6.2 Landau Theory and Ordered Atomic Structures -- 6.3 Orientational | |
Ordering -- 6.4 Orientational Order Versus Translational Order -- 6.5 Landau Theory and Amorphous Structures -- 6.6 Landau Theory and Liquid Crystals -- 6.7 Hydrodynamics -- 6.8 Fluctuations and the Landau Theory -- 6.9 Frustration and | |
the Disruption of Order -- 6.10 Defect-Dominated Structures -- 6.11 Overview -- 7. Tilings in One Dimension -- 7.1 Structures and Competing Periodic Potentials -- 7.2 Portrait of the Penrose Chain -- 7.3 Spatial Chaos and Amorphous | |
Structures -- 7.4 Summary -- 8. Ergodicity Breaking -- 8.1 Basic Ideas -- 8.2 Time Scales and Broken Ergodicity -- 8.3 Broken Ergodicity and Symmetry Breaking -- 8.4 The Spin Glass -- 8.5 The Case of Glass -- 8.6 Generalization -- 9. | |
Symmetry Breaking — A Second Look -- 9.1 Orbits and Strata in Crystal Physics -- 9.2 Symmetry Breaking and Strata -- 9.3 Isotropy Subgroups of the Euclidean Group E(3) -- 9.4 More About Extensions to E(3) -- 9.5 Patterns in | |
Nonequilibrium Systems -- 9.6 Cylindrical Crystallography -- Appendix: Special Topics -- A. Hydrodynamics -- A.1 Hydrodynamic Equations -- A.2 Ordered Media with Continuous Broken Symmetries -- A.2.1 Hydrodynamics of a Solid -- A.3 The | |
Poisson Bracket Method in Hydrodynamics -- A.4 Summary -- B. Curved Space and Parallel Transport of Vectors -- B.1 Parallel Transport of Vectors -- B.2 The Covariant Derivative -- B.3 The Curvature -- B.4 The Torsion -- B.5 Mapping | |
from Curved Space to Flat Space -- D. Some Aspects of Group Theory -- D.1 Group Morphisms -- D.2 Transformation Group, Group Action and Orbits -- E. A Brief Introduction to Homotopy and Lie Groups -- E.1 Topology -- E.2 Elements of | |
Homotopy Theory -- E.2.1 The First Homotopy Group -- E.2.2 Higher Homotopy Groups -- E.3 Continuous Groups and Lie Groups -- F. Local Gauge Invariance and Gauge Theories -- F.1 Internal Connection -- F.2 Gauge Field Theory -- F.3 U(1) | |
Gauge Symmetry -- F.4 Non-Abelian Gauge Groups -- F.5 Gauge Theory of Dislocations and Disclinations -- References -- Author Index | |
ISBN: | 9783642834349 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Series in Solid-State Sciences: 84 |
Keywords: | Physics , Solid state physics , Crystallography , Physics , Crystallography , Solid State Physics |
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Call number: | SPRINGER-1989-9783540460701:ONLINE Show nearby items on shelf |
Title: | Quantum Probability — Quantum Logic |
Author(s): |
Itamar Pitowsky |
Date: | 1989 |
Size: | 1 online resource (210 p.) |
Note: | 10.1007/BFb0021186 |
Contents: | Classical correlation polytopes and propositional logic -- Quantum correlations -- Quantum logic -- Hidden variables and Kolmogorovian models -- Philosophical remarks |
ISBN: | 9783540460701 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Physics: 321 |
Keywords: | Physics , Probabilities , Quantum physics , Quantum computers , Spintronics , Physics , Quantum Physics , Probability Theory and Stochastic Processes , Quantum Information Technology, Spintronics |
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Call number: | SPRINGER-1988-9783540459583:ONLINE Show nearby items on shelf |
Title: | Topology and Geometry — Rohlin Seminar |
Author(s): | |
Date: | 1988 |
Size: | 1 online resource (586 p.) |
Note: | 10.1007/BFb0082766 |
Contents: | On some problems in symplectic topology -- The structure of 1-dimensional wave fronts, non-standard legendrian loops and Bennequin’s theorem -- Massey operations in the cohomology of the infinite dimensional Lie algebra L1 -- New zeta |
functions for dynamical systems and Nielsen fixed point theory -- Invariant portrait of Hamiltonian integrable in Liouville sense -- On normal form of distribution jets -- Analytical theory of homotopy groups -- On stable manifolds for | |
class of two-dimensional diffeomorphisms -- Some integral calculus based on Euler characteristic -- Obstructions to the existence of free nonholonomic structure on a smooth manifold -- Non-diffeomorphic but homeomorphic knottings of | |
surfaces in the 4-sphere -- Automorphisms of Teichmüller modular groups -- Classification of oriented montesinos links via spin structures -- Towards the topological classification of geometric 3-manifolds -- Classification of | |
simply-connected topological 6-manifolds -- Plane real projective quartic curves -- Nonamphicheiral surfaces of degree 4 in ?P3 -- Extensions of the Gudkov-Rohlin congrunce -- Isotopy classification of plane seventh degree curves with | |
the only singular point Z15 -- Incomplete intersections and degenerations of complete intersections -- Projective varieties defined by small number of equations are complete intersections -- On the classification of non-singular curves | |
of degree 8 -- New M- and (M-1)-curves of degree 8 -- On topological properties of spaces of polytopes -- Configurations of seven points in ?P3 -- The universality theorems on the classification problem of configuration varieties and | |
convex polytopes varieties -- Isotopic but not rigidly isotopic plane systems of straight lines -- Topology of the convex polytopes’ manifolds, the manifold of the projective configurations of a given combinatorial type and | |
representations of lattices | |
ISBN: | 9783540459583 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1346 |
Keywords: | Mathematics , Geometry , Topology , Mathematics , Mathematics , Topology , Geometry , Mathematics Education |
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Call number: | SPRINGER-1987-9789400938892:ONLINE Show nearby items on shelf |
Title: | Numerical Integration Recent Developments, Software and Applications |
Author(s): | |
Date: | 1987 |
Size: | 1 online resource (394 p.) |
Note: | 10.1007/978-94-009-3889-2 |
Contents: | Theoretical Aspects of One-Dimensional Quadrature -- The convergence of noninterpolatory product integration rules -- Some quadrature rules for finite trigonometric and related integrals -- Modified Clenshaw-Curtis integration and |
applications to numerical computation of integral transforms -- Fast generation of quadrature rules with some special properties -- Quadrature methods for the determination of zeros of transcendental functions - a review -- Computation | |
of the index of an analytic function -- Approximate computation of strongly oscillatory integrals with compound precision -- Bounds and approximations for the zeros of classical orthogonal polynomials. Their use in generating | |
quadrature rules. -- Indefinite integration formulas based on the sinc expansion -- On positive quadrature rules -- Quadrature rules with end-point corrections - comments on a paper by Garloff, Solak and Szydelko -- Comparison of | |
Gauss-Hermite and midpoint quadrature with application to the Voigt function -- Theoretical Aspects of Multiple Quadrature -- On sequences of imbedded integration rules -- Asymptotic expansions and their applications in numerical | |
integration -- Construction of three-dimensional cubature formulae with points on regular and semi-regular polytopes -- Construction of sequences of embedded cubature formulae for circular symmetric planar regions -- On the | |
construction of higher degree three dimensional embedded integration rules -- Fully symmetric integration rules for the unit four-cube -- On the construction of cubature formulae with few nodes using Groebner bases -- Quasi-random | |
sequences for optimization and numerical integration -- Non-fortuitous, non-product, non-fully symmetric cubature structures -- Algorithms, Software and Applications -- A parallelization of adaptive integration methods -- The numerical | |
evaluation of multiple integrals on parallel computers -- Vectorisation of one dimensional quadrature codes -- Performance of self-validating adaptive quadrature -- Using weight functions in self-validating quadrature -- On the | |
construction of a practical Ermakov-Zolotukhin multiple integrator -- Interactive numerical quadrature -- The design of a generic quadrature library in Ada -- The integration of the multivariate normal density function for the | |
triangular method -- Numerical integration in scalar wave scattering, with application to acoustic scattering by fish -- Software Classification and Testing -- Testing multiple integrators -- A package for testing multiple integration | |
subroutines -- A test of some well known one dimensional general purpose automatic quadrature routines -- Development of useful quadrature software, with particular emphasis on microcomputers -- Appendix I: Final Program -- Appendix | |
II: Discussion -- List of Participants -- List of Contributors | |
ISBN: | 9789400938892 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | NATO ASI Series, Series C: Mathematical and Physical Sciences: 203 |
Keywords: | Computer science , Microprocessors , Computers , Numerical analysis , Computer Science , Theory of Computation , Processor Architectures , Numeric Computing |
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Call number: | SPRINGER-1987-9783540938163:ONLINE Show nearby items on shelf |
Title: | Geometry II |
Author(s): | |
Date: | 1987 |
Size: | 1 online resource (406 p.) |
Note: | 10.1007/978-3-540-93816-3 |
Contents: | Polytopes compact convex sets -- Quadratic forms -- Projective quadrics -- Affine quadrics -- Projective conics -- Euclidean conics -- The sphere for its own sake -- Elliptic and hyperbolic geometry -- The space of spheres |
ISBN: | 9783540938163 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Geometry , Mathematics , Geometry |
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Call number: | SPRINGER-1987-9783540479512:ONLINE Show nearby items on shelf |
Title: | Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem |
Author(s): |
David E Handelman |
Date: | 1987 |
Size: | 1 online resource (138 p.) |
Note: | 10.1007/BFb0078909 |
Contents: | Definitions and notation -- A random walk problem -- Integral closure and cohen-macauleyness -- Projective RK-modules are free -- States on ideals -- Factoriality and integral simplicity -- Meet-irreducibile ideals in RK -- |
Isomorphisms | |
ISBN: | 9783540479512 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1282 |
Keywords: | Mathematics , Algebra , Mathematical analysis , Analysis (Mathematics) , Geometry , Mathematics , Analysis , Algebra , Geometry |
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Call number: | SPRINGER-1986-9789400947603:ONLINE Show nearby items on shelf |
Title: | Geometric Crystallography An Axiomatic Introduction to Crystallography |
Author(s): |
Peter Engel |
Date: | 1986 |
Size: | 1 online resource (274p p.) |
Note: | 10.1007/978-94-009-4760-3 |
Contents: | 1. Basic definitions -- 1.1. Axioms of geometric crystallography -- 1.2. Euclidean vector space -- 1.3. Rigid motions -- 1.4. Symmetry operations -- 1.5. Classifications -- 1.6. Historical remarks -- 2. Dirichlet domains -- 2.1. |
Definition of the Dirichlet domain -- 2.2. Some properties of Dirichlet domains -- 2.3. Dirichlet domain partition -- 2.4. A practical method to calculate -- 3. Lattices -- 3.1. The theorem of Bieberbach -- 3.2. Lattice bases -- 3.3. | |
Orthogonal basis -- 3.4. Lattice planes -- 3.5. Dirichlet parallelotopes -- 4. Reduction of quadratic forms -- 4.1. Definition of the ?-reduced form -- 4.2. The reduction scheme of Lagrange -- 4.3. The reduction scheme of Seeber -- | |
4.4. The reduction scheme of Selling -- 4.5. The reduction scheme of Minkowski -- 4.6. Historical remarks -- 5. Crysta1lographic symmetry operations -- 5.1. Defini11ons -- 5.2. Rotations in E2 -- 5.3. Rotations in En -- 5.4. Symmetry | |
support -- 5.5. General symmetry operations in En -- 6. Crvstallographic point groups -- 6.1. Definitions -- 6.2. Point groups in E2 -- 6.3. Point groups in E3 -- 6.4. Point groups in En -- 6.5. Root classes -- 6.6. Isomorphsm types of | |
point groups -- 6.7. Historical remarks -- 7. Lattice symmetries -- 7.1. Definitions -- 7.2. Bravais point groups -- 7.3. Bravais types of lattices -- 7.4. Arithmetic crystal classes -- 7.5. Crystal forms -- 7.6. Historical remarks -- | |
8. Space groups -- 8.1. Definitions -- 8.2. Derivation of space groups -- 8.3. Normalizers of symmetry groups -- 8.4. Subgroups of space groups -- 8.5. Crystallographic orbits -- 8.6. Colour groups and colourings -- 8.7. Subperiodic | |
groups -- 8.8. Historical remarks -- 9. Space partitions -- 9.1. Definitions -- 9.2. Dirichlet domain partitions -- 9.3. Parallelotopes -- 9.4. The regularity condition -- 9.5. Dissections of polytopes -- 9.6. Historical remarks -- 10. | |
Packings of balls -- 10.1. Definitions -- 10.2. Packings of disks into E2 -- 10.3. Packings of balls into E3 -- 10.4. Lattice packings of balls in En -- 10.5. Historical remarks -- References | |
ISBN: | 9789400947603 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Geometry , Crystallography , Physics , Crystallography , Geometry |
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Call number: | SPRINGER-1985-9789400953154:ONLINE Show nearby items on shelf |
Title: | Graphs and Order The Role of Graphs in the Theory of Ordered Sets and Its Applications |
Author(s): | |
Date: | 1985 |
Size: | 1 online resource (816 p.) |
Note: | 10.1007/978-94-009-5315-4 |
Contents: | I. Graph Representations -- Comparability graphs -- Algorithmic aspects of comparability graphs and interval graphs -- The diagram -- II. Scheduling, Searching and Sorting -- The information theoretic bound for problems on ordered |
sets and graphs -- Sorting and graphs -- A graph-theoretic approach to the jump-number problem -- Acyclic subdigraphs and linear orderings: polytopes, facets, and a cutting plane algorithm -- III. Extremal Orders -- Parameters of | |
partial orders and graphs: packing, covering and representation -- Graphs and orders in Ramsey theory and in dimension theory -- Ordered ranked posets, representations of integers and inequalities from extremal poset problems -- IV. | |
Social Sciences -- Issues in the theory of uniqueness in measurement -- V. Decomposition -- Path-partitions in directed graphs and posets -- VI. Recursion -- Recursion theoretic aspects of graphs and orders -- VII. Well-Quasi-Ordering | |
-- Basic wqo- and bqo-theory -- Applications of well quasi-ordering and better quasi-ordering -- VIII. Problem Sessions -- Enumeration -- The diagram -- Ramsey theory -- Sorting, scheduling, computing, operations research, and social | |
science -- Structure theories -- Infinite sets and infinite graphs -- Souvenir session -- Order-preserving and edge-preserving maps -- Miscellaneous -- IX. A Bibliography -- X. Index | |
ISBN: | 9789400953154 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | NATO ASI Series, Series C: Mathematical and Physical Sciences: 147 |
Keywords: | Mathematics , Computer science , Algebra , Ordered algebraic structures , Mathematics , Order, Lattices, Ordered Algebraic Structures , Discrete Mathematics in Computer Science |
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Call number: | SPRINGER-1985-9783540397458:ONLINE Show nearby items on shelf |
Title: | Algebraic Topology Göttingen 1984 Proceedings of a Conference held in Göttingen, Nov. 9–15, 1984 |
Author(s): | |
Date: | 1985 |
Size: | 1 online resource (212 p.) |
Note: | 10.1007/BFb0074420 |
Contents: | On the localization theorem at the cochain level and free torus actions -- On homotopy classification problems of J.H.C. whitehead -- Regular polytopes and equivariant tessellations from a combinatorial point of view -- A problem of |
adams on H* (BGZp) -- On the stable cohomology of the mapping class group -- Homology operations derived from modular coinvariants -- Higher order homotopy invariants for higher dimensional link maps -- Smooth and locally linear g | |
homotopy representations -- Closed geodesics on stiefel manifolds -- Topological H0×H1-actions on spheres and linking numbers -- Verschlingung von Fixpunktmengen in Darstellungsformen. I -- Modular Representations of GL(n,FP) and | |
Homotopy Theory -- Quelques propriétés du foncteur | |
ISBN: | 9783540397458 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1172 |
Keywords: | Mathematics , Algebraic topology , Mathematics , Algebraic Topology |
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Call number: | SPRINGER-1984-9781475718362:ONLINE Show nearby items on shelf |
Title: | Problems in Geometry |
Author(s): |
Marcel Berger |
Date: | 1984 |
Size: | 1 online resource (268 p.) |
Note: | 10.1007/978-1-4757-1836-2 |
Contents: | 1. Groups Operating on a Set: Nomenclature, Examples, Applications -- 2. Affine Spaces -- 3. Barycenters the Universal Space -- 4. Projective Spaces -- 5. Affine-Projective Relationship: Applications -- 6. Projective Lines, |
Cross-Ratios, Homographies -- 7. Complexifications -- 8. More about Euclidean Vector Spaces -- 9. Euclidean Affine Spaces -- 10. Triangles, Spheres, and Circles -- 11. Convex Sets -- 12. Polytopes Compact Convex Sets -- 13. Quadratic | |
Forms -- 14. Projective Quadrics -- 15. Affine Quadrics -- 16. Projective Conics -- 17. Euclidean Conics -- 18. The Sphere for Its Own Sake -- 19. Elliptic and Hyperbolic Geometry -- 20. The Space of Spheres -- Suggestions and Hints -- | |
Solutions -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8 -- 9 -- 10 -- 11 -- 12 -- 13 -- 14 -- 15 -- 16 -- 17 -- 18 -- 19 -- 20 | |
ISBN: | 9781475718362 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Geometry , Mathematics , Geometry |
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Call number: | SPRINGER-1983-9781461211488:ONLINE Show nearby items on shelf |
Title: | An Introduction to Convex Polytopes |
Author(s): |
Arne Brøndsted |
Date: | 1983 |
Size: | 1 online resource (162 p.) |
Note: | 10.1007/978-1-4612-1148-8 |
Contents: | 1 Convex Sets -- A71. The Affine Structure of ?d -- A72. Convex Sets -- A73. The Relative Interior of a Convex Set -- A74. Supporting Hyperplanes and Halfspaces -- A75. The Facial Structure of a Closed Convex Set -- A76. Polarity -- 2 |
Convex Polytopes -- A77. Polytopes -- A78. Polyhedral Sets -- A79. Polarity of Polytopes and Polyhedral Sets -- A710. Equivalence and Duality of Polytopes -- A711. Vertex-Figures -- A712. Simple and Simplicial Polytopes -- A713. Cyclic | |
Polytopes -- A714. Neighbourly Polytopes -- A715. The Graph of a Polytope -- 3 Combinatorial Theory of Convex Polytopes -- A716. Eulerߣs Relation -- A717. The Dehn-Sommerville Relations -- A718. The Upper Bound Theorem -- A719. The | |
Lower Bound Theorem -- A720. McMullenߣs Conditions -- Appendix 1 Lattices -- Appendix 2 Graphs -- Appendix 3 Combinatorial Identities -- Bibliographical Comments -- List of Symbols | |
ISBN: | 9781461211488 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 90 |
Keywords: | Mathematics , Combinatorics , Mathematics , Combinatorics |
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Call number: | SPRINGER-1981-9783540389569:ONLINE Show nearby items on shelf |
Title: | Séminaire Bourbaki vol. 1980/81 Exposés 561–578 Avec table par noms d’auteurs de 1967/68 à 1980/81 |
Author(s): | |
Date: | 1981 |
Size: | 1 online resource (299 p.) |
Note: | 10.1007/BFb0097185 |
Contents: | Les arrangements d'hyperplans: Un chapitre de géométrie combinatoire -- Formes automorphes associées aux cycles géodésiques des surfaces de Riemann hyperboliques -- Smooth transformations of intervals -- Normalisation des champs de |
vecteurs holomorphes (d'après A.-D. Brjuno [2]) -- Varietes Toriques et Polytopes -- Algèbres de lie, systèmes hamiltoniens, courbes algébriques [d'après M. Adler et P. van Moerbeke] -- Stochastic methods and differential geometry -- | |
Classification des variétés de dimension 3 et plus [d'après T. Fujita, S. Iitaka, Y. Kawamata, K. Ueno, E. Viehweg] -- Minorations sur le ?1 des variétés riemanniennes -- Anneaux locaux et espaces de lacets à séries de Poincaré | |
irrationnelles [d'après Anick, Roos, etc...] -- Le théorème de Brill-Noether -- Groupes à croissance polynomiale -- Géométrie différentielle affine des hypersurfaces -- 1-Formes fermées non singulières sur les variétés compactes de | |
dimension 3 -- The work of Mazur and Wiles on cyclotomic fields -- Primality testing algorithms [after Adleman, Rumely and Williams] -- Affine lie algebras and modular forms -- Actions de Groupes Finis sur S3: La Conjecture de P.A. | |
Smith [d'après Thurston et Meeks-Yau] | |
ISBN: | 9783540389569 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 901 |
Keywords: | Mathematics , Mathematics , Mathematics, general |
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Call number: | SPRINGER-1981-9781461256489:ONLINE Show nearby items on shelf |
Title: | The Geometric Vein The Coxeter Festschrift |
Author(s): | |
Date: | 1981 |
Size: | 1 online resource (598p p.) |
Note: | 10.1007/978-1-4612-5648-9 |
Contents: | H. S. M. Coxeter: Published Works -- I: Polytopes and Honeycombs -- Uniform Tilings with Hollow Tiles -- Spherical Tilings with Transitivity Properties -- Some Isonemal Fabrics on Polyhedral Surfaces -- Convex Bodies which Tile Space |
-- Geometry of Radix Representations -- Embeddability of Regular Polytopes and Honeycombs in Hypercubes -- The Derivation of Schoenberg’s Star-Polytopes from Schoute’s Simplex Nets -- The Harmonic Analysis of Skew Polygons as a Source | |
of Outdoor Sculptures -- The Geometry of African Art III. The Smoking Pipes of Begho -- Crystallography and Cremona Transformations -- Cubature Formulae, Polytopes, and Spherical Designs -- Two Quaternionic 4-Polytopes -- | |
Span-Symmetric Generalized Quadrangles -- On Coxeter’s Loxodromic Sequences of Tangent Spheres -- II: Extremal Problems -- Elementary Geometry, Then and Now -- Some Researches Inspired by H. S. M. Coxeter -- Some Problems in the | |
Geometry of Convex Bodies -- On an Analog to Minkowski’s Lattice Point Theorem -- Intersections of Convex Bodies with Their Translates -- An Extremal Property of Plane Convex Curves— P. Ungar’s Conjecture -- III: Geometric | |
Transformations -- Polygons and Polynomials -- Algebraic Surfaces with Hyperelliptic Sections -- On the Circular Transformations of Möbius, Laguerre, and Lie -- The Geometry of Cycles, and Generalized Laguerre Inversion -- Inversive | |
Geometry -- Absolute Polarities and Central Inversions -- Products of Axial Affinities and Products of Central Collineations -- Normal Forms of Isometries -- Finite Geometries with Simple, Semisimple, and Quasisimple Fundamental Groups | |
-- Motions in a Finite Hyperbolic Plane -- IV: Groups and Presentations of Groups -- Generation of Linear Groups -- On Covering Klein’s Curve and Generating Projective Groups -- A Local Approach to Buildings -- Representations and | |
Coxeter Graphs -- Coinvariant Theory of a Coxeter Group -- Two-Generator Two-Relation Presentations for Special Linear Groups -- Groups Related to Fa,b,c Involving Fibonacci Numbers -- V: The Combinatorial Side -- Convex Polyhedra -- | |
Non-Hamilton Fundamental Cycle Graphs -- Some Combinatorial Identities -- Binary Views of Ternary Codes | |
ISBN: | 9781461256489 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Geometry , Mathematics , Geometry |
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Call number: | SPRINGER-1980-9783540392934:ONLINE Show nearby items on shelf |
Title: | Etude Géometrique des Espaces Vectoriels II Polyèdres et Polytopes Convexes |
Author(s): |
Jacques Bair |
Date: | 1980 |
Size: | 1 online resource (283 p.) |
Note: | 10.1007/BFb0089008 |
Contents: | Notations Et Terminologie -- Separation De Deux Ensembles Convexes -- Faces Et Facettes Des Convexes -- Les Polyedres Convexes -- Les Polytopes -- Representations De Polyedres -- Applications De La Theorie Des Representations -- |
Applications Des Polyedres A La Separation -- Retour Aux Simplexes De Choquet -- Systemes D’Inequations Lineaires | |
ISBN: | 9783540392934 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 802 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis |
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Call number: | SPRINGER-1979-9781461394389:ONLINE Show nearby items on shelf |
Title: | Join Geometries A Theory of Convex Sets and Linear Geometry |
Author(s): |
Walter Prenowitz |
Date: | 1979 |
Size: | 1 online resource (534 p.) |
Note: | 10.1007/978-1-4613-9438-9 |
Contents: | 1 The Join and Extension Operations in Euclidean Geometry -- 2 The Abstract Theory of Join Operations -- 3 The Generation of Convex Sets—Convex Hulls -- 4 The Operation of Extension -- 5 Join Geometries -- 6 Linear Sets -- 7 Extremal |
Structure of Convex Sets: Components and Faces -- 8 Rays and Halfspaces -- 9 Cones and Hypercones -- 10 Factor Geometries and Congruence Relations -- 11 Exchange Join Geometries—The Theory of Incidence and Dimension -- 12 Ordered Join | |
Geometries -- 13 The Structure of Polytopes in an Ordered Geometry -- References | |
ISBN: | 9781461394389 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Convex geometry , Discrete geometry , Mathematics , Convex and Discrete Geometry |
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Call number: | SPRINGER-1978-9783642007903:ONLINE Show nearby items on shelf |
Title: | Polyhedral Combinatorics Dedicated to the memory of D.R. Fulkerson |
Author(s): | |
Date: | 1978 |
Size: | 1 online resource (234 p.) |
Note: | 10.1007/BFb0121189 |
Contents: | Delbert Ray Fulkerson -- D.R. Fulkerson’s contributions to polyhedral combinatorics -- Notes on Bland’s pivoting rule -- An algorithm for finding hamiltonian circuits in certain graphs -- A primal algorithm for optimum matching -- An |
analysis of approximations for maximizing submodular set functions—II -- A practical algorithm for the Menger-type generalization of the independent assignment problem -- Colouring criteria for adjacency on 0–1-polyhedra -- On | |
permutations and permutation polytopes -- Symmetric blocking and anti-blocking relations for generalized circulations -- Elementary vectors and two polyhedral relaxations -- Support functions, blocking pairs, and anti-blocking pairs -- | |
On lattice polyhedra III: Blockers and anti-blockers of lattice clutters -- Adjoints of projective transformations and face-figures of convex polytopes -- Some applications of equalized matrices -- Multicoloring of a graph | |
ISBN: | 9783642007903 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematical Programming Studies: 8 |
Keywords: | Mathematics , Computer science , Mathematical optimization , Mathematics , Optimization , Mathematics of Computing |
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Location: | ONLINE |
Call number: | SPRINGER-1978-9783540357025:ONLINE Show nearby items on shelf |
Title: | Combinatorial Mathematics Proceedings of the International Conference on Combinatorial Theory Canberra, August 16–27, 1977 |
Author(s): | |
Date: | 1978 |
Size: | 1 online resource (353 p.) |
Note: | 10.1007/BFb0062510 |
Contents: | Reflections on the legitimate deck problem -- Some extremal problems on families of graphs and related problems -- Integral properties of combinatorial matrices -- A class of three-designs -- Isomorphic factorisations III: Complete |
multipartite graphs -- Biplanes and semi-biplanes -- Near-self-complementary designs and a method of mixed sums -- Recent progress and unsolved problems in dominance theory -- On the linear independence of sets of 2q columns of certain | |
(1, ?1) matrices with a group structure, and its connection with finite geometries -- The doehlert-klee problem: Part I, statistical background -- On the cayley index of a group -- A survey of extremal (r,?)-systems and certain | |
applications -- On the enumeration of certain graceful graphs -- Fixing subgraphs of Km,n -- Hadamard equivalence -- A note on equidistant permutation arrays -- The combinatorics of algebraic graph theory in theoretical physics -- | |
Graphs, groups and polytopes -- Decompositions of complete symmetric digraphs into the four oriented quadrilaterals -- Brick packing -- Colour symmetry in crystallographic space groups -- Generation of a frequency square orthogonal to | |
a 10×10 latin square -- Factorization in the monoid of languages -- On graphs as unions of eulerian graphs -- The analysis of colour symmetry -- Computing automorphisms and canonical labellings of graphs -- On a result of bose and | |
shrikhande -- Further results on a problem in the design of electrical circuits -- Transversals and finite topologies -- Asymptotic number of self-converse oriented graphs -- Some correspondences involving the schröder numbers and | |
relations -- A computer listing of hadamard matrices -- A class of codes generated by circulant weighing matrices -- An application of maximum-minimum distance circuits on hypercubes -- Decompositions of graphs and hypergraphs -- Some | |
extremal problems in combinatorial geometry -- Distance-regular graphs -- A note on baxter's generalization of the temperley-lieb operators -- Autocorrelation of (+1,?1) sequences -- Triangles in labelled cubic graphs -- Problems | |
ISBN: | 9783540357025 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 686 |
Keywords: | Mathematics , Mathematics , Mathematics, general |
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Call number: | SPRINGER-1974-9783642007583:ONLINE Show nearby items on shelf |
Title: | Pivoting and Extension In honor of A.W. Tucker |
Author(s): | |
Date: | 1974 |
Size: | 1 online resource (206 p.) |
Note: | 10.1007/BFb0121233 |
Contents: | Albert William Tucker -- Bibliography of Albert William Tucker to July 1974 -- In honor of A. W. Tucker’s contributions to mathematical programming -- Lower bounds for maximum diameters of polytopes -- Maximum diameter of abstract |
polytopes -- Existence of A-avoiding paths in abstract polytopes -- On two special classes of transportation polytopes -- Solution rays for a class of complementarity problems -- On fourier’s analysis of linear inequality systems -- | |
Solving piecewise linear convex equations -- On balanced matrices -- Derivation of a bound for error-correcting codes using pivoting techniques -- A new proof of the fundamental theorem of algebra -- Pivotal theory of determinants -- A | |
note on the Lemke-Howson algorithm -- Algorithm for a least-distance programming problem | |
ISBN: | 9783642007583 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematical Programming Studies: 1 |
Keywords: | Mathematics , Computer science , Mathematical optimization , Mathematics , Optimization , Mathematics of Computing |
Availability: | Click here to see Library holdings or inquire at
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Location: | ONLINE |
Call number: | QC20.7.S3E48::2015 Show nearby items on shelf |
Title: | Scattering amplitudes in gauge theory and gravity |
Author(s): |
University of Michigan Henriette Elvang Ann Arbor, Yu-tin Huang, National Taiwan University |
Date: | 2015 |
Publisher: | Cambridge : Cambridge University Press |
Size: | 323 p |
Contents: | 1. Introduction -- Part I. Trees: 2. Spinor helicity formalism -- 3. On-shell recursion relations at tree-level -- 4. Supersymmetry -- 5. Symmetries of N = 4 SYM -- Part II. Loops: 6. Loop amplitudes and generalized unitarity -- 7. BCFW reclusion fo r loops -- 8. Leading singularities and on-shell diagrams -- Part III. Topics: 9. Grassmannia -- 10. Polytopes -- 11. Amplitudes beyond four dimensions -- 12. Supergravity amplitudes -- 13. A colorful duality -- 14. Further reading. |
ISBN: | 9781107069251 |
Keywords: | SCIENCE / Mathematical Physics , Gauge fields (Physics) , Scattering amplitude (Nuclear physics) |
Availability: | Click
here to see Library holdings or inquire at Circ Desk (x3401)
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Location: | MAIN |
Call number: | QC174.17.M35P57::1989 Show nearby items on shelf |
Title: | Quantum probability--quantum logic |
Author(s): |
Itamar Pitowsky 1950- |
Date: | 1989 |
Publisher: | Springer-Verlag, Berlin |
Size: | 209 pgs. |
Contents: | 1. Introduciton, 2. Classical Correlation Polytopes and Propositional Logic, 3. Quantum Correlations, 4. Quantum Logic, 5. Hidden Variables and Kolmogorovian Models, 6. Philosophical Remarks |
ISBN: | 0387506799 |
Series: | Lecture notes in physics : 321 |
Keywords: | Logic, Symbolic and mathematical. |
Availability: | Click
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Location: | MAIN |
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