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Call number: | 9783319517537:ONLINE Show nearby items on shelf |
Title: | Extended Abstracts Summer 2015 Strategic Behavior in Combinatorial Structures Quantitative Finance |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (VI, 139 p. 5 illus., 3 illus. in color p.) |
Contents: | Part-I -- Foreword -- On the Push & Pull Protocol for Rumour Spreading -- Random Walks that Find Perfect Objects and the Lovasz Local Lemma -- Logit Dynamics with Concurrent Updates for Local Interaction Games -- Logit Dynamics with |
Concurrent Updates for Local Interaction Games -- Carpooling in Social Networks -- Who to Trust for Truthful Facility Location? -- Metric and Spectral Properties of Dense Inhomogeneous Random Graphs -- On-Line List Colouring of Random | |
Graphs -- Approximation Algorithms for Computing Maximin Share Allocations -- An Alternate Proof of the Algorithmic Lovász Local Lemma -- Learning Game-Theoretic Equilibria via Query Protocols -- The Lower Tail: Poisson Approximation | |
Revisited -- Population Protocols for Majority in Arbitrary Networks -- The Asymptotic Value in Finite Stochastic Games -- Almost All 5-Regular Graphs Have a 3-Flow -- Part-II -- Foreword -- On the Short-Time Behaviour of the Implied | |
Volatility Skew for Spread Options and Applications -- An Alternative to CARMA Models via Iterations of Ornstein-Uhlenbeck Processes -- Euler-Poisson Schemes for Levy Processes -- On Time-Consistent Portfolios with Time-Inconsistent | |
Preferences -- A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models -- A Highly Efficient Pricing Method for European-Style Options Based on Shannon Wavelets -- A New Pricing Measure in the | |
Barndor-Nielsen-Shephard Model for Commodity Markets | |
ISBN: | 9783319517537 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Dynamics , Ergodic theory , Differential equations , Actuarial science , Convex geometry , Discrete geometry , Probabilities , Combinatorics , Mathematics , Combinatorics , Ordinary Differential Equations , Dynamical Systems and Ergodic Theory , Convex and Discrete Geometry , Probability Theory and Stochastic Processes , Actuarial Sciences |
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Call number: | SPRINGER-2016-9789811009167:ONLINE Show nearby items on shelf |
Title: | Geometry of Cauchy-Riemann Submanifolds |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (390 p.) |
Note: | 10.1007/978-981-10-0916-7 |
Contents: | Chapter 1. CR-warped submanifolds in Kaehler manifolds -- Chapter 2. CR Submanifolds and -invariants -- Chapter 3. CR Submanifolds of the nearly Kahler 6-sphere -- Chapter 4. CR submanifolds of Hermitian manifolds and the tangential C-R equations - - Chapter 5. CR Submanifolds in (l.c.a.) Kaehler and S-manifolds -- Chapter 6. Lorentzian geometry and CR submanifolds -- Chapter 7. Submanifolds in holomorphic statistical manifolds -- Chapter 8. CR Submanifolds in complex and Sasakian space forms -- Cha pter 9. CR-Doubly warped product submanifolds -- Chapter 10. Ideal CR submanifolds -- Chapter 11. Submersions of CR submanifolds -- Chapter 12. CR Submanifolds of semi-Kaehler manifolds -- Chapter 13. Paraquaternionic CR submanifolds |
ISBN: | 9789811009167 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Convex geometry , Discrete geometry , Differential geometry , Mathematical physics , Mathematics , Differential Geometry , Mathematical Physics , Convex and Discrete Geometry |
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Call number: | SPRINGER-2016-9784431561040:ONLINE Show nearby items on shelf |
Title: | Mathematical Challenges in a New Phase of Materials Science Kyoto, Japan, August 2014 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (21 p.) |
Note: | 10.1007/978-4-431-56104-0 |
ISBN: | 9784431561040 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 166 |
Keywords: | Mathematics , Dynamics , Ergodic theory , Partial differential equations , Convex geometry , Discrete geometry , Physics , Mathematics , Partial Differential Equations , Mathematical Methods in Physics , Dynamical Systems and Ergodic Theory , Convex and Discrete Geometry |
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Call number: | SPRINGER-2016-9783319335728:ONLINE Show nearby items on shelf |
Title: | Open Problems in the Geometry and Analysis of Banach Spaces |
Author(s): |
Antonio J Guirao |
Date: | 2016 |
Size: | 1 online resource (169 p.) |
Note: | 10.1007/978-3-319-33572-8 |
Contents: | Preface -- Basic linear structure -- Basic linear geometry -- Biorthogonal systems -- Smoothness, smooth approximation -- Nonlinear geometry -- Some more nonseparable problems -- Some applications -- Bibliography -- List of concepts and problems -- Symbol index -- Subject index. |
ISBN: | 9783319335728 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Approximation theory , Functional analysis , Measure theory , Convex geometry , Discrete geometry , Algebraic topology , Mathematics , Functional Analysis , Approximations and Expansions , Measure and Integration , Convex and Discrete Geometry , Algebraic Topology |
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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-2016-9783319270760:ONLINE Show nearby items on shelf |
Title: | Surfaces in Classical Geometries A Treatment by Moving Frames |
Author(s): |
Gary R Jensen |
Date: | 2016 |
Size: | 1 online resource (61 p.) |
Note: | 10.1007/978-3-319-27076-0 |
Contents: | 1. Introduction -- 2. Lie Groups -- 3. Theory of Moving Frames -- 4. Euclidean Geometry -- 5. Spherical Geometry -- 6. Hyperbolic Geometry -- 7. Complex Structure -- 8. Minimal Immersions in Euclidean Space -- 9. Isothermic Immersions -- 10. The Bo nnet Problem -- 11. CMC 1 Surfaces in H3 -- 12. Möbius Geometry -- 13. Complex Structure and Möbius Geometry -- 14. Isothermic Immersions in Möbius Space -- 15. Lie Sphere Geometry -- Solutions to Select Problems -- References -- Index |
ISBN: | 9783319270760 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Convex geometry , Discrete geometry , Differential geometry , Mathematics , Differential Geometry , Convex and Discrete Geometry |
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Call number: | SPRINGER-2016-9783319242989:ONLINE Show nearby items on shelf |
Title: | Recent Trends in Combinatorics |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (14 p.) |
Note: | 10.1007/978-3-319-24298-9 |
Contents: | Section 1: Extremal and Probabilistic Combinatorics -- Problems Related to Graph Indices in Trees -- The edit distance in graphs: methods, results and generalizations -- Repetitions in graphs and sequences -- On Some Extremal Problems for Cycles in Graphs -- A survey of Turan problems for expansions -- Survey on matching, packing and Hamilton cycle problems on hypergraphs -- Rainbow Hamilton cycles in random graphs and hypergraphs -- Further applications of the Container Method -- Independent transv ersals and hypergraph matchings - an elementary approach -- Giant components in random graphs -- Infinite random graphs and properties of metrics -- Nordhaus-Gaddum Problems for Colin de Verdière Type Parameters, Variants of Tree-width, and Related Param eters -- Algebraic aspects of the normalized Laplacian -- Poset-free Families of Subsets.- Mathematics of causal sets -- Section 2: Additive and Analytic Combinatorics -- Lectures on Approximate groups and Hilbert's 5th Problem -- Character |
sums and arithmetic combinatorics -- On sum-product problem -- Ajtai-Szemerédi Theorems over quasirandom groups -- Section 3: Enumerative and Geometric Combinatorics -- Moments of orthogonal polynomials and combinatorics -- The combinatorics of kno t invariants arising from the study of Macdonald polynomials -- Some algorithmic applications of partition functions in combinatorics -- Partition Analysis, Modular Functions, and Computer Algebra -- A survey of consecutive patterns in permutations -- Uni modality Problems in Ehrhart Theory -- Face enumeration on simplicial complexes -- Simplicial and Cellular Trees -- Parametric Polyhedra with at least k Lattice Points: Their Semigroup Structure and the k-Frobenius Problem.- Dynamical Algebraic Combinator ics and the Homomesy Phenomenon | |
ISBN: | 9783319242989 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | The IMA Volumes in Mathematics and its Applications: 159 |
Keywords: | Mathematics , Dynamics , Ergodic theory , Functional analysis , Convex geometry , Discrete geometry , Combinatorics , Biomathematics , Mathematics , Combinatorics , Convex and Discrete Geometry , Dynamical Systems and Ergodic Theory , Functional Analysis , Genetics and Population Dynamics |
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Call number: | SPRINGER-2013-9788847028418:ONLINE Show nearby items on shelf |
Title: | Geometric Properties for Parabolic and Elliptic PDE's [electronic resource] |
Author(s): |
Rolando Magnanini Shigeru Sakaguchi Angelo Alvino |
Date: | 2013 |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understoodquite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad andwell-established research area, with contributions tha t often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name afew. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulatingfuture developments and perspectives in this very active area of research |
Note: | Springer eBooks |
Contents: | Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations |
Elvise Berchio, A family of Hardy | |
Rellich type inequalities involving the L2 | |
norm of the Hessian matrices | |
Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains | |
Lorenzo Brasco and Rolando Magnanini, The heart of a convex set | |
Giulio Ciraolo, A viscosity equation for minimizers of a class of very degenerate elliptic functionals | |
Adele Ferone, Kato's inequality in the half space: an alternative proof and relative i | |
ISBN: | 9788847028418 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer INdAM Series, 2281-518X : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Discrete groups , Global differential geometry , Mathematical optimization |
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Call number: | SPRINGER-2013-9783642388965:ONLINE Show nearby items on shelf |
Title: | Condition [electronic resource] : The Geometry of Numerical Algorithms |
Author(s): |
Peter Brgisser Felipe Cucker |
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 book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability andcomplexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis onthe probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching inits third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between thecurrent elementary expositions of the subject based on the simplex method and those focusing on convex programming |
Note: | Springer eBooks |
Contents: | Preface |
Overture: On the Condition of Numerical Problems and the Numbers that Measure It | |
I Condition in Linear Algebra (Adagio): 1 Normwise Condition of Linear Equation Solving | |
2 Probabilistic Analysis | |
3 Error Analysis of Triangular Linear Systems | |
4 Probabilistic Analysis of Rectangular Matrices | |
5 Condition Numbers and Iterative Algorithms | |
Intermezzo I: Condition of Structured Data | |
II Condition in Linear Optimization (Andante): 6 A Condition Number for Polyhedral Conic Systems | |
7 The Ellipsoid Method | |
8 Linear Programs and their Solution Sets | |
9 Interior | |
point Met | |
ISBN: | 9783642388965 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v349 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Computer science Mathematics , Algorithms , Mathematical optimization , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9783642309588:ONLINE Show nearby items on shelf |
Title: | Encyclopedia of Distances [electronic resource] |
Author(s): |
Michel Marie Deza Elena Deza |
Date: | 2013 |
Edition: | 2nd ed. 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 updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a field now regarded as an essential tool in many areas of pure and appliedmathematics. The publi cation of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, imageanalysis, speech recognition and information retrieval. Leaving aside the practical questions that arise during the selection of a good distance function, this work focuses on providing the research community with aninvaluable comprehensive listing of the main available distances. As well as provi ding standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links tocore entries. In addition to distances themselves, the authors have collated numerous fascinating curiosit ies in their Whos Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in othersectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate freshresearch |
Note: | Springer eBooks |
Contents: | Part I. Mathematics of Distances |
1 General Definitions | |
2 Topological Spaces | |
3 Generalization of Metric Spaces | |
4 Metric Transforms | |
5 Metrics on Normed Structures | |
Part II. Geometry and Distances | |
6 Distances in Geometry | |
7 Riemannian and Hermitian Metrics | |
8 Distances on Surfaces and Knots | |
9 Distances on Convex Bodies, Cones and Simplicial Complexes | |
Part III. Distances in Classical Mathematics | |
10 Distances in Algebra | |
11 Distances on Strings and Permutations | |
12 Distances on Numbers, Polynominals and Matrices | |
13 Distances in Functional Analysis | |
14 Dista | |
ISBN: | 9783642309588 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science Mathematics , Visualization , Geometry , Global differential geometry , Topology , Engineering mathematics |
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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-2013-9781461481188: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-2013-9781461451280:ONLINE Show nearby items on shelf |
Title: | Distance Geometry [electronic resource] : Theory, Methods, and Applications |
Author(s): |
Antonio Mucherino Carlile Lavor Leo Liberti Nelson Maculan |
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: | Distance Geometry:Theory, Methods, and Applications is the first collection of research surveys dedicated to distance geometry and its applications. The first part of the book discusses theoretical aspects of the DistanceGeometry Problem (DGP), where the relation between DGP and other related subjects are also presented. Covered topics include distance matrix theory, Euclidean distance matrix completion, multispherical structure of distance matrices,geometric algebra, algebraic distance geometry theo ry, visualization of K-dimensional structures in the plane, graph rigidity, and theory of discretizable DGP. The second part of this volume presents mathematical and computationalproperties of methods developed to the problems discussed in the first porti on, including continuous methods (based on Gaussian and hyperbolic smoothing, difference of convex functions, semidefinite programming, branch-and-bound),discrete methods (based on branch-and-prune, geometric build-up, graph rigidity), and also heuristics methods (based on simulated annealing, genetic algorithms, tabu search, variable neighborhood search). Applications comprise thethird part of the book, which is mainly devoted to the application of DGP to NMR structure calculation. This is an important a nd strongly multidisciplinary application in biology and biomedicine |
Note: | Springer eBooks |
Contents: | Preface |
1. Universal Rigidity of Bar Frameworks in General Position (A. Alfakih) | |
2. Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs (I. Emiris, E. Tsigaridas, A. Varvitsiotis) | |
3. (The discretizable molecular distance Geometry Problem Seems Easier on Proteins (L. Liberti, C. Lavor, A. Mucherino) | |
4. Spheres Unions and Intersections and Some of Their Applications in Molecular Modeling (M. Petitjean) | |
5. Is the Distance Geometry Problem in NP? (N. Beeker, S. Gaubert, C. Glusa, L. Liberti) | |
6. Solving Spatial Constraints with Generaliz | |
ISBN: | 9781461451280 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Visualization , Geometry |
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Call number: | SPRINGER-2013-9781461401100:ONLINE Show nearby items on shelf |
Title: | Thirty Essays on Geometric Graph Theory [electronic resource] |
Author(s): |
Jnos Pach |
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: | In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of abstract graph theory are often incapable of providing satisfactoryanswers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoningfield with many striking results and appealing open ques tions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughlyreviewed and written by excellent researchers in this field |
Note: | Springer eBooks |
Contents: | Introduction |
1) B. brego | |
S. Fernndez | |
Merchant | |
G. Salazar: The rectilinear crossing number of K_n: closing in (or are we?) | |
2) E. Ackerman: The maximum number of tangencies among convex regions with a triangle | |
free intersection graph | |
3) G. Aloupis | |
B. Ballinger | |
S. Collette | |
S. Langerman | |
A. Pr | |
D.R.Wood: Blocking coloured point sets | |
4) M. Al | |
Jubeh | |
G. Barequet | |
M. Ishaque | |
D. Souvaine | |
Cs. D. Tth | |
A. Winslow: Constrained tri | |
connected planar straight line graphs | |
5) S. Buzaglo | |
R. Pinchasi | |
G. Rote: Topological hypergraphs | |
6) J. Cano Vila | |
L. F. Barba | |
ISBN: | 9781461401100 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Combinatorics , Geometry |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-2013-9781447148203:ONLINE Show nearby items on shelf |
Title: | Functional Analysis, Calculus of Variations and Optimal Control [electronic resource] |
Author(s): |
Francis Clarke |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such asnonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis andincludes many novel elements as well as the stan dard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. Theauthor provides a comprehensive course on these subjects, from their inc eption through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximumprinciple, which appear here for the first time in a textbook. Other major themes include existen ce and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscositysolutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They a lso touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering.Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or secon d-year graduate level, on functional analysis, on the calculus of variations and optimalcontrol, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its ad vanced results in the calculus of variations and optimal control,its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth a |
Note: | Springer eBooks |
Contents: | Normed Spaces |
Convex sets and functions | |
Weak topologies | |
Convex analysis | |
Banach spaces | |
Lebesgue spaces | |
Hilbert spaces | |
Additional exercises for Part I | |
Optimization and multipliers | |
Generalized gradients | |
Proximal analysis | |
Invariance and monotonicity | |
Additional exercises for Part II | |
The classical theory | |
Nonsmooth extremals | |
Absolutely continuous solutions | |
The multiplier rule | |
Nonsmooth Lagrangians | |
Hamilton | |
Jacobi methods | |
Additional exercises for Part III | |
Multiple integrals | |
Necessary conditions | |
Existence and regularity | |
Inductive meth | |
ISBN: | 9781447148203 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v264 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Systems theory , Mathematical optimization |
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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-2013-9780817683979:ONLINE Show nearby items on shelf |
Title: | Groupoid Metrization Theory [electronic resource] : With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis |
Author(s): |
Dorina Mitrea Irina Mitrea Marius Mitrea Sylvie Monniaux |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. Thepresentation is self-contained with complete, detailed proofs, and a large number of examples and counterexamples are provided. Unique features of Metrization Theory for Groupoids: With Applications to Analysis on Quasi-Metric Spacesand Functional Analysis include: * treatment of metri zation from a wide, interdisciplinary perspective, with accompanying applications ranging across diverse fields * coverage of topics applicable to a variety of scientific areaswithin pure mathematics * useful techniques and extensive reference material * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be auseful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology andmetric properties and/or functional analysis and metric properties |
Note: | Springer eBooks |
Contents: | Introduction |
Semigroupoids and Groupoids | |
Quantitative Metrization Theory | |
Applications to Analysis on Quasi | |
Metric Spaces | |
Non | |
Locally Convex Functional Analysis | |
Functional Analysis on Quasi | |
Pseudonormed Groups | |
References | |
Symbol Index | |
Subject Index | |
Author Index | |
ISBN: | 9780817683979 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Global analysis (Mathematics) , Harmonic analysis , Functional analysis , Topology |
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Call number: | SPRINGER-2012-9783642298493:ONLINE Show nearby items on shelf |
Title: | Geometric Aspects of Functional Analysis [electronic resource] : Israel Seminar 20062010 |
Author(s): |
Bo'az Klartag Shahar Mendelson Vitali D Milman |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the generaltrends of Asymptotic Geome tric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convexbodies, inequalities involving volumes of such bo dies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensionalspaces and characterization of classical constructions in Geometry an d Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers |
Note: | Springer eBooks |
Contents: | The |
Cosine Transform and Intertwining Integrals on Real Grassmannians | |
On Modules Over Valuations | |
On Multiplicative Maps of Continuous and Smooth Functions | |
Order Isomorphisms on Convex Functions in Windows | |
Finite Transitive Graph Embeddings into a Hyperbolic | |
Metric Space Must Stretch or Squeeze | |
Tightness of Fluctuations of First Passage Percolation on Some Large Graphs | |
Finitely Supported Measures on SL2(R) which are Absolutely Continuous at Infinity | |
Interpolations, Convexity and Geometric Inequalities | |
Hypercontractive Measures, Talagrand's Inequality, and Inuences | |
ISBN: | 9783642298493 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2050 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Discrete groups , Distribution (Probability theory) |
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Call number: | SPRINGER-2012-9783034802123:ONLINE Show nearby items on shelf |
Title: | Methods of Geometric Analysis in Extension and Trace Problems [electronic resource] : Volume 2 |
Author(s): |
Alexander Brudnyi Yuri Brudnyi |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This is the second of a two-volume workpresenting a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a prioridifferential structure (Whit ney problems). The account covers the development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific,these problems have been from the very beginning a p owerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by theaforementioned problems the work is alsounified by the geometric analysis app roach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric spacetheory to Riemannian and Coarse geometry and more. The necessary facts are presented mostly with detail ed proofs to make the book accessible to a wide audience |
Note: | Springer eBooks |
Contents: | Part 3. Lipschitz Extensions from Subsets of Metric Spaces |
Chapter 6. Extensions of Lipschitz Maps | |
Chapter 7. Simultaneous Lipschitz Extensions | |
Chapter 8. Linearity and Nonlinearity | |
Part 4. Smooth Extension and Trace Problems for Functions on Subsets of Rn | |
Chapter 9. Traces to Closed Subsets: Criteria, Applications | |
Chapter 10. Whitney Problems | |
Bibliography | |
Index | |
ISBN: | 9783034802123 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monographs in Mathematics : v103 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2012-9783034802093:ONLINE Show nearby items on shelf |
Title: | Methods of Geometric Analysis in Extension and Trace Problems [electronic resource] : Volume 1 |
Author(s): |
Alexander Brudnyi Yuri Brudnyi |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This is the first of a two-volume workpresenting a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a prioridifferential structure (Whitn ey problems). The account covers the development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific,these problems have been from the very beginning a po werful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by theaforementioned problems the work is alsounified by the geometric analysis appr oach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric spacetheory to Riemannian and Coarse geometry and more. The necessary facts are presented mostly with detaile d proofs to make the book accessible to a wide audience |
Note: | Springer eBooks |
Contents: | Preface |
Basic Terms and Notation | |
Part 1. Classical Extension | |
Trace Theorems and Related Results | |
Chapter 1. Continuous and Lipschitz Functions | |
Chapter 2. Smooth Functions on Subsets of Rn | |
Part 2. Topics in Geometry of and Analysis on Metric Spaces | |
Chapter 3. Topics in Metric Space Theory | |
Chapter 4. Selected Topics in Analysis on Metric Spaces | |
Chapter 5. Lipschitz Embedding and Selections | |
Bibliography | |
Index | |
ISBN: | 9783034802093 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monographs in Mathematics : v102 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2012-9781461438342:ONLINE Show nearby items on shelf |
Title: | Geometric Optimal Control [electronic resource] : Theory, Methods and Examples |
Author(s): |
Heinz Schttler Urszula Ledzewicz |
Date: | 2012 |
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 book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of thetheory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structureof solutions for the underlying problem. The t ext includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapyapproaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced.Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the moreintroductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wideaudience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schttler is an Associate Professor at Washington University in St. Louis in the Department of Electrical andSystems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics |
Note: | Springer eBooks |
Contents: | The Calculus of Variations: A Historical Perspective |
The Pontryagin Maximum Principle: From Necessary Conditions to the Construction of an Optimal Solution | |
Reachable Sets of Linear Time | |
Invariant Systems: From Convex Sets to the Bang | |
Bang Theorem | |
The High | |
Order Maximum Principle: From Approximations of Reachable Sets to High | |
Order Necessary Conditions for Optimality | |
The Method of Characteristics: A Geometric Approach to Sufficient Conditions for a Local Minimum | |
Synthesis of Optimal Controlled Trajectories: FromLocal to Global Solutions | |
Control | |
Affine Systems in Low Dimensions | |
ISBN: | 9781461438342 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Interdisciplinary Applied Mathematics, 0939-6047 : v38 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential Equations , Global differential geometry , Mathematical optimization , Engineering mathematics |
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Call number: | SPRINGER-2012-9780817683108:ONLINE Show nearby items on shelf |
Title: | Mathematical Analysis [electronic resource] : Foundations and Advanced Techniques for Functions of Several Variables |
Author(s): |
Mariano Giaquinta Giuseppe Modica |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in anearlier introductory v olume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differentialforms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics.The authorsconclude with the study of measure and integration theory Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. Thiswork may be used as a supplementary text in the classroom or for self-study by advanced undergra duate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengthsof this presentation, along with the other four books on analysis published by the authors, is the motivation for und erstanding the subject through examples, observations, exercises, and illustrations. Other books published by theauthors all of which provide the reader with a strong foundation in modern-day analysis include: * Mathematical Analysis: Functions of One V ariable * Mathematical Analysis: Approximation and Discrete Processes * MathematicalAnalysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematica l Analysis: The presentation of the theory is clearly arranged,all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requ |
Note: | Springer eBooks |
Contents: | Preface |
Spaces of Summable Functions and Partial Differential Equations | |
Convex Sets and Convex Functions | |
The Formalism of the Calculus of Variations | |
Differential Forms | |
Measures and Integrations | |
Hausdorff and Radon Measures | |
Mathematicians and Other Scientists | |
Bibliographical Notes | |
Index | |
ISBN: | 9780817683108 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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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-2011-9780387754727:ONLINE Show nearby items on shelf |
Title: | The Colorado Mathematical Olympiad and Further Explorations [electronic resource] From the Mountains of Colorado to the Peaks of Mathematics |
Author(s): |
Alexander Soifer |
Date: | 2011 |
Publisher: | Boston, MA : Springer US |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book presents the 20-year account of the Colorado Mathematical Olympiad its dreams and rewards, hard work and conflict. It features more than just original wonderful problems and their ingenious solutions it tells acompelling story involving th e lives of those who have been part of the Olympiad. The reader will meet Olympians and follow their paths as professionals. In the vast field of competition books, this book is unique, for it buildsbridges between Olympiads and real mathematics by demons trating through 20 Further Explorations, the trains of mathematical thought, showing how a solved Olympiad problem gives birth to deeper problems and leads to theforefront of mathematical research full of striking results and open problems. Like Gauss, Al exander Soifer would not hesitate to inject Eureka! at the right moment. Like van der Waerden, he can transform a dispassionate exercise inlogic into a compelling account of sudden insights and ultimate triumph. Cecil Rousseau Chair, USA Mathematical Oly mpiad Committee ... this book is not so much mathematical literature as it is literature built aroundmathematics with the Further Explorations sections, anyone so inclined could spend a lifetime on the mathematics sprouting from this volume. Peter D. John son, Jr., Auburn University I finished reading the book in one sitting I just could not put it down. Professor Soifer has indebted us all by first making the effort to organize the Colorado Mathematical Olympiads, and then making the additional effort to tell us about it in such an engaging and usefulway. Branko Grnbaum, University of Washington A delightful feature of the book is that in the second part more related problems are discussed. Some of them are still unsolved. Paul Erds The book is a gold min e of brilliantreasoning with special emphasis on the power and beauty of coloring proofs. Strongly recommended to both serious and recreational mathematicians on |
Note: | Springer eBooks |
Contents: | Preface |
Olympiad History: What it is and How it Started | |
Three Celebrated Ideas | |
Year 1 | |
Year 2 | |
Year 3 | |
Year 4 | |
Year 5 | |
Year 6 | |
Year 7 | |
Year 8 | |
Year 9 | |
Year 10 | |
Further Explorations | |
Rooks in Space | |
Chromatic Number of the Plane | |
Polygons in a Colored Circle, Polyhedra in a colored Sphere | |
How Does one Cut a Triangle? | |
Points in Convex Figures | |
Triangles in a Colored Plane | |
Rectangles in a Colored Plane | |
Colored Polygons | |
Infinite | |
Finite | |
Schur Theorem | |
Bibliography | |
Year 11 | |
Year 12 | |
Year 13 | |
Year 14 | |
Year 15 | |
Year 16 | |
Year 17 | |
ISBN: | 9780387754727 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry , Logic, Symbolic and mathematical , Number theory |
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Call number: | SPRINGER-2011-9780387682761:ONLINE Show nearby items on shelf |
Title: | Inequalities: Theory of Majorization and Its Applications [electronic resource] |
Author(s): |
Albert W Marshall Ingram Olkin Barry C Arnold |
Date: | 2011 |
Edition: | Second |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
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Note: | This books first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. Inequalities: Theory of Majorization and its Applications merits strong praise. It is innovative,coherent, well written and, mos t importantly, a pleasure to read. This work is a valuable resource! (Mathematical Reviews). The authors present an extremely rich collection of inequalities in a remarkably coherent andunified approach. The book is a major work on inequalities, rich in content and original in organization. (Siam Review). The appearance of Inequalities in 1979 had a great impact on the mathematical sciences. By showing how asingle concept unified a staggering amount of material from widely diverse disciplinesprobabilit y, geometry, statistics, operations research, etc.this work was a revelation to those of us who had been trying to make sense of hisown corner of this material. (Linear Algebra and its Applications). This greatly expanded new edition includes recent resea rch on stochastic, multivariate and group majorization, Lorenz order, and applications in physics andchemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled |
Note: | Springer eBooks |
Contents: | Introduction |
Doubly Stochastic Matrices | |
Schur | |
Convex Functions | |
Equivalent Conditions for Majorization | |
Preservation and Generation of Majorization | |
Rearrangements and Majorization | |
Combinatorial Analysis | |
Geometric Inequalities | |
Matrix Theory | |
Numerical Analysis | |
Stochastic Majorizations | |
Probabilistic, Statistical, and Other Applications | |
Additional Statistical Applications | |
Orderings Extending Majorization | |
Multivariate Majorization | |
Convex Functions and Some Classical Inequalities | |
Stochastic Ordering | |
Total Positivity | |
Matrix Factorizations, Compounds | |
ISBN: | 9780387682761 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Series in Statistics, 0172-7397 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Mathematical statistics |
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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 |
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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-2010-9783540681212:ONLINE Show nearby items on shelf |
Title: | Markets with Transaction Costs [electronic resource] : Mathematical Theory |
Author(s): |
Yuri Kabanov Mher Safarian |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
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Note: | The central mathematical concept in the theory of frictionless markets is a martingale measure. In this, the first monograph devoted to the theory of financial markets with transaction costs, the authors argue that, for financialmarkets with proporti onal transaction costs, this concept should be replaced by that of the consistent price system, which is a martingale evolving in the duals to the solvency cones. Three main subjects are considered: 1. The Lelandapproach to the hedging of contingent claim s based on approximate replication. 2. Arbitrage theory for markets with proportional transaction costs based on a geometric approach. 3. The consumption-investment problem analyzed usingviscosity solutions of the Hamilton-Jacobi-Bellman equation. The fir st part contains recent findings on hedging errors and limit theorems for Leland-type strategies. The rigorous mathematical analysis presented in the book is designedto serve as a platform for further studies. The second part includes a chapter on the arb itrage theory for frictionless markets in discrete time. It is presented as an introduction to the theory of markets with transaction costs, butcan also be read independently. The main subjects of the second part are no-arbitrage criteria and hedging theo rems for European and American options under transaction costs. In contrast to the classical theory, the value processes arevector-valued and the concept of the martingale measure is replaced by the concept of the consistent price system. Hedging theorems give dual descriptions of the set of initial endowments needed to super-replicate contingent claims.These descriptions are expressed in terms of consistent price systems. This volume provides a detailed study of various new phenomena arising in the prese nce of market friction in discrete and continuous time. The mathematics needed isa synthesis of ideas from finite-dimensional geometry, geometric functional analysis, and general theory of stochastic pr |
Note: | Springer eBooks |
Contents: | 1.Approximative Hedging |
2.Arbitrage Theory for Frictionless Markets | |
3.Arbitrage Theory under Transaction Costs | |
4.Consumption | |
Investment Problems | |
A.Appendices: A.1.Facts from Convex Analysis | |
A.2.Csaro Convergence | |
A.3.Facts from Probability | |
A.4.Measurable Selection | |
A.5.Fatou | |
Convergence and Bipolar Theorem in L0 | |
A.6.Skorohod Problem and SDE with Reflections | |
B.Bibliographical comments | |
References | |
ISBN: | 9783540681212 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Finance |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Distribution (Probability theory) |
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Call number: | SPRINGER-2010-9783034602136:ONLINE Show nearby items on shelf |
Title: | Mean Curvature Flow and Isoperimetric Inequalities [electronic resource] |
Author(s): |
Manuel Ritor Carlo Sinestrari |
Date: | 2010 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
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Note: | Springer 2013 e-book collections |
Note: | Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is thegradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstractriemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions ofgeometric parabolic equations, can be considered as an alternative tool to pr ove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows.Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds |
Note: | Springer eBooks |
Contents: | Formation of Singularities in the Mean Curvature Flow |
Geometry of hypersurfaces | |
Examples | |
Local existence and formation of singularities | |
Invariance properties | |
Singular behaviour of convex surfaces | |
Convexity estimates | |
Rescaling near a singularity | |
Huiskens monotonicity formula | |
Cylindrical and gradient estimates | |
Mean curvature flow with surgeries | |
Geometric Flows, Isoperimetric Inequalities and Hyperbolic Geometry | |
The classical isoperimetric inequality in Euclidean space | |
Surfaces | |
Higher dimensions | |
Some applications to hyperbolic geometry | |
ISBN: | 9783034602136 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemtica |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry |
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Call number: | SPRINGER-2010-9781441906007:ONLINE Show nearby items on shelf |
Title: | Classical Topics in Discrete Geometry [electronic resource] |
Author(s): |
Kroly Bezdek |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
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Note: | About the author: Karoly Bezdek received his Dr.rer.nat.(1980) and Habilitation (1997) degrees in mathematics from the Etvs Lornd University, in Budapest and his Candidate of Mathematical Sciences (1985) and Doctor ofMathematical Sciences (1994) degr ees from the Hungarian Academy of Sciences. He is the author of more than 100 research papers and currently he is professor and Canada Research Chair of mathematics at the University of Calgary. Aboutthe book: This multipurpose book can serve as a textboo k for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers ofthe most recent research developments in the classical core part of discrete g eometry. Finally, the forty-some selected research problems offer a great chance to use the book as a short problem book aimed at advanced undergraduate andgraduate students as well as researchers. The text is centered around four major and by now classic al problems in discrete geometry. The first is the problem of densest sphere packings, which has more than 100 years of mathematicallyrich history. The second major problem is typically quoted under the approximately 50 years old illumination conjecture o f V. Boltyanski and H. Hadwiger. The third topic is on covering by planks and cylinders with emphases on theaffine invariant version of Tarski's plank problem, which was raised by T. Bang more than 50 years ago. The fourth topic is centered around the Kne ser-Poulsen Conjecture, which also is approximately 50 years old. All four topicswitnessed very recent breakthrough results, explaining their major role in this book |
Note: | Springer eBooks |
Contents: | Preface |
Part I | |
Sphere Packings | |
Finite Packings by Translates of Convex Bodies | |
Coverings by Homothetic Bodies | |
Illumination and Related Topics | |
Coverings by Planks and Cylinders | |
On the Volume of Finie Arrangements of Spheres | |
Ball | |
Polyhedra as Interesctions of Congruent Balls | |
Part II | |
Selected Proofs on Sphere Packagings | |
Selected Proofs on Finite Packagings of Translates of Convex Bodies | |
Selected Proofs on Illumination and Related Topics | |
Selected Proofs on Coverings by Planks and Cylinders | |
Selected Proofs on the Kesner | |
Poulsen Conjecture | |
Selected Proofs o | |
ISBN: | 9781441906007 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | CMS Books in Mathematics, Ouvrages de mathmatiques de la SMC, 1613-5237 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry |
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Call number: | SPRINGER-2010-9780387709147:ONLINE Show nearby items on shelf |
Title: | Functional Analysis, Sobolev Spaces and Partial Differential Equations [electronic resource] |
Author(s): |
Haim Brezis |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct worlds, functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have agood background in real analys is. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there aremany books on functional analysis and many on PDEs , this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research.This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important Analyse Fonctionnelle (1983). Since the French book was firstpublished, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chin ese. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operatortheory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specifi c differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theoryof PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs wh ich arise, for example, in differential geometry, harmonic analysis, engineering, mechanics,physics etc. and belong in the toolbox of any graduate student studying analysis |
Note: | Springer eBooks |
Contents: | Preface |
1. The HahnBanach Theorems. Introduction to the Theory of Conjugate Convex Functions | |
2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators | |
3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity | |
4. L^p Spaces | |
5. Hilbert Spaces | |
6. Compact Operators. Spectral Decomposition of Self | |
Adjoint Compact Operators | |
7. The HilleYosida Theorem | |
8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension | |
9. Sobolev Spaces and the Vari | |
ISBN: | 9780387709147 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Differential equations, partial |
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Call number: | SPRINGER-2009-9783642002342:ONLINE Show nearby items on shelf |
Title: | Encyclopedia of Distances [electronic resource] |
Author(s): |
Elena Deza Michel Marie Deza |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Distance metrics and distances have become an essential tool in many areas of pure and applied Mathematics, and this encyclopedia is the first one to treat the subject in full. The book appears just as research intensifies intometric spaces and espec ially, distance design for applications. These distances are particularly crucial, for example, in computational biology, image analysis, speech recognition, and information retrieval. Here, an assessment of thepractical questions arising during selection of a good'' distance function has been left aside in favor of a comprehensive listing of the main available distances, a useful tool for the distance design community. This reader-friendlyreference offers both independent introductions and definitions, w hile at the same time making cross-referencing easy through hyperlink-like boldfaced references to original definitions. This high-quality publication is a mix ofreference resource and coffee-table book. A number of fascinating curiosities appear in this Whos Who' of distances. Besides distances themselves, the authors have collected many distance-related notions and paradigms, givingapplied mathematicians in other sectors easy access to those research tools that are arcane for non-specialists. Whats more , they come in ready-to-use fashion. This, as well as the appearance of some distances in different contexts,will be a stimulus to new research |
Note: | Springer eBooks |
Contents: | Part I. Mathematics of Distances |
1 General Definitions | |
2 Topological Spaces | |
3 Generalization of Metric Spaces | |
4 Metric Transforms | |
5 Metrics on Normed Structures | |
Part II. Geometry and Distances | |
6 Distances in Geometry | |
7 Riemannian and Hermitian Metrics | |
8 Distances on Surfaces and Knots | |
9 Distances on Convex Bodies, Cones and Simplicial Complexes | |
Part III. Distances in Classical Mathematics | |
10 Distances in Algebra | |
11 Distances on Strings and Permutations | |
12 Distances on Numbers, Polynominals and Matrices | |
13 Distances in Functional Analysis | |
14 Dista | |
ISBN: | 9783642002342 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science Mathematics , Visualization , Geometry , Global differential geometry , Topology , Engineering mathematics |
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Call number: | SPRINGER-2009-9783034600507:ONLINE Show nearby items on shelf |
Title: | Inequalities [electronic resource] : A Mathematical Olympiad Approach |
Author(s): |
Radmila Bulajich Manfrino Jos Antonio Gmez Ortega Rogelio Valdez Delgado |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This book presents classical inequalities and specific inequalities which are particularly useful for attacking and solving optimization problems. Most of the examples, exercises and problems that appear in the book originatefrom Mathematical Olympia d contests around the world. The material is divided into four chapters. In Chapter 1 algebraic inequalities are presented, starting with the basic ones and ending with more sophisticated techniques Chapter 2deals with geometric inequalities and Chapter 3 comprises a comprehensive list of recent problems that appeared in those contests during the last 14 years. Finally, hints and solutions to all exercises and problems are given in Chapter4 |
Note: | Springer eBooks |
Contents: | Introduction |
1 Numerical Inequalities | |
1.1 Order in the real numbers | |
1.2 The quadratic function ax2 + 2bx + c | |
1.3 A fundamental inequality, arithmetic mean | |
geometric mean | |
1.4. A wonderful inequality: the rearrangement inequality | |
1.5 Convex functions | |
1.6 A helpful inequality | |
1.7 The substitutions strategy | |
1.8 Muirhead's theorem | |
2 Geometric Inequalities | |
2.1 Two basic inequalities | |
2.2 Inequalities between the sides of a triangle | |
2.3 The use of inequalities in the geometry of the triangle | |
2.4 Euler's inequality and some applications | |
2.5 Symmetric functio | |
ISBN: | 9783034600507 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2009-9780817647438:ONLINE Show nearby items on shelf |
Title: | Riemannian Topology and Geometric Structures on Manifolds [electronic resource] |
Author(s): |
Krzysztof Galicki Santiago R Simanca |
Date: | 2009 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque. The various contributions to this volume discuss recent advances in theareas of positive secti onal curvature, Khler and Sasaki geometry, and their interrelation to mathematical physics, notably M and superstring theory. Focusing on these fundamental ideas, this collection presents articles with originalresults, and plausible problems of interest f or future research. Contributors: C.P. Boyer, J. Cheeger, X. Dai, K. Galicki, P. Gauduchon, N. Hitchin, L. Katzarkov, J. Kollr, C. LeBrun, P. Rukimbira, S.R. Simanca, J. Sparks, C. vanCoevering, and W. Ziller |
Note: | Springer eBooks |
Contents: | Preface |
Charles P. BoyerAn Autobiographical Sketch | |
Charles P. BoyerList of Publications | |
Jeff Cheeger and Xianzhe Dai L2 | |
cohomology of non | |
isolated conical singularities and non | |
multiplicativity of the signature | |
Paul Gauduchon Hirzebruch surfaces and weighted projective planes | |
Nigel Hitchin Quaternionic Khler moduli spaces | |
Ludmil Katzarkov Homological mirror symmetry and Weyl tori | |
Jnos Kollr Positive Sasakian structures on 5 | |
manifolds | |
Claude LeBrun Four | |
manifolds, curvature bounds, and convex geometry | |
Phillipe Rukimbira The 1 | |
nullity of Sasakian manifolds | |
ISBN: | 9780817647438 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v271 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Geometry , Mathematical physics |
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Call number: | SPRINGER-2009-9780387873633:ONLINE Show nearby items on shelf |
Title: | Twentieth Anniversary Volume: [electronic resource] : Discrete & Computational Geometry |
Author(s): |
Richard Pollack Jnos Pach Jacob E Goodman |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry, and presents a comprehensive picture of the current state of thefield. Formed during the pa st few decades by the merger of the classical discipline of combinatorial and discrete geometry with the new field of computational geometry that sprang up in the 1970s, discrete and computational geometrynow claims the allegiance of a sizeable number of mathematicians and computer scientists all over the world, whose most important work has been appearing since 1986 in the pages of the journal. The articles in this volume, a number ofwhich solve long-outstanding problems in the field, were chosen by the editors of DCG for the importance of their results, for the breadth of their scope, and to show the intimate connections that have arisen between discrete andcomputational geometry and other areas of both computer science and mathematics. Apart from the a rticles, the editors present an expanded preface, along with a set of photographs of groups and individuals who have played a major rolein the history of the field during the past twenty years. Contributors include: E. Ackerman P.K. Agarwal I. Aliev I. Br ny A. Barvinok S. Basu L.J. Billera J.-D. Boissonnat C. Borcea E. Boros K. Borys B. Braun K. Buchin O. Cheong D.Cohen-Steiner M. Damian K. Elbassioni R. Flatland T. Gerken J.E. Goodman X. Goaoc P. Gronchi V. Gurvich S. Har-Peled J. Hershberger A. Holmsen S.K. Hsiao A. Hubard J. Jernimo L. Khachiyan R. Klein C. Knauer S. Langerman J.-Y. Lee M.Longinetti E. Miller P. Morin U. Nagel E. Nevo P. Niyogi I. Novik J. ORourke J. Pach I. Pak M.J. Pelsmajer S. Petitjean F. Pfender R. Pinchasi R. Pollack J.S. Provan K. Przeslawski R.M. Richardson G. Rote M. Schaefer Y. Schreiber M.Sharir J.R. Shewchuk S. Smale B. Solomyak M. Soss D. tefankovic G. Vegter V.H. Vu S. Weinberger L. Wu D. Yost H. Yu T. Zell |
Note: | Springer eBooks |
Contents: | Preface |
There are Not too Many Magic Configurations | |
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D | |
Robus Shape Fitting via Peeling and Grating Coresets | |
Siegel's LEmaa and Sum | |
Distinct Sets | |
Slicing Convex Sets and Measures by a Hyperplane | |
A Centrally Symmetric Version of the Cyclic Polytope | |
On Projections of Semi | |
Algebraic Sets Defined by Few Quadratic Inequalities | |
Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres | |
Isotopic Implicit Surface Meshing | |
Line Transversals to Disjoint Balls | |
Generating all | |
ISBN: | 9780387873633 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computational complexity , Computer graphics , Geometry, algebraic , Computer science Mathematics , Discrete groups |
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Call number: | SPRINGER-2009-9780387799360:ONLINE Show nearby items on shelf |
Title: | Optimal Design and Related Areas in Optimization and Statistics [electronic resource] |
Author(s): |
Luc Pronzato Anatoly Zhigljavsky |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This edited volume, dedicated to Henry P. Wynn, reflects his broad range of research interests, focusing in particular on the applications of optimal design theory in optimization and statistics. It covers algorithms forconstructing optimal experimen tal designs, general gradient-type algorithms for convex optimization, majorization and stochastic ordering, algebraic statistics, Bayesian networks and nonlinear regression. Written by leading specialistsin the field, each chapter contains a survey of th e existing literature along with substantial new material. This work will appeal to both the specialist and the non-expert in the areas covered. By attracting the attention of expertsin optimization to important interconnected areas, it should help stimul ate further research with a potential impact on applications |
Note: | Springer eBooks |
Contents: | Preface |
B. Torsney: W | |
iterations and Ripples Therefrom | |
R. Haycroft, L. Pronzato, H.P. Wynn, A. Zhigljavsky: Studying Convergence of Gradient Algorithms via Optimal Experimental Design Theory | |
L. Pronzato, H.P. Wynn, A. Zhigljavsky: A Dynamical | |
System Analysis of the Optimum S | |
Gradient Algorithm | |
A. Giovagnoli, J. Marzialetti, H.P. Wynn: Bivariate Dependence Orderings for Unordered Categorical Variables | |
G. Pistone, E. Riccomagno, M.P. Rogantin: Methods in Algebraic Statistics for the Design of Experiments | |
E. Riccomagno, J.Q. Smith:The Geometry of Causal Probability Trees that ar | |
ISBN: | 9780387799360 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Optimization and Its Applications, 1931-6828 : v28 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer software , Algorithms , Mathematical optimization , Operations research , Statistics |
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Call number: | SPRINGER-2009-9780387763569:ONLINE Show nearby items on shelf |
Title: | Polytopes, Rings, and K-Theory [electronic resource] |
Author(s): |
Joseph Gubeladze Winfried Bruns |
Date: | 2009 |
Edition: | 1 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, thealgebras derived from the m, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphismproblems and automorphism groups, homological prope rties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. Thismonograph has been written with a view towards graduate students and resear chers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, alsospecialists in lattice polytopes and related objects will find an up-to-date discussion of affine m onoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructiveapproach wherever possible. Winfried Bruns is Professor of Mathematics at Universitt Osnabrck. Joseph Gubeladze is Professor of Mathematics at San Francisco State University |
Note: | Springer eBooks |
Contents: | Preface |
Polytopes, cones, and complexes | |
Affine monoids and their Hilbert bases | |
Multiples of lattice polytopes | |
Monoid algebras | |
Isomorphisms and automorphisms | |
Homological properties and Hilbert functions | |
Grbner bases, triangulations, and Koszul algebras | |
Projective modules over monoid rings | |
Bass | |
Whitehead groups of monoid rings | |
Varieties | |
References | |
Notation | |
Index | |
ISBN: | 9780387763569 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , K-theory , Discrete groups |
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Call number: | SPRINGER-2009-9780387746524:ONLINE Show nearby items on shelf |
Title: | How Does One Cut a Triangle? [electronic resource] |
Author(s): |
Alexander Soifer |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | How Does One Cut a Triangle? is a work of art, and rarely, perhaps never, does one find the talents of an artist better suited to his intention than we find in Alexander Soifer and this book. Peter D. Johnson, Jr. Thisdelightful book considers and so lves many problems in dividing triangles into n congruent pieces and also into similar pieces, as well as many extremal problems about placing points in convex figures. The book is primarily meant forclever high school students and college students intere sted in geometry, but even mature mathematicians will find a lot of new material in it. I very warmly recommend the book and hope the readers will have pleasure in thinking aboutthe unsolved problems and will find new ones. Paul Erds It is impossible to c onvey the spirit of the book by merely listing the problems considered or even a number of solutions. The manner of presentation and the gentle guidancetoward a solution and hence to generalizations and new problems takes this elementary treatise out of t he prosaic and into the stimulating realm of mathematical creativity. Not only young talented people but dedicated secondaryteachers and even a few mathematical sophisticates will find this reading both pleasant and profitable. L.M. Kelly Mathematical Rev iews [How Does One Cut a Triangle?] reads like an adventure story. In fact, it is an adventure story,complete with interesting characters, moments of exhilaration, examples of serendipity, and unanswered questions. It conveys the spirit of mathematical di scovery and it celebrates the event as have mathematicians throughout history.Cecil Rousseau The beginner, who is interested in the book, not only comprehends a situation in a creative mathematical studio, not only is exposed to good mathematical taste, b ut also acquires elements of modern mathematicalculture. And (not less important) the reader imagines the role and place of intuition and analogy in mathematical investigation he or she f |
Note: | Springer eBooks |
Contents: | Forewords |
Preface | |
Part I: The Original Book | |
Pool Table, Irrational Numbers, and Integral Independence | |
How does One Cut a Triangle? I | |
Excursions in Algebra | |
How Does One Cut a Triangle? II | |
Excursion in Trigonometry | |
Is There Anything Beyond the Solution? | |
Pursuit of the Best Result | |
Convex Figures and the Function S(F) | |
Faul Erdos: Our Joint Problems | |
Convex Figures and Erdos' Function | |
Part II: Developments of the Subsequent 20 Years | |
An Alternative Proof of the Grand Problem II | |
Miklos Lasckovich on Cutting Triangles | |
Soifer's $50 Problem and Mitya Karaba | |
ISBN: | 9780387746524 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Combinatorics , Geometry |
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Call number: | SPRINGER-2008-9783764387228:ONLINE Show nearby items on shelf |
Title: | Gradient Flows [electronic resource] : in Metric Spaces and in the Space of Probability Measures |
Author(s): |
Luigi Ambrosio Nicola Gigli Giuseppe Savar |
Date: | 2008 |
Edition: | Second Edition |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spacesand the second one dev oted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance. The two parts have some connections, due to the fact that thespace of probability measures provides an important model to which the metric theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested innon-smooth analysis and analysis in metric spaces, and the second one b y the reader more orientated towards the applications in partial differential equations, measure theory and probability |
Note: | Springer eBooks |
Contents: | 1. Introduction |
Part I. Gradient flow in metric spaces | |
2. Curves and gradients in metric spaces | |
3. Existence of curves of maximal slope | |
4. Proofs of the convergence theorems | |
5. Generation of contraction semigroups | |
Part II. Gradient flow in the Wasserstein spaces of probability measures | |
6. Preliminary results on measure theory | |
7. The optimal transportation problem | |
8. The Wasserstein distance and its behaviour along geodesics | |
9. A.c. curves and the continuity equation | |
10. Convex functionals | |
11. Metric slope and subdifferential calculus | |
12. Gradient flows and curves of | |
ISBN: | 9783764387228 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lectures in Mathematics ETH Zrich |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry , Distribution (Probability theory) |
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Call number: | SPRINGER-2008-9783540788591:ONLINE Show nearby items on shelf |
Title: | Stochastic and Integral Geometry [electronic resource] |
Author(s): |
Rolf Schneider Wolfgang Weil |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Stochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminentspecialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry -- random sets, point processes of geometric objects (particles, flats), and random mosaics. It develops, in ameasure-theoretic setting, the integral geometry for the moti on and the translation group, as needed for the investigation of these models under the usual invariance assumptions. A characteristic of the book is the interplay betweenstochastic and geometric arguments, leading to various major results. Its main theme , once the foundations have been laid, is the quantitative investigation of the basic models. This comprises the introduction of suitable parameters,in the form of functional densities, relations between them, and approaches to their estimation. Much addi tional information on stochastic geometry is collected in the section notes. As a combination of probability theory and geometry,the volume is intended for readers from either field. Probabilists with interest in random spatial structures, or motivated by the prospect of applications, will find an in-depth presentation of the geometric background. Geometers cansee integral geometry at work and may be surprised to learn how classical results from convex geometry have elegant applications in a stochastic se tting |
Note: | Springer eBooks |
Contents: | 1.Prologue |
Part I: Foundations of Stochastic Geometry | |
2.Random Closed Sets | |
3.Point Processes | |
4.Geometric Models | |
Part II: Integral Geometry | |
5.Averaging with Invariant Measures | |
6.Extended Concepts of Integral Geometry | |
7.Integral | |
geometric Transformations | |
Part III: Selected Topics from Stochastic Geometry | |
8.Some Geometric Probability Problems | |
9.Mean Values for Random Sets | |
10.Random Mosaics | |
11.Non | |
stationary Models | |
Part IV: Appendix | |
12.Facts from General Topology | |
13.Invariant Measures | |
14.Facts from Convex Geometry | |
References | |
Index | |
ISBN: | 9783540788591 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Probability and Its Applications, 1431-7028 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Discrete groups , Distribution (Probability theory) |
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Call number: | SPRINGER-2008-9783540737926:ONLINE Show nearby items on shelf |
Title: | Generalized Curvatures [electronic resource] |
Author(s): |
Jean-Marie Morvan |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The intent of this book is to set the modern foundations of the theory of generalized curvature measures. This subject has a long history, beginning with J. Steiner (1850), H. Weyl (1939), H. Federer (1959), P. Wintgen (1982),and continues today with young and brilliant mathematicians. In the last decades, a renewal of interest in mathematics as well as computer science has arisen (finding new applications in computer graphics, medical imaging,computational geometry, visualization ). Following a hist orical and didactic approach, the book introduces the mathematical background of the subject, beginning with curves and surfaces, going on with convex subsets, smoothsubmanifolds, subsets of positive reach, polyhedra and triangulations, and ending with su rface reconstruction. We focus on the theory of normal cycle, which allows to compute and approximate curvature measures of a large class ofsmooth or discrete objects of the Euclidean space. We give explicit computations when the object is a 2 or 3 dimens ional polyhedron. This book can serve as a textbook to any mathematician or computer scientist, engineer or researcherwho is interested in the theory of curvature measures |
Note: | Springer eBooks |
Contents: | Motivations |
Motivation: Curves | |
Motivation: Surfaces | |
Background: Metrics and Measures | |
Distance and Projection | |
Elements of Measure Theory | |
Background: Polyhedra and Convex Subsets | |
Polyhedra | |
Convex Subsets | |
Background: Classical Tools in Differential Geometry | |
Differential Forms and Densities on EN | |
Measures on Manifolds | |
Background on Riemannian Geometry | |
Riemannian Submanifolds | |
Currents | |
On Volume | |
Approximation of the Volume | |
Approximation of the Length of Curves | |
Approximation of the Area of Surfaces | |
The Steiner Formula | |
The Steiner Formula for | |
ISBN: | 9783540737926 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Geometry and Computing, 1866-6795 : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Computer science Mathematics , Global differential geometry |
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Call number: | SPRINGER-2008-9780387797113:ONLINE Show nearby items on shelf |
Title: | Combinatorics and Graph Theory [electronic resource] |
Author(s): |
John Harris Jeffry L Hirst Michael Mossinghoff |
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: | This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recentresults appear in the text, illustrating the fact that mathematics is a living discipline. The second edition includes many new topics and features: New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths. New material on partitions, multinomial coefficient s, and the pigeonhole principle. Expanded coverage of Plya Theory to include de Bruijns method for counting arrangements when a second symmetry group acts on the set ofallowed colors. Topics in combinatorial geometry, including Erdos and Szekeres develo pment of Ramsey Theory in a problem about convex polygons determined by sets of points. Expanded coverage of stable marriage problems, andnew sections on marriage problems for infinite sets, both countable and uncountable. Numerous new exercises through out the book. About the First Edition: . . . this is what a textbook should be! The book is comprehensive withoutbeing overwhelming, the proofs are elegant, clear and short, and the examples are well picked. Ioana Mihaila, MAA Reviews |
Note: | Springer eBooks |
Contents: | Preface to the second edition |
Preface | |
Graph theory | |
Combinatorics | |
Infinite combinatorics and graphs | |
References | |
Index | |
ISBN: | 9780387797113 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Combinatorics , Logic, Symbolic and mathematical |
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Call number: | SPRINGER-2007-9783540720539:ONLINE Show nearby items on shelf |
Title: | Geometric Aspects of Functional Analysis [electronic resource] : Israel Seminar 20042005 |
Author(s): |
Vitali D Milman Gideon Schechtman |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) during the years 2004-2005 follows the long tradition of the previous volumes that reflect the general trends ofthe Theory and are a source of inspiration for research. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis, ranging from classical topics in the geometry of convex bodies, to inequalities involvingvolumes of such bodies or, more generally, lo g-concave measures, to the study of sections or projections of convex bodies. In many of the papers Probability Theory plays an important role in some limit laws for measures associatedwith convex bodies, resembling Central Limit Theorems, are derive and in others probabilistic tools are used extensively. There are also papers on related subjects, including a survey on the behavior of the largest eigenvalue of randommatrices and some topics in Number Theory |
Note: | Springer eBooks |
Contents: | S. Alesker: Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure |
S. Artstein | |
Avidan, O. Friedland, V. Milman: Geometric Applications of Chernoff | |
Type Estimates | |
S.G. Bobkov: A Remark on the Surface BrunnMinkowski | |
Type Inequality | |
S.G. Bobkov: On Isoperimetric Constants for Log | |
Concave Probability Distributions | |
J. Bourgain: A Remark on Quantum Ergodicity for CAT Maps | |
J. Bourgain: Some Arithmetical Applications of the Sum | |
Product Theorems in Finite Fields | |
D. Gatzouras, A. Giannopoulos, N. Markoulakis: On the Maximal Number of Facets of 0/1 Poly | |
ISBN: | 9783540720539 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1910 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Discrete groups , Distribution (Probability theory) |
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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-2007-9780817645960:ONLINE Show nearby items on shelf |
Title: | History of Banach Spaces and Linear Operators [electronic resource] |
Author(s): |
Albrecht Pietsch |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Named for Banach, one of the great mathematicians of the twentieth century, the concept of Banach spaces figures prominently in the study of functional analysis with applications to integral and differential equations,approximation theory, harmonic a nalysis, convex geometry, numerical mathematics, analytic complexity, and probability theory. Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment ofthe history of Banach spaces and (abstract bounded) linear operators. While other historical texts on the subject focus on developments before 1950, this one is mainly devoted to the second half of the 20th century. Banach space theoryis presented in a broad mathematical context, using tools from such area s as set theory, topology, algebra, combinatorics, probability theory, and logic. Equal emphasis is given to both spaces and operators. Numerous examples andcounterexamples elucidate the scope of the underlying concepts. As a stimulus for further research , the text also contains many problems which have not been previously solved. The book may serve as a reference for researchers and as anintroduction for graduate students who want to learn Banach space theory with some historical flavor. Helpful informat ion is also provided for professors preparing their own lectures on functional analysis |
Note: | Springer eBooks |
Contents: | Preface |
Acknowledgements | |
Introduction | |
The Birth of Banach Spaces | |
Historical Roots and Basic Results | |
Weak Topologies | |
Classical Banach Spaces | |
Basic Results from the Post | |
Banach Period | |
Modern Banach Space Theory Selected Topics | |
Miscellaneous Topics | |
Mathematics is Made by Mathematicians | |
Chronology | |
Quotations | |
Bibliography | |
Index | |
ISBN: | 9780817645960 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory , Mathematics_$xHistory |
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Call number: | SPRINGER-2006-9783764375539:ONLINE Show nearby items on shelf |
Title: | Near Polygons [electronic resource] |
Author(s): |
Bart Bruyn |
Date: | 2006 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Near polygons were introduced about 25 years ago and studied intensively in the 1980s. In recent years the subject has regained interest. This monograph gives an extensive overview of the basic theory of general near polygons. Thefirst part of the bo ok includes a discussion of the classes of dense near polygons, regular near polygons, and glued near polygons. Also valuations, one of the most important tools for classifying dense near polygons, are treated indetail. The second part of the book discuss es the classification of dense near polygons with three points per line. The book is self-contained and almost all theorems are accompanied with proofs. Several new results are presented. Manyknown results occur in a more general form and the proofs are o ften more streamlined than their original versions. The volume is aimed at advanced graduate students and researchers in the fields of combinatorics and finite geometry |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Dense Near Polygons | |
Regular Near Polygons | |
Glued Near Polygons | |
Valuations | |
The Known Slim Dense Near Polygons | |
Slim Dense Near Hexagons | |
Slim Dense Near Polygons With a Nice Chain of Convex Subpolygons | |
Slim Dense Near Octagons | |
Appendices | |
Bibliography | |
Index | |
ISBN: | 9783764375539 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Combinatorics |
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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-2006-9780387312569:ONLINE Show nearby items on shelf |
Title: | Convex Analysis and Nonlinear Optimization [electronic resource] : Theoryand Examples |
Author(s): |
Jonathan Borwein Adrian Lewis |
Date: | 2006 |
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: | A cornerstone of modern optimization and analysis, convexity pervades applications ranging through engineering and computation to finance. This concise introduction to convex analysis and its extensions aims at first yeargraduate students, and includ es many guided exercises. The corrected Second Edition adds a chapter emphasizing concrete models. New topics include monotone operator theory, Rademacher's theorem, proximal normal geometry, Chebyshevsets, and amenability. The final material on partial s moothness won a 2005 SIAM Outstanding Paper Prize. Jonathan M. Borwein, FRSC is Canada Research Chair in Collaborative Technology at Dalhousie University. A Fellow of the AAASand a foreign member of the Bulgarian Academy of Science, he received his Doctor ate from Oxford in 1974 as a Rhodes Scholar and has worked at Waterloo, Carnegie Mellon and Simon Fraser Universities. Recognition for his extensivepublications in optimization, analysis and computational mathematics includes the 1993 Chauvenet prize. Adr ian S. Lewis is a Professor in the School of Operations Research and Industrial Engineering at Cornell. Following his 1987Doctorate from Cambridge, he has worked at Waterloo and Simon Fraser Universities. He received the 1995 Aisenstadt Prize, from the Un iversity of Montreal, and the 2003 Lagrange Prize for Continuous Optimization, from SIAM and theMathematical Programming Society. About the First Edition: ...a very rewarding book, and I highly recommend it... - M.J. Todd, in the International Journal of Robust and Nonlinear Control ...a beautifully written book... highlyrecommended... - L. Qi, in the Australian Mathematical Society Gazette This book represents a tour de force for introducing so many topics of present interest in such a small space and w ith such clarity and elegance. - J.-P.Penot, in Canadian Mathematical Society Notes There is a fascinating interweaving of theory and applications... - J.R. Giles, in Mathematical Reviews .. |
Note: | Springer eBooks |
Contents: | Background |
Inequality Constraints | |
Fenchel Duality | |
Convex Analysis | |
Special Cases | |
Nonsmooth Optimization | |
KarushKuhnTucker Theory | |
Fixed Points | |
More Nonsmooth Structure | |
Postscript: Infinite Versus Finite Dimensions | |
List of Results and Notation | |
ISBN: | 9780387312569 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | CMS Books in Mathematics, 1613-5237 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Mathematical optimization , Operations research |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-2006-9780387310770:ONLINE Show nearby items on shelf |
Title: | Convex Functions and Their Applications [electronic resource] : A Contemporary Approach |
Author(s): |
Constantin P Niculescu Lars-Erik Persson |
Date: | 2006 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Convex functions play an important role in many branches of mathematics, as well as other areas of science and engineering. The present text is aimed to a thorough introduction to contemporary convex function theory, whichentails a powerful and elega nt interaction between analysis and geometry. A large variety of subjects are covered, from one real variable case (with all its mathematical gems) to some of the most advanced topics such as the convexcalculus, Alexandrovs Hessian, the variational approa ch of partial differential equations, the Prkopa-Leindler type inequalities and Choquet's theory. This book can be used for a one-semester graduate course on Convex Functionsand Applications, and also as a valuable reference and source of inspiration for researchers working with convexity. The only prerequisites are a background in advanced calculus and linear algebra. Each section ends with exercises,while each chapter ends with comments covering supplementary material and historical information. Many re sults are new, and the whole book reflects the authors own experience, both in teaching and research. About the authors:Constantin P. Niculescu is a Professor in the Department of Mathematics at the University of Craiova, Romania. Dr. Niculescu directs th e Centre for Nonlinear Analysis and Its Applications and also the graduate program in AppliedMathematics at Craiova. He received his doctorate from the University of Bucharest in 1974. He published in Banach Space Theory, Convexity Inequalities and Dynami cal Systems, and has received several prizes both for research andexposition. Lars Erik Persson is Professor of Mathematics at Lule University of Technology and Uppsala University, Sweden. He is the director of Center of Applied Mathematics at Lule, a mem ber of the Swedish National Committee ofMathematics at the Royal Academy of Sciences, and served as President of the Swedish Mathematical Society (1996-1998). He received his doctorate from |
Note: | Springer eBooks |
Contents: | Convex Functions on Intervals |
Comparative Convexity on Intervals | |
Convex Functions on a Normed Linear Space | |
Choquets Theory and Beyond | |
ISBN: | 9780387310770 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Canadian Mathematical Society, 1613-5237 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Discrete groups |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-2005-9783764373092:ONLINE Show nearby items on shelf |
Title: | Gradient Flows [electronic resource] : in Metric Spaces and in the Space of Probability Measures |
Author(s): |
Luigi Ambrosio Nicola Gigli Giuseppe Savar |
Date: | 2005 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spacesand the second one dev oted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance. The two parts have some connections, due to the fact that thespace of probability measures provides an important model to which the metric theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested innon-smooth analysis and analysis in metric spaces, and the second one b y the reader more orientated towards the applications in partial differential equations, measure theory and probability |
Note: | Springer eBooks |
Contents: | 1. Introduction |
Part I. Gradient flow in metric spaces | |
2. Curves and gradients in metric spaces | |
3. Existence of curves of maximal slope | |
4. Proofs of the convergence theorems | |
5. Generation of contraction semigroups | |
Part II. Gradient flow in the Wasserstein spaces of probability measures | |
6. Preliminary results on measure theory | |
7. The optimal transportation problem | |
8. The Wasserstein distance and its behaviour along geodesics | |
9. A.c. curves and the continuity equation | |
10. Convex functionals | |
11. Metric slope and subdifferential calculus | |
12. Gradient flows and curves of | |
ISBN: | 9783764373092 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lectures in Mathematics ETH Zrich |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry , Distribution (Probability theory) |
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Location: | ONLINE |
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