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SPIRES-BOOKS: FIND KEYWORD HYPERBOLIC GEOMETRY *END*INIT* use /tmp/qspiwww.webspi1/17499.67 QRY 131.225.70.96 . find keyword hyperbolic geometry ( in books using www Cover
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Call number:9789462392403:ONLINE Show nearby items on shelf
Title:Topics in Modern Differential Geometry
Author(s):
Date:2017
Size:1 online resource (VII, 284 p. 30 illus., 4 illus. in color p.)
Contents:1.The Riemannian and Lorentzian Splitting Theorems -- 2.Periodic trajectories of dynamical systems having a one-parameter group of symmetries -- 3.Geometry and Materials -- 4.On deciding whether a submanifold is parabolic or
hyperbolic using its mean curvature -- 5.Contact Forms in Geometry and Topology -- 6.Farkas and Janos Bolyai -- 7.Spectrum Estimates and Applications to Geometry -- 8.Variational problems on curves -- 9.Special Submanifolds in
Hermitian Manifolds -- 10.An introduction to certain topics on Lorentzian geometry
ISBN:9789462392403
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Differential geometry , Mathematics , Differential Geometry
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Call number:9783319516585:ONLINE Show nearby items on shelf
Title:Inverse Problems for Partial Differential Equations
Author(s): Victor Isakov
Date:2017
Edition:3rd ed. 2017
Size:1 online resource (XV, 406 p. 4 illus p.)
Contents:Inverse Problems -- Ill-Posed Problems and Regularization -- Uniqueness and Stability in the Cauchy Problem -- Elliptic Equations: Single Boundary Measurements -- Elliptic Equations: Many Boundary Measurements -- Scattering Problems
and Stationary Waves -- Integral Geometry and Tomography -- Hyperbolic Problems -- Inverse Parabolic Problems -- Some Numerical Methods -- Appendix: Functional Spaces
ISBN:9783319516585
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Remote sensing , Partial differential equations , Computer mathematics , Physics , Mathematics , Partial Differential Equations , Computational Mathematics and Numerical Analysis , Theoretical, Mathematical and Computational Physics , Remote Sensing/Photogrammetry
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Call number:SPRINGER-2016-9783319338774:ONLINE Show nearby items on shelf
Title:Spectral Theory of Infinite-Area Hyperbolic Surfaces
Author(s): David Borthwick
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (37 p.)
Note:10.1007/978-3-319-33877-4
Contents:Introduction -- Hyperbolic Surfaces -- Selberg Theory for Finite-Area Hyperbolic Surfaces -- Spectral Theory for the Hyperbolic Plane -- Model Resolvents for Cylinders -- The Resolvent -- Spectral and Scattering Theory -- Resonances and Scattering Poles -- Growth Estimates and Resonance Bounds -- Selberg Zeta Function -- Wave Trace and Poisson Formula -- Resonance Asymptotics -- Inverse Spectral Geometry -- Patterson-Sullivan Theory -- Dynamical Approach to the Zeta Function -- Numerical Computatio ns -- Appendix -- References -- Notation Guide -- Index
ISBN:9783319338774
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics: 318
Keywords: Mathematics , Functional analysis , Functions of complex variables , Partial differential equations , Hyperbolic geometry , Physics , Mathematics , Functional Analysis , Partial Differential Equations , Functions of a Complex Variable , Hyperbolic Geometry , Mathematical Methods in Physics
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Call number:SPRINGER-2016-9783319320854:ONLINE Show nearby items on shelf
Title:Geometry, Algebra and Applications: From Mechanics to Cryptography
Author(s):
Date:2016
Size:1 online resource (198 p.)
Note:10.1007/978-3-319-32085-4
Contents:1 W. Batat, P. M. Gadea, J. A. Oubiña, A survey on homogeneous structures on the classical hyperbolic spaces -- 2 A. Bejancu, On the (1 + 3) threading of spacetime -- 3 M. Brozos-Vázquez, E. Calviño-Louzao, E. García-Río, R. Vázquez-Lorenzo, L ocal structure of self-dual gradient Yamabe solitons -- 4 G. Calvaruso, The prescribed curvature problem in low dimension -- 5 M. Castrillón López, P. L. García, Euler-Poincare reduction by a subgroup of symmetries as an optimal control problem -- 6 M. Castrillón López, T. S. Ratiu, Morse families and Lagrangian submanifolds -- 7 R. Durán Díaz, L. Hernández Encinas, Special primes: properties and applications -- 8 F. Etayo, Rotation Minimizing vector fields and frames in Riemannian manifolds -- 9 R. Ferreiro Pérez, Local anomaly cancellation and equivariant cohomology of jet bundles -- 10 A. Fúster-Sabater, F. Montoya Vitini, Classes of nonlinear filters for stream ciphers -- 11 V. Gayoso Martínez, L. Hernández Encinas, A. Martín Muñoz,
Implementation of cryptographic algorithms for elliptic curves -- 12 R. Hernández-Amador, J. Monterde, J. Vallejo, Supermanifolds, symplectic geometry and curvature -- 13 A. Marcelo, F. Marcelo, C. Rodríguez, Prime submodules and symmetric algebra s -- 14 A. Martín del Rey, G. Rodríguez Sánchez, Application to cybersecurity of the stability theory of the systems of ordinary differential equations -- 15 I. V. Mykytyuk, On the non-triviality of the eight-form T4(w) on manifolds with a Spin(9)-stru cture -- 16 A. Peinado, Flaws in the application of Number Theory in Key Distribution Schemes for Multicast Networks -- 17 L. Pozo, E. Rosado, Einstein-Hilbert Lagrangian induced on the linear frame bundle
ISBN:9783319320854
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 161
Keywords: Mathematics , Data structures (Computer science) , Data encryption (Computer science) , Coding theory , Differential geometry , Mathematical physics , Mathematics , Mathematical Physics , Differential Geometry , Data Encryption , Data Structures , Coding and Information Theory
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Call number:SPRINGER-2016-9783319313382:ONLINE Show nearby items on shelf
Title:Essays in Mathematics and its Applications In Honor of Vladimir Arnold
Author(s):
Date:2016
Size:1 online resource (22 p.)
Note:10.1007/978-3-319-31338-2
Contents:A new way to compute the Rodrigues coefficients of functions of the Lie groups of matrices (D. Andrica, O.L. Chender) -- Quasimodes in integrable systems and semi-classical limit (M. Baldo, F. Raciti) -- Manifolds which are complex and symplectic bu t not Kahler (G. Bazzoni, V. Munoz) -- Solvability of a non clamped frictional contact problem with adhesion (O. Chau, D. Goeleven, R. Oujja) -- The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence (A. Fortunati, S. Wi ggins) -- Iterative Methods for the Elastography Inverse Problem of Locating Tumors (B. Jadamba, A.A. Khan, F. Raciti, C. Tammer, B. Winkler) -- Transversality theory with applications to differential equations (D. Motreanu, V.V. Motreanu) -- Lattice-like subsets of Euclidean Jordan algebras (A.B. Nemeth, S.Z. Nemeth) -- Simultaneous Diophantine approximation: Searching for analogues of Hurwitz’ theorem (W.G. Nowak) -- On the fixed points of a Hamiltonian diffeomorphism in presence of
fundamental group (K. Ono, A. Pajitnov) -- Some Generalizations of Fixed Point Theorems on S-Metric Spaces (N.Y. Ozgur, N.A. Tas) -- Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces (C. Park, J.R. Lee, T.M. Rassias) -- The Maslov Ind ex in PDEs Geometry (A. Prastaro) -- On the infimum of certain functionals (B. Ricceri) -- The Algebra of Gyrogroups: Cayley Theorem, Lagrange Theorem, and Isomorphism Theorems (T. Suksumran) -- Mild continuity properties of relations and relators in rela tor spaces (A. Szaz, A. Zakaria) -- Contraction Maps in Pseudometric Structures (M. Turinici) -- Novel Tools to Determine Hyperbolic Triangle Centers (A.A. Ungar)
ISBN:9783319313382
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Dynamics , Ergodic theory , Global analysis (Mathematics) , Manifolds (Mathematics) , Algebraic topology , Complex manifolds , Mathematics , Dynamical Systems and Ergodic Theory , Algebraic Topology , Manifolds and Cell Complexes (incl. Diff.Topology) , Global Analysis and Analysis on Manifolds
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Call number:SPRINGER-2016-9783319276663:ONLINE Show nearby items on shelf
Title:The Spectrum of Hyperbolic Surfaces
Author(s): Nicolas Bergeron
Date:2016
Edition:1st ed. 2016
Size:1 online resource (370 p.)
Note:10.1007/978-3-319-27666-3
Contents:Preface -- Introduction -- Arithmetic Hyperbolic Surfaces -- Spectral Decomposition -- Maass Forms -- The Trace Formula -- Multiplicity of lambda1 and the Selberg Conjecture -- L-Functions and the Selberg Conjecture -- Jacquet-Langlands Corresponde nce -- Arithmetic Quantum Unique Ergodicity -- Appendices -- References -- Index of notation -- Index -- Index of names
ISBN:9783319276663
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Harmonic analysis , Dynamics , Ergodic theory , Hyperbolic geometry , Mathematics , Hyperbolic Geometry , Abstract Harmonic Analysis , Dynamical Systems and Ergodic Theory
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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-2016-9783319247113:ONLINE Show nearby items on shelf
Title:Dessins d'Enfants on Riemann Surfaces
Author(s): Gareth A Jones
Date:2016
Edition:1st ed. 2016
Size:1 online resource (259 p.)
Note:10.1007/978-3-319-24711-3
Contents:Historical and introductory background -- Graph embeddings -- Dessins and triangle groups -- Galois actions -- Quasiplatonic surfaces, and automorphisms -- Regular maps -- Regular embeddings of complete graphs -- Wilson operations -- Further exampl es -- Arithmetic aspects -- Beauville surfaces
ISBN:9783319247113
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebraic geometry , Group theory , Functions of complex variables , Hyperbolic geometry , Mathematics , Algebraic Geometry , Group Theory and Generalizations , Functions of a Complex Variable , Several Complex Variables and Analytic Spaces , Hyperbolic Geometry
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Call number:SPRINGER-2014-9783319056692:ONLINE Show nearby items on shelf
Title:Lobachevsky Geometry and Modern Nonlinear Problems [electronic resource]
Author(s): Andrey Popov
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Birkhuser
Size:1 online resource
Note:This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundredyears. The central sect ions cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives,and their applications to the analysis of th e physical models. As the sine-Gordon equation appears to have profound geometrical roots and numerous applications to modern nonlinear problems, it is treated as a universalobject of investigation, connecting many of the problems discussed. The aim of th is book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the contextof non-Euclidean hyperbolic geometry
Contents:Introduction
1 Foundations of Lobachevsky geometry: axiomatics, models, images in Euclidean space
2 The problem of realizing the Lobachevsky geometry in Euclidean space
3 The sine
Gordon equation: its geometry and applications of current interest
4 Lobachevsky geometry and nonlinear equations of mathematical physics
5 Non
Euclidean phase spaces. Discrete nets on the Lobachevsky plane and numerical integration algorithms for 2
equations
Bibliography
Index
ISBN:9783319056692
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Differential equations, partial
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Call number:SPRINGER-2014-9783319048079:ONLINE Show nearby items on shelf
Title:Analytic and Probabilistic Approaches to Dynamics in Negative Curvature [electronic resource]
Author(s): Franoise Dal'Bo
Marc Peign
Andrea Sambusetti
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The work of E. Hopf and G.A. Hedlund, in the 1930s, on transitivity and ergodicity of the geodesic flow for hyperbolic surfaces, marked the beginning of the investigation of the statistical properties and stochastic behavior ofthe flow. The first cen tral limit theorem for the geodesic flow was proved in the 1960s by Y. Sinai for compact hyperbolic manifolds. Since then, strong relationships have been found between the fields of ergodic theory, analysis, andgeometry. Different approaches and new tools have been developed to study the geodesic flow, including measure theory, thermodynamic formalism, transfer operators, Laplace operators, and Brownian motion. All these different points ofview have led to a deep understanding of more general dynamical sy stems, in particular the so-called Anosov systems, with applications to geometric problems such as counting, equirepartition, mixing, and recurrence properties of theorbits. This book comprises two independent texts that provide a self-contained introduct ion to two different approaches to the investigation of hyperbolic dynamics. The first text, by S. Le Borgne, explains the method of martingalesfor the central limit theorem. This approach can be used in several situations, even for weakly hyperbolic flow s, and the author presents a good number of examples and applications to equirepartition and mixing. The second text, by F.Faure and M. Tsujii, concerns the semiclassical approach, by operator theory: chaotic dynamics is described through the spectrum of the associated transfer operator, with applications to the asymptotic counting of periodic orbits. Thebook will be of interest for a broad audience, from PhD and Post-Doc students to experts working on geometry and dynamics
ISBN:9783319048079
Series:eBooks
Series:SpringerLink
Series:Springer INdAM Series, 2281-518X : v9
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Operator theory , Global differential geometry , Distribution (Probability theory)
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Call number:SPRINGER-2014-9783034806220:ONLINE Show nearby items on shelf
Title:Real Quaternionic Calculus Handbook [electronic resource]
Author(s): Joo Pedro Morais
Svetlin Georgiev
Wolfgang Sprig
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, suchas complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysishas become a well established branch in ma thematics and has been greatly successful in many different directions. This book is based onconcrete examples and exercises rather than general theorems, thus making it suitable for anintroductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises atthe end of each chapter and its straightforward writing style the book addresses readers w ho have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis,ordinary differential equations, partial differential equations, and theory of distributions
Contents:1 An introduction to quaternions
2 Quaternions and spatial rotation
3 Quaternion sequences
4 Quaternion series and infinite products
5 Exponents and logarithms
6 Trigonometric functions
7 Hyperbolic functions
8 Inverse hyperbolic and trigonometric functions
9 Quaternion matrices
10 Monomials, polynomials and binomials
11 Solutions
Bibliography
Index
ISBN:9783034806220
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Algebra , Functions of complex variables , Combinatorics , Geometry
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Call number:SPRINGER-2014-9781493907816:ONLINE Show nearby items on shelf
Title:Rigidity and Symmetry [electronic resource]
Author(s): Robert Connelly
Asia Ivi Weiss
Walter Whiteley
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry,algebra, and combinatorics . Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. Contributions present recent trends andadvances in discrete geometry, particularly in the the ory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry,group theory, classical geometry, hyperbolic geometry and topology. The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating thesurprising impact of symmetry. It will appeal to students at both the advanced undergraduate and grad uate levels, as well as postdocs, structural engineers, and chemists
Contents:Volumes of Polytopes in Spaces of Constant Curvature (N. Abrosimov, A. Mednykh)
Cubic Cayley Graphs and Snarks (H. Ademir, K. Kutnar, D. Marui)
Local, Dimensional and Universal Rigidities: A unified Gram Matrix Approach (A. Alfakih)
Geometric Constructions for Symmetric 6
Configurations (L.W. Berman)
On External Symmetry Groups of Regular Maps (M.D.E. Conder, Y.S. Kwon, J. ir)
Variance Groups and the Structure of Mixed Polytopes (G. Cunningham)
Mobility in Symmetry
Regular Bar
and
Joint Frameworks (P.W. Fowler, S.D. Guest, B. Schulze)
Generic Global Rigidity in C
ISBN:9781493907816
Series:eBooks
Series:SpringerLink
Series:Fields Institute Communications, 1069-5265 : v70
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Discrete groups , Topology
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Call number:SPRINGER-2014-9781493902583:ONLINE Show nearby items on shelf
Title:Analytic Number Theory, Approximation Theory, and Special Functions [electronic resource] : In Honor of Hari M. Srivastava
Author(s): Gradimir V Milovanovi
Michael Th Rassias
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematicalcommunity, including bot h research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions andquadratures, orthogonality, and special and co mplex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results,methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fieldsof mathematics, physics, and other computational and applied sciences
Contents:Part I. Analytic Number Theory, Combinatorics, and Special Sequences of Numbers and Polynomials
The mean values of the Riemann Zeta function on the critical line (A. Ivi)
Explicit bounds concerning non
trivial zeros of the Riemann Zeta function (M. Hassani)
On the value
distribution of logarithmic derivatives of Dirichlet L
functions (Y. Ihara, K. Matsumoto)
Multiple Gamma functions and their applications (J. Choi)
On partition functions of hyperbolic three
geometry and associated Hilbert schemes (A.A. Bytsenko and E. Elizalde)
Families of twisted Bernoulli numbers, twisted
ISBN:9781493902583
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional equations , Functional analysis , Number theory
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Call number:SPRINGER-2013-9789462390034:ONLINE Show nearby items on shelf
Title:Normally Hyperbolic Invariant Manifolds [electronic resource] : The Noncompact Case
Author(s): Jaap Eldering
Date:2013
Publisher:Paris : Atlantis Press : Imprint: Atlantis Press
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems. First, normally hyperbolic invariantmanifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due tononcompactness are discussed in great detail with examples. The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-knownresults by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompac tness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed toanalyze ODEs in a differential geometric context. Finally, the main result is extended to time and parame ter dependent systems and overflowing invariant manifolds
Note:Springer eBooks
Contents:Introduction
Manifolds of bounded geometry
Persistence of noncompact NHIMs
Extension of results
ISBN:9789462390034
Series:e-books
Series:SpringerLink (Online service)
Series:Atlantis Series in Dynamical Systems : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems
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Call number:SPRINGER-2013-9783642396267:ONLINE Show nearby items on shelf
Title:Constant Mean Curvature Surfaces with Boundary [electronic resource]
Author(s): Rafael Lpez
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:The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence ofgravity, where they separat e two different media, or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also ofgreat interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of compact surfaceswith boundaries, narrowing its focus to a geometric view. Basic issues incl ude the discussion whether the symmetries of the curve inherit to the surface the possible values of the mean curvature, area and volume stability thecircular boundary case and the existence of the Plateau problem in the non-parametric case. The expositio n provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambientspaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate stude nts and researchers in the field of differential geometry and especially theory of surfaces, includinggeometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems
Note:Springer eBooks
Contents:Introduction
Surfaces with Constant Mean Curvature
Constant Mean Curvature Embedded Surfaces
The Flux Formula for Constant Mean Curvature Surfaces
The Area and the Volume of a Constant Mean Curvature Surface
Constant Mean Curvature Discs with Circular Boundary
The Dirichlet Problem of the CMC Equation
The Dirichlet Problem in Unbounded Domains
Constant Mean Curvature Surfaces in Hyperbolic Space
The Dirichlet Problem in Hyperbolic Space
Constant Mean Curvature Surfaces in Lorentz
Minkowski Space
Appendix: A. The Variation Formula of the Area and the Volume
B
ISBN:9783642396267
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Geometry , Global differential geometry
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Call number:SPRINGER-2013-9783642309946:ONLINE Show nearby items on shelf
Title:Linear Algebra and Geometry [electronic resource]
Author(s): Igor R Shafarevich
Alexey O Remizov
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 on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements ofmatrix theory and continue s with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but areusually not covered in such courses: exterior alge bras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitelygenerated periodic modules (similar to Jordan normal forms of linear opera tors). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equationsand differential geometry, as well as from mechanics and physics
Note:Springer eBooks
Contents:Preface
Preliminaries
1. Linear Equations
2. Matrices and Determinants
3. Vector Spaces
4. Linear Transformations of a Vector Space to Itself
5. Jordan Normal Form
6. Quadratic and Bilinear Forms
7. Euclidean Spaces
8. Affine Spaces
9. Projective Spaces
10. The Exterior Product and Exterior Algebras
11. Quadrics
12. Hyperbolic Geometry
13. Groups, Rings, and Modules
14. Elements of Representation Theory
Historical Note
References
Index
ISBN:9783642309946
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Matrix theory , Geometry
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Call number:SPRINGER-2013-9783642306747:ONLINE Show nearby items on shelf
Title:Rational Points and Arithmetic of Fundamental Groups [electronic resource] : Evidence for the Section Conjecture
Author(s): Jakob Stix
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of itsfundamental group. Whi le the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only oneagainst rational points on curves. This monogr aph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and thelocal-to-global approach is studied in detail. The monograph concl udes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birationalanalogue in lieu of the fundamental group extension
Note:Springer eBooks
Contents:Part I Foundations of Sections
1 Continuous Non
abelian H1 with Profinite Coefficients
2 The Fundamental Groupoid
3 Basic Geometric Operations in Terms of Sections
4 The Space of Sections as a Topological Space
5 Evaluation of Units
6 Cycle Classes in Anabelian Geometry
7 Injectivity in the Section Conjecture
Part II Basic Arithmetic of Sections
7 Injectivity in the Section Conjecture
8 Reduction of Sections
9 The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers
Part III On the Passage from Local to Global
10 Local Obstructions
ISBN:9783642306747
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2054
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Number theory
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Call number:SPRINGER-2013-9783319008882:ONLINE Show nearby items on shelf
Title:Markov's Theorem and 100 Years of the Uniqueness Conjecture [electronic resource] : A Mathematical Journey from Irrational Numbers to Perfect Matchings
Author(s): Martin Aigner
Date:2013
Publisher:Heidelberg : Springer International Publishing : Imprint: Springer
Size:1 online resource
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Note:This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markovs theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything fallsinto place in the proof o f Markovs theorem.What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to theworld of graphs and words. On the way, there are als o introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraicwords. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with somebackground in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts Numbers, Trees, Groups,Words, Finale the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematic al achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics
Note:Springer eBooks
Contents:Approximation of IrrationalNumbers
Markov's Theorem and the Uniqueness Conjecture
The Markov Tree
The Cohn Tree
The Modular Group SL(2,Z)
The Free Group F2
Christoffel Words
Sturmian Words
Proof of Markov's Theorem
The Uniqueness Conjecture.
ISBN:9783319008882
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Combinatorics , Number theory
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Call number:SPRINGER-2013-9783034804813:ONLINE Show nearby items on shelf
Title:Complex Kleinian Groups [electronic resource]
Author(s): Angel Cano
Juan Pablo Navarrete
Jos Seade
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:This monograph lays down the foundations of the theory of complex Kleinian groups, a newborn area of mathematics whose origin can be traced back to the work of Riemann, Poincar, Picard and many others. Kleinian groupsare, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions,there is a dichotomy: Should we look at conformal automorp hisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In thefirst case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition in the second, about an area of mathematics that is still in its infancy, and this is the focus ofstudy in this monograph. It brings together several important areas of mathematics, e.g. classical Kleini an group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds
Note:Springer eBooks
Contents:Preface
Introduction
Acknowledgments
1 A glance of the classical theory
2 Complex hyperbolic geometry
3 Complex Kleinian groups
4 Geometry and dynamics of automorphisms of P2C
5 Kleinian groups with a control group
6 The limit set in dimension two
7 On the dynamics of discrete subgroups of PU(n,1)
8 Projective orbifolds and dynamics in dimension two
9 Complex Schottky groups
10 Kleinian groups and twistor theory
Bibliography
Index.
ISBN:9783034804813
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v303
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Differentiable dynamical systems , Differential equations, partial
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Call number:SPRINGER-2013-9781461479727:ONLINE Show nearby items on shelf
Title:Harmonic Analysis on Symmetric SpacesEuclidean Space, the Sphere, and the Poincar Upper Half-Plane [electronic resource]
Author(s): Audrey Terras
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar upper half plane. This book is intended for beginning graduate students inmathematics or researchers in phy sics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, andengineering. Many corrections, new topics, and updates have be en incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T.Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question Can y ou hear the shape of a drum?, Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maasswaveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summationformula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon tr ansform, non-Euclidean geometry on the Poincar upper half plane H or unit disc andapplications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg tra ce formula and its applications in spectral theory as wellas number theory
Note:Springer eBooks
Contents:Chapter1 Flat Space. Fourier Analysis on R^m
1.1 Distributions or Generalized Functions
1.2 Fourier Integrals
1.3 Fourier Series and the Poisson Summation Formula
1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions
1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyls Criterion for Uniform Distribution
Chapter2 A Compact Symmetric Space
The Sphere
2.1 Fourier Analysis on the Sphere
2.2 O(3) and R^3. The Radon Transform
Chapter 3 The Poincar Upper Half
Plane
3.1 Hyperbolic Geometry
3.2 Harmonic Analysis on H
3.3 Fundamental Domains for
ISBN:9781461479727
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Topological Groups , Harmonic analysis , Fourier analysis , Functions of complex variables , Functions, special
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Call number:SPRINGER-2013-9781461451280: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
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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-2013-9781441973238:ONLINE Show nearby items on shelf
Title:Complex Analysis [electronic resource] : In the Spirit of Lipman Bers
Author(s): Rub E Rodrguez
Irwin Kra
Jane P Gilman
Date:2013
Edition:2nd ed. 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 book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas ofmathematics, including the theor y of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects inmathematics and to other sciences. Thus this material will also be of interest to computer scientists, physicists, and engineers. The book covers most, if not all, of the material contained in Lipman Berss courses on first yearcomplex analysis. In addition, topics of current interest, such as zeros of holom orphic functions and the connection between hyperbolic geometry and complex analysis, are explored. In addition to many new exercises, this second editionintroduces a variety of new and interesting topics. New features include a section on Bers's theorem on isomorphisms between rings of holomorphic functions on plane domains necessary and sufficient conditions for the existence of abounded analytic function on the disc with prescribed zeros sections on subharmonic functions and Perron's principle and a se ction on the ring of holomorphic functions on a plane domain. There are three new appendices: the first isa contribution by Ranjan Roy on the history of complex analysis, the second contains background material on exterior differential calculus, and the t hird appendix includes an alternate approach to the Cauchy theory
Note:Springer eBooks
Contents:Preface to Second Edition
Preface to First Edition
Standard Notation and Commonly Used Symbols
1 The Fundamental Theorem in Complex Function Theory
2 Foundations
3 Power Series
4 The Cauchy Theory
A Fundamental Theorem
5 The Cauchy Theory
Key Consequences
6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions
7 Sequences and Series of Holomorphic Functions
8 Conformal Equivalence and Hyperbolic Geometry
9 Harmonic Functions
10 Zeros of Holomorphic Functions
Bibliographical Notes
Bibliography
Index
ISBN:9781441973238
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v245
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables
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Call number:SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf
Title:New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number
Author(s): Garret Sobczyk
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
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Note:The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s
Note:Springer eBooks
Contents:1 Modular Number Systems
2 Complex and Hyperbolic Numbers
3 Geometric Algebra
4 Vector Spaces and Matrices
5 Outer Product and Determinants
6 Systems of Linear Equations
7 Linear Transformations on R^n
8 Structure of a Linear Operator
9 Linear and Bilinear Forms
10 Hermitian Inner Product Spaces
11 Geometry of Moving Planes
12 Representations of the Symmetric Group
13 Calculus on m
Surfaces
14 Differential Geometry of Curves
15 Differential Geometry of k
Surfaces
16 Mappings Between Surfaces
17 Non
Euclidean and Projective Geometries
18 Lie Gr
ISBN:9780817683856
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2013-9780817683825:ONLINE Show nearby items on shelf
Title:A Tale of Two Fractals [electronic resource]
Author(s): A.A Kirillov
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
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Note:Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of researcharticles and books have beenpublished on the topic of fractals. Despite thevolume of literature in the field,the general level of theoreticalunderstanding has remained low most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use.Written bycelebrated mathematician and educator A.A. Kirillov,A Tale of Two Fractals helpsbridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The workis designedto give young,non-specialist mathematiciansa solid foundation in the theory of fractals. As its title sugges ts, this book focuses primarily on twofractals: theSierpiskigasket and the Apollonian gasket.Over the course of the book, theyare developed and discussed in various contexts. Along with fundamentaldefinitions and properties, some of the keyconcepts and ap proachescovered include * the Laplace operator * harmonic functions * generalized numerical systems* Descartes' theorem * rational paramaterizations * group action on fractals * generalization to multiple dimensions In addition to its explicit goal of pro viding undergraduate and graduate students with a sound foundation in fractaltheory,A Tale of Two Fractalsserves to enhance their overall understanding of mathematics by drawing on a wide variety of techniques from other subfields. Furthermore, by virtue of the subject matter, it provides a uniqueopportunity for students to develop their capacity for recognizing patterns and formulating interesting questions. It is therefore a valuable text not only for any course on fractals or hyperbolic geometry, but a lso for any surveycourse with an aim of honing creative-problem-solving skills
Note:Springer eBooks
Contents:Introduction
Part 1. The Sierpiski Gasket
Definition and General Properties
The Laplace Operator on the Sierpiski Gasket
Harmonic Functions on the Sierpiski Gasket
Part 2. The Apollonian Gasket
Introduction
Circles and Disks on Spheres
Definition of the Apollonian Gasket
Arithmetic Properties of Apollonian Gaskets
Geometric and Group
Theoretic Approach
Many
Dimensional Apollonian Gaskets
Bibliography
ISBN:9780817683825
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Global analysis (Mathematics) , Functions, special , Visualization , Geometry
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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-2012-9783642244971:ONLINE Show nearby items on shelf
Title:Mathematics and Modern Art [electronic resource] : Proceedings of the First ESMA Conference, held in Paris, July 19-22, 2010
Author(s): Claude Bruter
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:The link between mathematics and art remains as strong today as it was in the earliest instances of decorative and ritual art. Arts, architecture, music and painting have for a long time been sources of new developments inmathematics, and vice versa. Many great painters have seen no contradiction between artistic and mathematical endeavors, contributing to the progress of both, using mathematical principles to guide their visual creativity, enrichingtheir visual environment with the new objects creat ed by the mathematical science. Owing to the recent development of the so nice techniques for visualization, while mathematicians can better explore these new mathematical objects,artists can use them to emphasize their intrinsic beauty, and create quite new sceneries. This volume, the content of the first conference of the European Society for Mathematics and the Arts (ESMA), held in Paris in 2010, gives anoverview on some significant and beautiful recent works where maths and art, including architecture and music, are interwoven. The book includes a wealth of mathematical illustrations from several basic mathematical fields includingclassical geometry, topology, differential geometry, dynamical systems. Here, artists and mathematicians alike elucidate t he thought processes and the tools used to create their work
Note:Springer eBooks
Contents:Preface
A Mathematician and an Artist. The Story of a Collaboration by R.Palais
Dimensions, a Math Movie by A.Alvarez, J.Leys
Old and new Mathematical Models: saving the Heritage of the Institute Henri Poincar by F.Apry
An Introduction to the Construction of some Mathematical Objects by C.P.Bruter
Computer, Mathematics and Art by J
F.Colonna
Structure of Visualization and Symmetry in iterated Function Systems by J.Constant
Polyhedral eversions of the sphere gastrulation by R.Denner
M.C. Eschers Use of the Poincar Models of Hyperbolic Geometry by D.Dunham
M
ISBN:9783642244971
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics, 2190-5614 : v18
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Computer vision , Visualization , Geometry
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Call number:SPRINGER-2012-9783034804202:ONLINE Show nearby items on shelf
Title:Classical Geometries in Modern Contexts [electronic resource] : Geometry of Real Inner Product Spaces Third Edition
Author(s): Walter Benz
Date:2012
Edition:3rd ed. 2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
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Note:The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolicgeometry with respect to nat ural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Mbius and Lie as well as geometries where Lorentz transformations play thekey role. Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentztransformations. A real benefit is the dimension-free approach to important geome trical theories. New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these samespaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz -Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1. Another new and fundamental result inthis edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the ge ometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all xin X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments. The only prerequisites for read ing this book are basic linear algebra and basic 2- and 3-dimensional real geometry.This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in m odern and general contexts
Note:Springer eBooks
Contents:Preface
1 Translation Groups
2 Euclidean and Hyperbolic Geometry
3 Sphere Geometries of Mbius and Lie
4 Lorentz Transformations
5 Projective Mappings, Isomorphism Theorems
6 Planes of Leibniz, Lines of Weierstrass, Varia
A Notation and symbols
B Bibliography
Index
ISBN:9783034804202
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Mathematical physics
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Call number:SPRINGER-2012-9781447129844:ONLINE Show nearby items on shelf
Title:Partial Differential Equations 2 [electronic resource] : Functional Analytic Methods
Author(s): Friedrich Sauvigny
Date:2012
Edition:2nd ed. 2012
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
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Note:This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this second volume, special emphasis is placed onfunctional analytic metho ds and applications to differential geometry. The following topics are treated: solvability of operator equations in Banach spaces linear operators in Hilbert spaces and spectral theory Schauder's theory oflinear elliptic differential equations weak solut ions of differential equations nonlinear partial differential equations and characteristics nonlinear elliptic systems boundary value problems from differential geometry This newsecond edition of this volume has been thoroughly revised and a new chapter o n boundary value problems from differential geometry has been added. In the first volume, partial differential equations by integral representations aretreated in a classical way. This textbook will be of particular use to graduate and postgraduate studen ts interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study
Note:Springer eBooks
Contents:Operators in Banach Spaces
Linear Operators in Hilbert Spaces
Linear Elliptic Differential Equations
Weak Solutions of Elliptic Differential Equations
Nonlinear Partial Differential Equations
Nonlinear Elliptic Systems
Boundary Value Problems from Differential Geometry
ISBN:9781447129844
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Differential equations, partial , Mathematical physics
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Call number:SPRINGER-2012-9781447129813:ONLINE Show nearby items on shelf
Title:Partial Differential Equations 1 [electronic resource] : Foundations and Integral Representations
Author(s): Friedrich Sauvigny
Date:2012
Edition:2nd ed. 2012
Publisher:London : Springer London
Size:1 online resource
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Note:This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed ongeometric and complex vari able methods involving integral representations. The following topics are treated: integration and differentiation on manifolds foundations of functional analysis Brouwer's mapping degree generalized analytic functions potential theory and spherical h armonics linear partial differential equations This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior ofCauchys integral has been added. The second volume will present functional analytic methods and applications to problems in differential geometry. This textbook will be of particular use to graduate and postgraduate studentsinterested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study
Note:Springer eBooks
Contents:Differentiation and Integration on Manifolds
Foundations of Functional Analysis
Brouwers Degree of Mapping
Generalized Analytic Functions
Potential Theory and Spherical Harmonics
Linear Partial Differential Equations in Rn
ISBN:9781447129813
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Mathematical physics
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Call number:SPRINGER-2012-9780817682835:ONLINE Show nearby items on shelf
Title:A New Approach to Differential Geometry using Clifford's Geometric Algebra [electronic resource]
Author(s): John Snygg
Date:2012
Publisher:Boston, MA : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
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Note:Differential geometry is the study of curvature and calculus of curves and surfaces. Because of an historical accident, the Geometric Algebra devised by William Kingdom Clifford (18451879) has been overlooked in favor of themore complicated and less powerful formalism of differential forms and tangent vectors to deal with differential geometry. Fortuitously a student who has completed an undergraduate course in linear algebra is better prepared to dealwith the intricacies of Clifford algebra than wit h the formalism currently used. Clifford algebra enables one to demonstrate a close relation between curvature and certain rotations. This is an advantage both conceptually andcomputationallyparticularly in higher dimensions. Key features and topics inclu de: * a unique undergraduate-level approach to differential geometry * brief biographies of historically relevant mathematicians and physicists * someaspects of special and general relativity accessible to undergraduates with no knowledge of Newtonian phy sics * chapter-by-chapter exercises. The textbook will also serve as a useful classroom resource primarily forundergraduates aswell as beginning-level graduate students researchers in the algebra and physics communities may also find the book useful as a self-study guide
Note:Springer eBooks
Contents:Preface
Introduction
Clifford Algebra in Euclidean 3
Space
Clifford Algebra in Minkowski 4
Space
Clifford Algebra in Flat n
Space
Curved Spaces
The Gauss
Bonnet Formula
Non
Euclidean (Hyperbolic) Geometry
Some Extrinsic Geometry in E^n
Ruled Surfaces Continued
Lines of Curvature
Minimal Surfaces
Some General Relativity
Matrix Representation of a Clifford Algebra
Construction of Coordinate Dirac Matrices
A Few Terms of the Taylor's Series for the Urd
Copernican Model for the Outer Planets
A Few Terms of the Taylor's Series for Kepler's Orbits
ISBN:9780817682835
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Global differential geometry , Mathematical physics
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Call number:SPRINGER-2011-9783642179778:ONLINE Show nearby items on shelf
Title:Geometry of Minkowski Space-Time [electronic resource]
Author(s): Francesco Catoni
Dino Boccaletti
Roberto Cannata
Vincenzo Catoni
Paolo Zampetti
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences ofspecial relativity are m erely a manifestation of space-time geometry. The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied andallows the solution of any problem of relativisti c kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous TwinParadox is completely solved for all kinds of motions. The novelty of the pres entation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of thekinematics in the Minkowski space-time. Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields
Note:Springer eBooks
Contents:Introduction
Hyperbolic Numbers
Geometrical Representation of Hyperbolic Numbers
Trigonometry in the Hyperbolic (Minkowski) Plane
Equilateral Hyperbolas and Triangles in the Hyperbolic Plane
The Motions in Minkowski Space
Time (Twin Paradox)
Some Final Considerations
ISBN:9783642179778
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Physics
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematics
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Call number:SPRINGER-2011-9783642172861:ONLINE Show nearby items on shelf
Title:Perspectives on Projective Geometry [electronic resource] : A Guided Tour Through Real and Complex Geometry
Author(s): Jrgen Richter-Gebert
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry.It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic andelliptic geometry or eve n relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications.In particular, itexplains how metric concepts may be best understood inprojective terms. One of the major themes that appears throughout this book is the beauty of the interplaybetweengeometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objectsand operations may be most elegantly expressed in algebraic terms, making it a va luable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the authors experience in implementinggeometric software and includes hundreds ofhigh-qualityillustrations
Note:Springer eBooks
Contents:1 Pappos's Theorem: Nine Proofs and Three Variations
2 Projective Planes
3 Homogeneous Coordinates
4 Lines and Cross
Ratios
5 Calculating with Points on Lines
6 Determinants
7 More on Bracket Algebra
8 Quadrilateral Sets and Liftings
9 Conics and Their Duals
10 Conics and Perspectivity
11 Calculating with Conics
12 Projective $d$
space
13 Diagram Techniques
14 Working with diagrams
15 Configurations, Theorems, and Bracket Expressions
16 Complex Numbers: A Primer
17 The Complex Projective Line
18 Euclidean Geometry
19 Euclidean Structures fr
ISBN:9783642172861
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algorithms , Visualization , Geometry , Discrete groups
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Call number:SPRINGER-2011-9781441995544:ONLINE Show nearby items on shelf
Title:Nonlinear Conservation Laws and Applications [electronic resource]
Author(s): Alberto Bressan
Gui-Qiang G Chen
Marta Lewicka
Dehua Wang
Date:2011
Publisher:Boston, MA : Springer US
Size:1 online resource
Note:Springer e-book platform
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Note:This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 130-31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorousgrowth in recent years . The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the followingtopics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability anddynamics of viscous shock waves, singular limits for viscous systems, basic p rinciples in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models ofnonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In additi on, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids,granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks
Note:Springer eBooks
Contents:Foreword
Preface
Open questions in the theory of one dimensional hyperbolic conservation laws
Multidimensional conservation laws: Overview, problems, and perspective
Mathematical analysis of fluids in motion
Selected topics in approximate solutions of nonlinear conservation laws
High
resolution central schemes
Stability and dynamics of viscous shock waves
Mathematical aspects of a model for granular flow
The flow associated to weakly differentiable vector fields: recent results and open problems
Existence and uniqueness results for the continuity equation and appl
ISBN:9781441995544
Series:e-books
Series:SpringerLink (Online service)
Series:The IMA Volumes in Mathematics and its Applications, 0940-6573 : v153
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Mathematical physics
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Call number:SPRINGER-2011-9780817681081:ONLINE Show nearby items on shelf
Title:Fourier Integral Operators [electronic resource]
Author(s): J.J Duistermaat
Date:2011
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume is a useful introduction to the subject of Fourier integral operators and is based on the author's classic set of notes. Covering a range of topics from Hrmanders exposition of the theory, Duistermaat approachesthe subject from symplectic geometry and includes applications to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical)physicists with an interest in (linear) partial differential equations, especially in wave propagation, resp. WKB-methods. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful.Additionally, this book is designed for a one-semester introductory course on Fourier integral operators aimed at a broad audience. This book remains a superb introduction to the theory of Fourier integral operators. While there arefurther advances discussed in other sources, this book can still be recommended as perhaps the ver y best place to start in the study of this subject. SIAM Review This book is still interesting, giving a quick and elegantintroduction to the field, more adapted to nonspecialists. Zentralblatt MATH The book is completed with applications to the Cauchy pr oblem for strictly hyperbolic equations and caustics in oscillatory integrals. The reader shouldhave some background knowledge in analysis (distributions and Fourier transformations) and differential geometry. Acta Sci. Math
Note:Springer eBooks
Contents:Preface
0. Introduction
1. Preliminaries
1.1 Distribution densities on manifolds
1.2 The method of stationary phase
1.3 The wave front set of a distribution
2. Local Theory of Fourier Integrals
2.1 Symbols
2.2 Distributions defined by oscillatory integrals
2.3 Oscillatory integrals with nondegenerate phase functions
2.4 Fourier integral operators (local theory)
2.5 Pseudodifferential operators in Rn
3. Symplectic Differential Geometry
3.1 Vector fields
3.2 Differential forms
3.3 The canonical 1
and 2
form T* (X)
3.4 Symplectic vector spaces
3
ISBN:9780817681081
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Integral equations , Operator theory , Differential equations, partial
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Call number:SPRINGER-2011-9780817646226:ONLINE Show nearby items on shelf
Title:The Geometry of Complex Domains [electronic resource]
Author(s): Robert E Greene
Kang-Tae Kim
Steven G Krantz
Date:2011
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The geometry of complex domains is a subject with roots extending back more than a century, to the uniformization theorem of Poincar and Koebe and the resulting proof of existence of canonical metrics for hyperbolic Riemannsurfaces. In modern times, developments in several complex variables by Bergman, Hrmander, Andreotti-Vesentini, Kohn, Fefferman, and others have opened up new possibilities for the unification of complex function theory and complexgeometry. In particular, geometry can be used to st udy biholomorphic mappings in remarkable ways. This book presents a complete picture of these developments. Beginning with the one-variable casebackground information which cannotbe found elsewhere in one placethe book presents a complete picture of the s ymmetries of domains from the point of view of holomorphic mappings. It describes all the relevant techniques, from differential geometry to Lie groups topartial differential equations to harmonic analysis. Specific concepts addressed include: covering sp aces and uniformization Bergman geometry automorphism groups invariant metrics the scaling method. All modern results areaccompanied by detailed proofs, and many illustrative examples and figures appear throughout. Written by three leading experts in the field, The Geometry of Complex Domains is the first book to provide systematic treatment of recentdevelopments in the subject of the geometry of complex domains and automorphism groups of domains. A unique and definitive work in this subject area, it will be a valuable resource for graduate students and a useful reference forresearchers in the field
Note:Springer eBooks
Contents:Preface
1 Preliminaries
2 Riemann Surfaces and Covering Spaces
3 The Bergman Kernel and Metric
4 Applications of Bergman Geometry
5 Lie Groups Realized as Automorphism Groups
6 The Significance of Large Isotropy Groups
7 Some Other Invariant Metrics
8 Automorphism Groups and Classification of Reinhardt Domains
9 The Scaling Method, I
10 The Scaling Method, II
11 Afterword
Bibliography
Index
ISBN:9780817646226
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v291
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differentiable dynamical systems , Differential equations, partial , Geometry
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Call number:SPRINGER-2010-9789048186372:ONLINE Show nearby items on shelf
Title:Hyperbolic Triangle Centers [electronic resource] : The Special Relativistic Approach
Author(s): A.A Ungar
Date:2010
Publisher:Dordrecht : Springer Netherlands : Imprint: Springer
Size:1 online resource
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Note:After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einsteins special theory of relativity, the purpose of his new book is tointroduce hyperbolic baryc entric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates arerelated to the Newtonian mass, barycentric coordinate s are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to general belief, Einsteins relativistic mass hence meshes up extraordinarily well withMinkowskis four-vector formalism of special relativity. In Euclidean geometry, bary centric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolictriangle centers are known, and none of the known hyperbolic triangle centers has been determined analytically with respect to its hyperbolic triangle vertices. In his recent research, the author set the ground for investigatinghyperbolic triangle centers via hyperbolic barycentric coordinates, and one of the purposes of this book is to initiate a study of hyperb olic triangle centers in full analogy with the rich study of Euclidean triangle centers. Owing toits novelty, the book is aimed at a large audience: it can be enjoyed equally by upper-level undergraduates, graduate students, researchers and academics in g eometry, abstract algebra, theoretical physics and astronomy. For a fruitfulreading of this book, familiarity with Euclidean geometry is assumed. Mathematical-physicists and theoretical physicists are likely to enjoy the study of Einsteins special relativ ity in terms of its underlying hyperbolic geometry.Geometers may enjoy the hunt for new hyperbolic triangle centers and, finally, astronomers may use hyperbolic barycentric coordinates in th
Note:Springer eBooks
Contents:The Special Relativistic Approach To Hyperbolic Geometry
Einstein Gyrogroups
Einstein Gyrovector Spaces
When Einstein Meets Minkowski
Mathematical Tools For Hyperbolic Geometry
Euclidean and Hyperbolic Barycentric Coordinates
Gyrovectors
Gyrotrigonometry
Hyperbolic Triangle Centers
Gyrotriangle Gyrocenters
Gyrotriangle Exgyrocircles
Gyrotriangle Gyrocevians
Epilogue
ISBN:9789048186372
Series:e-books
Series:SpringerLink (Online service)
Series:Fundamental Theories of Physics : v166
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematics , Astronomy
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Call number:SPRINGER-2010-9783764399092:ONLINE Show nearby items on shelf
Title:Conformal Differential Geometry [electronic resource] : Q-Curvature and Conformal Holonomy
Author(s): Helga Baum
Andreas Juhl
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples ofconformally covariant operators are the Yamabe, the Paneitz, the Dirac and the twistor operator. These operators are intimely connected with the notion of Bransons Q-curvature. The aim of these lectures is to present the basic ideasand some of the recent developments around Q -curvatur e and conformal holonomy. The part on Q -curvature starts with a discussion of its origins and its relevance in geometry and spectral theory. The following lectures describe thefundamental relation between Q -curvature and scattering theory on asymptotica lly hyperbolic manifolds. Building on this, they introduce the recent concept of Q -curvature polynomials and use these to reveal the recursive structure ofQ -curvatures. The part on conformal holonomy starts with an introduction to Cartan connections and its holonomy groups. Then we define holonomy groups of conformal manifolds, discuss its relation to Einstein metrics and recentclassification results in Riemannian and Lorentzian signature. In particular, we explain the connection between conformal holon omy and conformal Killing forms and spinors, and describe Fefferman metrics in CR geometry as Lorentzianmanifold with conformal holonomy SU(1,m)
Note:Springer eBooks
ISBN:9783764399092
Series:e-books
Series:SpringerLink (Online service)
Series:Oberwolfach Seminars : v40
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry
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Call number:SPRINGER-2010-9783034605489:ONLINE Show nearby items on shelf
Title:Recent Trends in Toeplitz and Pseudodifferential Operators [electronic resource] : The Nikolai Vasilevskii Anniversary Volume
Author(s): Roland Duduchava
Israel Gohberg
Sergei M Grudsky
Vladimir Rabinovich
Date:2010
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The aim of the book is to present new results in operator theory and its applications. In particular, the book is devoted to operators with automorphic symbols, applications of the methods of modern operator theory anddifferential geometry to some pr oblems of theory of elasticity, quantum mechanics, hyperbolic systems of partial differential equations with multiple characteristics, Laplace-Beltrami operators on manifolds with singular points.Moreover, the book comprises new results in the theory of W iener-Hopf operators with oscillating symbols, large hermitian Toeplitz band matrices, commutative algebras of Toeplitz operators, and discusses a number of other topics
Note:Springer eBooks
Contents:The Life and Work of Nikolai Vasilevski
On the Structure of the Eigenvectors of Large Hermitian Toeplitz Band Matrices
Complete Quasi
wandering Sets and Kernels of Functional Operators
Lions Lemma, Korns Inequalities and the Lam Operator on Hypersurfaces
On the Bergman Theory for Solenoidal and Irrotational Vector Fields, I: General Theory
Weighted Estimates of Generalized Potentials in Variable Exponent Lebesgue Spaces on Homogeneous Spaces
Wiener
Hopf Operators with Oscillating Symbols on Weighted Lebesgue Spaces
On the Ill
posed Hyperbolic Systems with a Multipl
ISBN:9783034605489
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v210
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Operator 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
Note:Springer e-book platform
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-2010-9780817649920:ONLINE Show nearby items on shelf
Title:Geometry and Spectra of Compact Riemann Surfaces [electronic resource]
Author(s): Peter Buser
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This classic monograph is a self-contained introduction to the geometry of Riemann surfaces of constant curvature 1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemannsurfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. The first part of the book is written in textbook form at the graduate level, with only minimal requisites in eitherdifferential geometry or complex Riemann surface theory. The second part of the book is a self-contained introduction to the spectrum of the Laplacian based on the heat equation. Later chapters deal with recent developments onisospectrality, Sunadas construction, a simplified proof of Wolperts theorem, and an estimate of the number of pairwise isospectral non-isometric examples which depends only on genus. Researchers and graduate students interestedin compact Riemann surfaces will find this book a useful reference. Anyone familiar with the author's ha nds-on approach to Riemann surfaces will be gratified by both the breadth and the depth of the topics considered here. Theexposition is also extremely clear and thorough. Anyone not familiar with the author's approach is in for a real treat. Mathematical ReviewsThis is a thick and leisurely book which will repay repeated study with many pleasanthours both for the beginner and the expert. It is fortunately more or less self-contained, which makes it easy to read, and it leads one from essential mathemati cs to the state of the art in the theory of theLaplaceBeltrami operator on compact Riemann surfaces. Although it is not encyclopedic, it is so rich in information and ideas the reader will be grateful for what has been included in this very satisfying bo ok. Bulletin ofthe AMS The book is very well written and quite accessible there is an excellent bibliography at the end. Zentralblatt MATH
Note:Springer eBooks
Contents:Preface
Chapter 1: Hyperbolic Structures
Chapter 2: Trigonometry
Chapter 3: Y
Pieces and Twist Parameters
Chapter 4:The Collar Theorem
Chapter 5: Bers Constant and the Hairy Torus
Chapter 6: The Teichmller Space
Chapter 7: The Spectrum of the Laplacian
Chapter 8: Small Eigenvalues
Chapter 9: Closed Geodesics and Hubers Theorem
Chapter 10: Wolperts Theorem
Chapter 11: Sunadas Theorem
Chapter 12: Examples of Isospectral Riemann surfaces
Chapter 13: The Size of Isospectral Families
Chapter 14: Perturbations of the Laplacian in Hilbert Space
App
ISBN:9780817649920
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Differential equations, partial
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Call number:SPRINGER-2010-9780817649135:ONLINE Show nearby items on shelf
Title:Hyperbolic Manifolds and Discrete Groups [electronic resource]
Author(s): Michael Kapovich
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is onThurstons hyperbolization t heorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to thehyperbolization theorem as well as rich discussions on related t opics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich setof examples, numerous exercises, and an extensive bibliography and index, Hyperbolic M anifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairlyself-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem,this is an important book which had to be written some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolizationtheorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. -- -Zentralbatt MATH This book can act as source material for a postgraduatecourse and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide
Note:Springer eBooks
Contents:Preface
Three
dimensional Topology
Thurston Norm
Geometry of the Hyperbolic Space
Kleinian Groups
Teichmller Theory of Riemann Surfaces
Introduction to the Orbifold Theory
Complex Projective Structures
Sociology of Kleinian Groups
Ultralimits of Metric Spaces
Introduction to Group Actions on Trees
Laminations, Foliations and Trees
Rips Theory
Brooks' Theorem and Circle Packings
Pleated Surfaces and Ends of Hyperbolic Manifolds
Outline of the Proof of the Hyperbolization Theorem
Reduction to The Bounded Image Theorem
The Bounded Image Theorem
ISBN:9780817649135
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Geometry , Topology , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9780387754772:ONLINE Show nearby items on shelf
Title:Mathematica in Action [electronic resource] : Problem Solving Through Visualization and Computation
Author(s): Stan Wagon
Date:2010
Edition:3
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:In this third edition of Mathematica in Action, award-winning author Stan Wagon guides beginner and veteran users alike through Mathematica's powerful tools for mathematical exploration. The transition to Mathematica 7 is madesmooth with plenty of ex amples and case studies that utilize Mathematica's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting. Mathematica in Action also emphasizes the breadth of Mathematica and theimpressive results of combining techniques from different areas. This material enables the reader to use Mathematica to solve a variety of complex problems. Case studies ranging from elementary to sophisticated are provided throughout.Whenever possible, the book shows how Mathematica can be used to di scover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, anillustration of the BanachTarski Paradox via hyperbolic geometry, new and surprising formulas for p, the discovery of shadow orbits for chaotic systems, and the use of powerful new capabilities for three-dimensional graphics.Visualization is emphasized throughout, with finely crafted graphics in each chapter. Wagon is the author of eleven books on ma thematics, including A Course in Computational Number Theory, named one of the ten best math books of 2000by the American Library Association. He has written extensively on the educational applications of Mathematica, including the books VisualDSolve: Vis ualizing Differential Equations with Mathematica, and Animating Calculus: MathematicaNotebooks for the Laboratory. From reviews of the second edition: In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to ourunderstanding and enjoyment of mathematics. Richard Walker, The Mathematical Gazette The bottom line is that Mathematica in Action i
Note:Springer eBooks
Contents:Preface
A Brief Introduction
Plotting
Prime Numbers
Rolling Wheels
Surfaces
Dynamic Manipulation
The Cantor Set, Real and Complex
The Quadratic Map
The Recursive Turtle
Parametric Plotting of Surfaces
Penrose Tiles
Complex Dynamics (by Mark McClure)
Solving Equations
Optimization
Differential Equations
Computational Geometry
Check Digits and the Pentagon
Coloring Planar Maps
New Directions for pi. The Banach
Tarski Paradox
The Riemman Zeta Function
Miscellany
References
Index
ISBN:9780387754772
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science Mathematics , Visualization , Computer software
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Call number:SPRINGER-2010-9780387712789:ONLINE Show nearby items on shelf
Title:Modeling of Curves and Surfaces with MATLAB [electronic resource]
Author(s): Vladimir Rovenski
Date:2010
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 text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines.This book presents eleme ntary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful toolsof MATLAB including 2D and 3D animation of g eometric images with shadows and colors, transformations using matrices, and then studies more complex geometrical modeling problems related to analysis of curves and surfaces. With over150 stimulating exercises and problems, this text integrates traditio nal differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text greatly extends the authorsprevious title, Geometry of Curves and Surfaces with Maple (Birkhuser, 2000), and has a differe nt focus. In addition to being applications driven and motivated by numerous examples and exercises from real-world fields, the bookalso contains over 60 percent new material, including new sections with complex numbers, quaternions, matrices and transfor mations, hyperbolic geometry, fractals, and surface-splines and over 300 figures reproducible using MATLABprograms. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines, engineers, com puter scientists, and instructors of applied mathematics
Note:Springer eBooks
Contents:Preface
Part 1: Functions and Transformations
Functions and Graphs
Rigid Motions (Isometries)
Affine and Projective Transformations
Mobius Transformations
Part 2: Curves and Surfaces
Examples of Curves
Geometry of Curves
Surfaces
Geometry of Surfaces
Examples of Surfaces
Piecewise Curves and Surfaces
Appendix: M
files
References
Index
ISBN:9780387712789
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Undergraduate Texts in Mathematics and Technology, 1867-5506
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer graphics , Computer science , Differential equations, partial , Visualization , Geometry , Global differential geometry
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Call number:SPRINGER-2009-9783642027802:ONLINE Show nearby items on shelf
Title:Quantum Field Theory on Curved Spacetimes [electronic resource] : Concepts and Mathematical Foundations
Author(s): Christian Br
Klaus Fredenhagen
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:After some decades of work a satisfactory theory of quantum gravity is still not available moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, tofirst approximation, one i s left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions,the most famous one being the Hawking radiation of black holes. Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure,and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. This primer is anoutgrowth of a compact course given by the editors and contributing authors to an audience of adva nced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysison the part of the reader
Note:Springer eBooks
Contents:C*
algebras
Lorentzian Manifolds
Linear Wave Equations
Microlocal Analysis
Quantum Field Theory on Curved Backgrounds
ISBN:9783642027802
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v786
Series:Physics and Astronomy (Springer-11651)
Keywords: Cell aggregation Mathematics , Mathematical physics , Quantum theory
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Call number:SPRINGER-2009-9783034600002:ONLINE Show nearby items on shelf
Title:Schwarz-Pick Type Inequalities [electronic resource]
Author(s): Farit G Avkhadiev
Karl-Joachim Wirths
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book discusses in detail the extension of the Schwarz-Pick inequality to higher order derivatives of analytic functions with given images. It is the first systematic account of the main results in this area. Recent results ingeometric function t heory presented here include the attractive steps on coefficient problems from Bieberbach to de Branges, applications of some hyperbolic characteristics of domains via Beardon-Pommerenke's theorem, a newinterpretation of coefficient estimates as certain p roperties of the Poincar metric, and a successful combination of the classical ideas of Littlewood, Lwner and Teichmller with modern approaches. The material is complementedwith historical remarks on the Schwarz Lemma and a chapter introducing some challe nging open problems. The book will be of interest for researchers and postgraduate students in function theory and hyperbolic geometry
Note:Springer eBooks
ISBN:9783034600002
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics)
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Call number:SPRINGER-2009-9781848002906:ONLINE Show nearby items on shelf
Title:Bridging the Gap to University Mathematics [electronic resource]
Author(s): Edward Hurst
Martin Gould
Date:2009
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Full-worked solutions to all exercises available at www.springer.com Written by students for students, Bridging the Gap to University Mathematics is a refreshing, new approach to making the transition into undergraduate-levelmathematics or a similar numerate degree. Suitable for students of all backgrounds, whether A-level, Scottish Higher, International Baccalaureate or similar, the book helps readers to shape their existing knowledge and build uponcurrent strengths in order to get the most out of t heir undergraduate studies. The book can be used as a source of private study before embarking on a degree or as a textbook for an introductory course. Clear descriptions and a vastassortment of exercises complete with solutions enable the reader to dev elop and then practice new skills. Topics are delivered as twenty self-contained, manageable chapters, allowing students to dip in and out as they require,easily identifying those areas on which they need practice, whilst skimming over more familiar mater ial. Important concepts are introduced in an easy-to-read manner with a sustained emphasis on worked examples and applications ratherthan abstract theory. Each chapter also includes an insight into where the readers new skills will be employed during the course of their studies, providing a springboard to further research where desired
Note:Springer eBooks
Contents:Inequalities
Trigonometry, Differentiation and Exponents
Polar Coordinates
Complex Numbers
Vectors
Matrices
Matrices as Maps
Separable Differential Equations
Integrating Factors
Mechanics
Logic, Sets and Functions
Proof Methods
Probability
Distributions
Making Decisions
Geometry
Hyperbolic Trigonometry
Motion and Curvature
Sequences
Series
ISBN:9781848002906
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Science (General) , Computer science , Engineering
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Call number:SPRINGER-2008-9783764387266:ONLINE Show nearby items on shelf
Title:Commutative Algebras of Toeplitz Operators on the Bergman Space [electronic resource]
Author(s): Nikolai L Vasilevski
Date:2008
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 the spectral theory of commutative C*-algebras of Toeplitz operators on the Bergman space and its applications. For each such commutative algebra there is a unitary operator which reduces Toeplitzoperators from this algebra to certain multiplication operators, thus providing their spectral type representations. This yields a powerful research tool giving direct access to the majority of the important properties of the Toeplitzoperators studied herein, such as boundedness, comp actness, spectral properties, invariant subspaces. The presence and exploitation of these spectral type representations forms the core for many results presented in the book. Amongother results it contains a criterion of when the algebras are commutative on each commonly considered weighted Bergman space together with their explicit descriptions a systematic study of Toeplitz operators with unbounded symbols aclarification of the difference between compactness of commutators and semi-commutators of Toepli tz operators the theory of Toeplitz and related operators with symbols having more than two limit values at boundary points and a kindof semi-classical analysis of spectral properties of Toeplitz operators. The book is addressed to a wide audience of math ematicians, from graduate students to researchers, whose primary interests lie in complex analysis and operatortheory
Note:Springer eBooks
Contents:1. Prologue
2. Bergman and Poly
Bergman Spaces
3. Bergman
Type Spaces on the Unit Disk
4. Toeplitz Operators with Commutative Symbol Algebras
5. Toeplitz Operators on the Unit Disk with Radial Symbols
6. Toeplitz Operators with Homogeneous Symbols
7. Anatomy of the Algebra Generated by Toeplitz Operators
8. Toeplitz Operators and Hyperbolic Geometry
9. Weighted Bergman spaces
10. Commutative Algebras of Toeplitz Operators
11. Dynamics of Properties, Radial Symbols
12. Dynamics of Properties, Parabolic case
13. Dynamics of Properties, Hyperbolic case
Appen
ISBN:9783764387266
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v185
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Functions of complex variables , Operator theory
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Call number:SPRINGER-2008-9783764386146:ONLINE Show nearby items on shelf
Title:The Mathematics of Minkowski Space-Time [electronic resource] With an Introduction to Commutative Hypercomplex Numbers
Author(s): Francesco Catoni
Dino Boccaletti
Roberto Cannata
Vincenzo Catoni
Enrico Nichelatti
Paolo Zampetti
Date:2008
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers isextensively studied in t he book. In particular, an exhaustive solution of the twin paradox is given, followed by a detailed exposition of space-time geometry and trigonometry. Finally, an appendix on general properties ofcommutative hypercomplex systems with four unities is pres ented
Note:Springer eBooks
Contents:N
Dimensional Commutative Hypercomplex Numbers
The Geometries Generated by Hypercomplex Numbers
Trigonometry in the Minkowski Plane
Uniform and Accelerated Motions in the Minkowski Space
Time (Twin Paradox)
General Two
Dimensional Hypercomplex Numbers
Functions of a Hyperbolic Variable
Hyperbolic Variables on Lorentz Surfaces
Constant Curvature Lorentz Surfaces
Generalization of Two
Dimensional Special Relativity (Hyperbolic Transformations and the Equivalence Principle)
ISBN:9783764386146
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis (Mathematics) , Geometry , Global differential geometry , Mathematical physics
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Call number:SPRINGER-2008-9783540747987:ONLINE Show nearby items on shelf
Title:Probability and Real Trees [electronic resource] : cole d't de Probabilits de Saint-Flour XXXV - 2005
Author(s): Steven Neil Evans
Date:2008
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Random trees and tree-valued stochastic processes are of particular importance in combinatorics, computer science, phylogenetics, and mathematical population genetics. Using the framework of abstract tree-like metric spaces(so-called real trees) and ideas from metric geometry such as the Gromov-Hausdorff distance, Evans and his collaborators have recently pioneered an approach to studying the asymptotic behaviour of such objects when the number ofvertices goes to infinity. These notes survey the rele vant mathematical background and present some selected applications of the theory
Note:Springer eBooks
Contents:Preface
1. Introduction
2. Around the continuum random tree
3. R
trees and 0
hyperbolic spaces
4. Hausdorff and GromovHausdorff distance
5. Root growth with re
grafting
6. The wild chain and other bipartite chains
7. Diffusions on a R
tree without leaves: snakes and spiders
8. Rtrees from coalescing particle systems
9. Subtree prune and re
graft
A. Summary of Dirichlet form theory
B. Some fractal notions
References
Index
ISBN:9783540747987
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1920
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics , Geometry , Distribution (Probability theory)
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Call number:SPRINGER-2008-9781402087585:ONLINE Show nearby items on shelf
Title:Partial Differential Equations [electronic resource] : Modeling and Numerical Simulation
Author(s): Roland Glowinski
Pekka Neittaanmki
Date:2008
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural atfirst and then those ori ginating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling anddesign, but a little less than a century ago the S chrdinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but thenfor systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this bookseveral experts in this field present their latest results and discuss trends in the numerical an alysis of partial differential equations. The first part is devoted to discontinuous Galerkin and mixed finite element methods, bothmethodologies of fast growing popularity. They are applied to a variety of linear and nonlinear problems, including the Sto kes problem from fluid mechanics and fully nonlinear elliptic equations of the Monge-Ampre type. Numericalmethods for linear and nonlinear hyperbolic problems are discussed in the second part. The third part is concerned with domain decomposition methods, with applications to scattering problems for wave models and to electronic structurecomputations. The next part is devoted to the numerical simulation of problems in fluid mechanics that involve free surfaces and moving boundaries. The finite difference solution of a problem from spectral geometry has also beenincluded in this part. Inverse problems are known to be efficient models used in geology, medicine, mechanics and many other natural science
Note:Springer eBooks
ISBN:9781402087585
Series:e-books
Series:SpringerLink (Online service)
Series:Computational Methods in Applied Sciences, 1871-3033 : v16
Series:Physics and Astronomy (Springer-11651)
Keywords: Differential equations, partial , Engineering mathematics
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