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SPIRES-BOOKS: FIND KEYWORD CELL AGGREGATION MATHEMATICS *END*INIT* use /tmp/qspiwww.webspi1/4239.45 QRY 131.225.70.96 . find keyword cell aggregation mathematics ( in books using www Cover
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Call number:SPRINGER-2014-9783642315435:ONLINE Show nearby items on shelf
Title:An Introduction to Compactness Results in Symplectic Field Theory [electronic resource]
Author(s): Casim Abbas
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in thelast decade. The author presents a systematic introduction providing a lot of background material, much of which is scattered throughout the literature. Since the content grew out of lectures given by the author, the main aim is toprovide an entry point into symplectic field the ory for non-specialists and for graduate students. Extensions of certain compactness results, which are believed to be true by the specialists but have not yet been published in theliterature in detail, top off the scope of this monograph
ISBN:9783642315435
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2014-9783319081533:ONLINE Show nearby items on shelf
Title:Algebraic K-theory of Crystallographic Groups [electronic resource] : The Three-Dimensional Splitting Case
Author(s): Daniel Scott Farley
Ivonne Johanna Ortiz
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to be a theorem, it gives apowerful method for comput ing the lower algebraic K-theory of a group. This book contains a computation of the lower algebraic K-theory of the split three-dimensional crystallographic groups, a geometrically important class ofthree-dimensional crystallographic group, representing a third of the total number. The book leads the reader through all aspects of the calculation. The first chapters describe the split crystallographic groups and their classifyingspaces. Later chapters assemble the techniques that are needed to apply the i somorphism theorem. The result is a useful starting point for researchers who are interested in the computational side of the Farrell-Jones isomorphismconjecture, and a contribution to the growing literature in the field
ISBN:9783319081533
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2113
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , K-theory , Cell aggregation Mathematics
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Call number:SPRINGER-2014-9783319064772:ONLINE Show nearby items on shelf
Title:Finiteness Properties of Arithmetic Groups Acting on Twin Buildings [electronic resource]
Author(s): Stefan Witzel
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains onlytwo places. While th e proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory oftwin buildings
Contents:Basic Definitions and Properties
Finiteness Properties of G(Fq[t])
Finiteness Properties of G(Fq[t t
1])
Affine Kac
Moody Groups
Adding Places
ISBN:9783319064772
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2109
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Geometry , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2014-9783319063737:ONLINE Show nearby items on shelf
Title:Geometry of Manifolds with Non-negative Sectional Curvature [electronic resource] : Editors: Rafael Herrera, Luis Hernndez-Lamoneda
Author(s): Owen Dearricott
Fernando Galaz-Garca
Lee Kennard
Catherine Searle
Gregor Weingart
Wolfgang Ziller
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Providing an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area. The lectures cover a wide range of topics such asgeneral isometric grou p actions, circle actions on positively curved four manifolds, cohomogeneity one actions on Alexandrov spaces, isometric torus actions on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds,isoparametric hypersurfaces in spheres, contact C R and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. Also included is an introduction to the theory of exterior differential systems
Contents:Riemannian manifolds with positive sectional curvature
An introduction to isometric group actions
A note on maximal symmetry rank, quasipositive curvature and low dimensional manifolds
Lectures on n
Sasakian manifolds
On the Hopf conjecture with symmetry
An Introduction to Exterior Differential Systems
ISBN:9783319063737
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2110
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2014-9783319059570:ONLINE Show nearby items on shelf
Title:A Short Course in Computational Geometry and Topology [electronic resource]
Author(s): Herbert Edelsbrunner
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:With the aim to bring the subject of Computational Geometry and Topology closer to the scientific audience, this book is written in thirteen ready-to-teach sections organized in four parts: TESSELLATIONS, COMPLEXES, HOMOLOGY,PERSISTENCE. To speak to the non-specialist, detailed formalisms are often avoided in favor of lively 2- and 3-dimensional illustrations. The book is warmly recommended to everybody who loves geometry and the fascinating world ofshapes
Contents:Roots of Geometry and Topology
Voronoi and Delaunay Diagrams
Weighted Diagrams
Three Dimensions
Alpha Complexes
Holes
Area Formulas
Topological Spaces
Homology Groups
Complex Construction
Filtrations
PL Functions
Matrix Reduction
Epilogue
ISBN:9783319059570
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Applied Sciences and Technology, 2191-530X
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Cell aggregation Mathematics , Biomedical engineering
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Call number:SPRINGER-2014-9781461495215:ONLINE Show nearby items on shelf
Title:Computational Methods for Three-Dimensional Microscopy Reconstruction [electronic resource]
Author(s): Gabor T Herman
Joachim Frank
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Approaches to the recovery of three-dimensional information on a biological object, which are often formulated or implemented initially in an intuitive way, are concisely described here based on physical models of the object andthe image-formation pr ocess. Both three-dimensional electron microscopy and X-ray tomography can be captured in the same mathematical framework, leading to closely-related computational approaches, but the methodologies differ indetail and hence pose different challenges. The editors of this volume, Gabor T. Herman and Joachim Frank, are experts in the respective methodologies and present research at the forefront of biological imaging and structural biology. Computational Methods for Three-Dimensional Microscopy Reconstructio n will serve as a useful resource for scholars interested in the development of computational methods for structural biology and cell biology, particularly in thearea of 3D imaging and modeling
Contents:1 Introduction
2 Interchanging geometry conventions in 3DEM: Mathematical context for the development of standards
3 Fully automated particle selection and verification in single
particle cryo
EM
4 Quantitative analysis in iterative classification schemes for cryo
EM applications
5 High
resolution cryo
EM structure of the Trypanosoma brucei ribosome of a case study
6 Computational methods for electron tomography of influenza virus
7 Reconstruction from microscopic projections with defocus
gradient and attenuation effects
8 Soft X
ray tomography imaging for biological sampl
ISBN:9781461495215
Series:eBooks
Series:SpringerLink
Series:Applied and Numerical Harmonic Analysis, 2296-5009
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Bioinformatics , Physiology Mathematics , Visualization , Cell aggregation Mathematics
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Call number:SPRINGER-2014-9781447154969:ONLINE Show nearby items on shelf
Title:Morse Theory and Floer Homology [electronic resource]
Author(s): Michle Audin
Mihai Damian
Date:2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the numberof 1-periodic trajecto ries of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool ofdifferential topology. It defines the Morse complex a nd the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology isan infinite-dimensional analogue of Morse homology. Its involvement has bee n crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology aremore intricate and imply the use of more sophisticated analytical methods, all of which are expla ined in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. Thebook originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercis es. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students
Contents:Introduction to Part I
Morse Functions
Pseudo
Gradients
The Morse Complex
Morse Homology, Applications
Introduction to Part II
What You Need To Know About Symplectic Geometry
The Arnold Conjecture and the Floer Equation
The Maslov Index
Linearization and Transversality
Spaces of Trajectories
From Floer To Morse
Floer Homology: Invariance
Elliptic Regularity
Technical Lemmas
Exercises for the Second Part
Appendices: What You Need to Know to Read This Book
ISBN:9781447154969
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9783642343643:ONLINE Show nearby items on shelf
Title:A Guide to the Classification Theorem for Compact Surfaces [electronic resource]
Author(s): Jean Gallier
Dianna Xu
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those withoutdetailed background know ledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy andformal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be awork-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincar characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learningwhere it is required, without interrupting the carefully planned structure of the core expositi on. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuineconfidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and val uable techniques available in algebraic topology
Note:Springer eBooks
Contents:The Classification Theorem: Informal Presentation
Surfaces
Simplices, Complexes, and Triangulations
The Fundamental Group, Orientability
Homology Groups
The Classification Theorem for Compact Surfaces
Viewing the Real Projective Plane in R3
Proof of Proposition 5.1
Topological Preliminaries
History of the Classification Theorem
Every Surface Can be Triangulated
Notes
ISBN:9783642343643
Series:e-books
Series:SpringerLink (Online service)
Series:Geometry and Computing, 1866-6795 : v9
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9783642333026:ONLINE Show nearby items on shelf
Title:Guts of Surfaces and the Colored Jones Polynomial [electronic resource]
Author(s): David Futer
Efstratia Kalfagianni
Jessica Purcell
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 monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that thegrowth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for theknot in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternatingknots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of thecomplement to the combinatorics of certain surface spines (state graphs). Since state graphs have previously appeared in the study of Jones polynomials, our method bridges the gap between quantum and geometric knot invariants
Note:Springer eBooks
Contents:1 Introduction
2 Decomposition into 3balls
3 Ideal Polyhedra
4 Ibundles and essential product disks
5 Guts and fibers
6 Recognizing essential product disks
7 Diagrams without non
prime arcs
8 Montesinos links
9 Applications
10 Discussion and questions
ISBN:9783642333026
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2069
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9781461480426:ONLINE Show nearby items on shelf
Title:Introduction to Global Optimization Exploiting Space-Filling Curves [electronic resource]
Author(s): Yaroslav D Sergeyev
Roman G Strongin
Daniela Lera
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family ofderivative-free numerical alg orithms applying space-filling curves to reduce the dimensionality of the global optimization problem along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitzconstant, balancing global and local information to acce lerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This workalso contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremaland partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals,operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and t he environmental sciences will find this title useful .
Note:Springer eBooks
Contents:1. Introduction
2. Approximations to Peano curves
3. Global optimization algorithms using curves to reduce dimensionality of the problem
4. Ideas for acceleration
5. A brief conclusion
References
ISBN:9781461480426
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Optimization, 2190-8354
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Computer software , Numerical analysis , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9781461477327:ONLINE Show nearby items on shelf
Title:First Steps in Differential Geometry [electronic resource] : Riemannian, Contact, Symplectic
Author(s): Andrew McInerney
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels ofabstraction and proof encounte red at the upper division by mathematics majors. Today it is possible to describe differential geometry as the study of structures on the tangent space, and this text develops this point of view. Thisbook, unlike other introductory texts in differential g eometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduatestudent who already has a solid foundation in the standard mathematics curri culum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful useof examples and constructions in order to explore those consequences
Note:Springer eBooks
Contents:Basic Objects and Notation
Linear Algebra Essentials
Advanced Calculus
Differential Forms and Tensors
Riemannian Geometry
Contact Geometry
Symplectic Geometry
References
Index
ISBN:9781461477327
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9781461445814:ONLINE Show nearby items on shelf
Title:Attractors for infinite-dimensional non-autonomous dynamical systems [electronic resource]
Author(s): Alexandre N Carvalho
Jos A Langa
James C Robinson
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book treats the theory of pullback attractors for non-autonomous dynamical systems. While the emphasis is on infinite-dimensional systems, the results are also applied to a variety of finite-dimensional examples. Thepurpose of the book is to pr ovide a summary of the current theory, starting with basic definitions and proceeding all the way to state-of-the-art results. As such it is intended as a primer for graduate students, and a reference formore established researchers in the field. The bas ic topics are existence results for pullback attractors, their continuity under perturbation, techniques for showing that their fibres are finite-dimensional, and structural resultsfor pullback attractors for small non-autonomous perturbations of gradient systems (those with a Lyapunov function). The structural results stem from a dynamical characterisation of autonomous gradient systems, which shows inparticular that such systems are stable under perturbation. Application of the structural results relies on the continuity of unstable manifolds under perturbation, which in turn is based on the robustness of exponential dichotomies: aself-contained development of these topics is given in full. After providing all the necessary theory the book treats a numb er of model problems in detail, demonstrating the wide applicability of the definitions and techniquesintroduced: these include a simple Lotka-Volterra ordinary differential equation, delay differential equations, the two-dimensional Navier-Stokes equatio ns, general reaction-diffusion problems, a non-autonomous version of theChafee-Infante problem, a comparison of attractors in problems with perturbations to the diffusion term, and a non-autonomous damped wave equation. Alexandre N. Carvalho is a Professo r at the University of Sao Paulo, Brazil. Jos A.Langa is a Profesor Titular at the University of Seville, Spain. James C. Robinson is a Professor at the University of Warwick, UK
Note:Springer eBooks
Contents:The pullback attractor
Existence results for pullback attractors
Continuity of attractors
Finite
dimensional attractors
Gradient semigroups and their dynamical properties
Semilinear Differential Equations
Exponential dichotomies
Hyperbolic solutions and their stable and unstable manifolds
A non
autonomous competitive Lotka
Volterra system
Delay differential equations
The NavierStokes equations with non
autonomous forcing
Applications to parabolic problems
A non
autonomous ChafeeInfante equation
Perturbation of diffusion and continuity of attractors w
ISBN:9781461445814
Series:e-books
Series:SpringerLink (Online service)
Series:Applied Mathematical Sciences, 0066-5452 : v182
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Differential equations, partial , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9783642315640:ONLINE Show nearby items on shelf
Title:Diffeomorphisms of Elliptic 3-Manifolds [electronic resource]
Author(s): Sungbok Hong
John Kalliongis
Darryl McCullough
J. Hyam Rubinstein
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 work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed3-manifolds that hav e a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. Theoriginal Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The mainresults establish the Smale Conjecture for all elliptic 3-manifold s containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3manifold V, the space of Seifert fiberings has contractible components, and apart from a small list of known exceptions, is contractible. Considerable foundational and background material on diffeomorphism groups is included
Note:Springer eBooks
Contents:1 Elliptic 3
manifolds and the Smale Conjecture
2 Diffeomorphisms and Embeddings of Manifolds
3 The Method of Cerf and Palais
4 Elliptic 3
manifolds Containing One
sided Klein Bottles
5 Lens Spaces
ISBN:9783642315640
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2055
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9783642303623:ONLINE Show nearby items on shelf
Title:Algebraic Operads [electronic resource]
Author(s): Jean-Louis Loday
Bruno Vallette
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:In many areas of mathematics some higher operations are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key tounderstanding and comparing them, to cre ating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such asalgebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study allkinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a concept ual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality forassociative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiarwith elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and num erous figures are included. After an elementary chapter on classical algebra, accessible toundergraduate students,the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three ap pendices review the basic results needed in order to understand thevarious chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, thebook can also be used as a reference work by researchers.
Note:Springer eBooks
Contents:Preface
1.Algebras, coalgebras, homology
2.Twisting morphisms
3.Koszul duality for associative algebras
4.Methods to prove Koszulity of an algebra
5.Algebraic operad
6 Operadic homological algebra
7.Koszul duality of operads
8.Methods to prove Koszulity of an operad
9.The operads As and A\infty
10.Homotopy operadic algebras
11.Bar and cobar construction of an algebra over an operad
12.(Co)homology of algebras over an operad
13.Examples of algebraic operads
Apendices: A.The symmetric group
B.Categories
C.Trees
References
Index
List of Not
ISBN:9783642303623
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v346
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9783642255885:ONLINE Show nearby items on shelf
Title:Manfredo P. do Carmo Selected Papers [electronic resource]
Author(s): Manfredo P do Carmo
Keti Tenenblat
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards,the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the mainfocus of this selection, though it also co ntains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featuredpapers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of currentinterest to researchers, including a paper co-authored with Frank Warner on the convexity of hy persurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the authorand his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collecti on pays tribute to one of the most distinguished mathematicians
Note:Springer eBooks
Contents:Preface
A Summary of the Scientific Activities of Manfredo P. do Carmo
Summary of thePapers in this Volume by Manfredo P. do Carmo
Contributions
Complete List of Publications of Manfredo P. do Carmo
List of D.Sc. Students of Manfredo P. do Carmo
ISBN:9783642255885
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9783642244407:ONLINE Show nearby items on shelf
Title:Quantum Triangulations [electronic resource] : Moduli Spaces, Strings, and Quantum Computing
Author(s): Mauro Carfora
Annalisa Marzuoli
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemannmoduli space theory, str ings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physicaltheories are typically formulated, but their appear ance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a waywhich makes manifest the basic geometric structures of the physical intera ctions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physicaltheory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of casesstudies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied m athematicians and theoretical physicists working in the field of quantum geometry and its applications.
Note:Springer eBooks
Contents:Triangulated Surfaces and Polyhedral Structures
Singular Euclidean Structures an Riemann Surfaces
Polyhedral Surfaces and the Weil
Petersson Form
The Quantum Geometry of Polyhedral Surfaces
State Sum Models and Observables
Combinatorial Framework for Topological Quantum Computing
A Capsule of Moduli Space Theory
Spectral Theory on Polyhedral Surfaces
Index
ISBN:9783642244407
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v845
Series:Physics and Astronomy (Springer-11651)
Keywords: Cell aggregation Mathematics , Quantum theory
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Call number:SPRINGER-2012-9781461407096:ONLINE Show nearby items on shelf
Title:Buildings, Finite Geometries and Groups [electronic resource] : Proceedings of a Satellite Conference, International Congress of Mathematicians, Hyderabad, India, 2010
Author(s): N.S. Narasimha Sastry
Date:2012
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:This volume collects articles inspired by the Proceedings of the ICM 2010 Satellite Conference on Buildings, Finite Geometries and Groups organized at the Indian Statistical Institute, Bangalore, from August 29 31,2010. These contributors include so me of the most active researchers in areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lietheory, and more. Contributions reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective that the authors bring to their articles on currentdevelopments and major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these fields
Note:Springer eBooks
Contents:1. On Characterizing Designs By Their Codes (B. Bagchi)
2. The Geometry of Extremal Elements in a Lie Algebra (A.M. Cohen)
3. Properties of a 27
dimensional Space of Symmetric Bilinear Forms Acted on by E6 (R. Gow)
4. On the Geometry of Global Function Fields, the Riemann
Roch Theorem, and Finiteness Properties of S
arithmetic Groups (R. Gramlich)
5. Some Remarks on Two
Transitive Permutation Groups as Multiplication Groups of Quasigroups (G. Hiss, F. Lbeck)
6. Curve Complexes Versus Tits Buildings: Structures and Applications (Lizhen Ji)
7. On Isotypies Between Galois Conj
ISBN:9781461407096
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics, 2190-5614 : v10
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9781441978387:ONLINE Show nearby items on shelf
Title:The Geometry of Minkowski Spacetime [electronic resource] An Introduction to the Mathematics of the Special Theory of Relativity
Author(s): Gregory L Naber
Date:2012
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usualmenu of topics one is accu stomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeemans characterization of the causal automorphisms of Minkowski spacetime,the Penrose theorem on the apparent shape of a relat ivistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology forMinkowski spacetime whose homeomorphism group is essentially the Lorentz grou p, and a careful discussion of Diracs famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. Thissecond edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presenceof gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recentastronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a know ledge of linear algebra in the first three chapters, a bit of real analysis in thefourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: a valuable contribution to thepedagogical literature which will be enjoyed by all who delight in precise mathematics and physics. (American Mathematic
Note:Springer eBooks
ISBN:9781441978387
Series:e-books
Series:SpringerLink (Online service)
Series:Applied Mathematical Sciences, 0066-5452 : v92
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Cell aggregation Mathematics , Mathematical physics
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Call number:SPRINGER-2012-9780817683436:ONLINE Show nearby items on shelf
Title:Singularities of Differentiable Maps, Volume 2 [electronic resource] : Monodromy and Asymptotics of Integrals
Author(s): V.I Arnold
S.M Gusein-Zade
A.N Varchenko
Date:2012
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Originally published inthe 1980s, Singularities of DifferentiableMaps: Monodromy and Asymptotics of Integrals was thesecond oftwovolumes that togetherformed a translation of the authors'influential Russian monographon singularity theory.This uncorrec ted softcover reprint of the work brings its still-relevant content back into the literature, making it availableand affordableto a global audience of researchers and practitioners. Whilethe first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable mapsthat is, was devoted to a description of what, where, and how singularities could beencounteredthis second volume concentrates on elements of theanatomy and physiology of singu larities of differentiable functions. The questions considered here are about the structure of singularities and how they function. Inthe first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanis hing cycles distinguished bases intersection matricesmonodromy groupsthe variation operatorand theirinterconnections and method of calculation. The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary pha se, which is widely met within applications. The third and last part dealswith integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function. Thismonograph is suitablefor mathematicians, researchers, postgradua tes, and specialists in the areas ofmechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps
Note:Springer eBooks
Contents:Part I. The topological structure of isolated critical points of functions
Introduction
Elements of the theory of Picard
Lefschetz
The topology of the non
singular level set and the variation operator of a singularity
The bifurcation sets and the monodromy group of a singularity
The intersection matrices of singularities of functions of two variables
The intersection forms of boundary singularities and the topology of complete intersections
Part II. Oscillatory integrals
Discussion of results
Elementary integrals and the resolution of singularities of the phase
As
ISBN:9780817683436
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9780817683405:ONLINE Show nearby items on shelf
Title:Singularities of Differentiable Maps, Volume 1 [electronic resource] : Classification of Critical Points, Caustics and Wave Fronts
Author(s): V.I Arnold
S.M Gusein-Zade
A.N Varchenko
Date:2012
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Originally published inthe 1980s, Singularities of DifferentiableMaps: The Classificationof Critical Points, Caustics and Wave Fronts was the first oftwovolumes that togetherformed a translation of theauthors'influential Russian monograph on singular ity theory.This uncorrected softcover reprint of the work brings its still-relevant content back into the literature, making it availableand affordableto a global audience ofresearchers and practitioners. Singularity theory isa far-reaching extension of m axima and minima investigations of differentiable functions, withimplications for many different areas of mathematics, engineering (catastrophe theoryand the theory of bifurcations), and science. The three parts of this first volume deal with the stabilit y problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. Building onthese concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixedHodge structures of singularities. Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates the needs of non-mathematicians,presupposing a limited mathematical background andbeginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explorean unparalleled breadth ofapplications
Note:Springer eBooks
Contents:Part I. Basic concepts
The simplest examples
The classes Sigma^ I
The quadratic differential of a map
The local algebra of a map and the Weierstrass preparation theorem
The local multiplicity of a holomorphic map
Stability and infinitesimal stability
The proof of the stability theorem
Versal deformations
The classification of stable germs by genotype
Review of further results
Part II. Critical points of smooth functions
A start to the classification of critical points
Quasihomogeneous and semiquasihomogeneous singularities
The classification of quasih
ISBN:9780817683405
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9780817682712:ONLINE Show nearby items on shelf
Title:Differentiable Manifolds [electronic resource] : A Theoretical Physics Approach
Author(s): Gerardo F Torres del Castillo
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The works first three chaptersintroduce the basic concep ts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequentlyemployed in the study of differential equations ( Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked outin detail, as well as exercises intended to show how the formalism is a pplied to actual computations and to emphasize the connections among various areas of mathematics. Differentiable Manifolds is addressed to advanced undergraduateor beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics
Note:Springer eBooks
Contents:Preface
1 Manifolds
2 Lie Derivatives
3 Differential Forms
4 Integral Manifolds
5 Connections
6. Riemannian Manifolds
7 Lie Groups
8 Hamiltonian Classical Mechanics
References
Index
ISBN:9780817682712
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Cell aggregation Mathematics , Mathematical physics , Mechanics
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Call number:SPRINGER-2011-9783642225345:ONLINE Show nearby items on shelf
Title:Pseudo-periodic Maps and Degeneration of Riemann Surfaces [electronic resource]
Author(s): Yukio Matsumoto
Jos Mara Montesinos-Amilibia
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. Inthis book, the conjuga cy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsens incomplete classification is corrected. The second part applies the results of the first part to the topologyof degeneration of Riemann surfaces. It is show n that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set ofconjugacy classes of the pseudo-periodic maps of negative twists. The corres pondence is given by the topological monodromy
Note:Springer eBooks
Contents:Part I: Conjugacy Classification of Pseudo
periodic Mapping Classes
1 Pseudo
periodic Maps
2 Standard Form
3 Generalized Quotient
4 Uniqueness of Minimal Quotient
5 A Theorem in Elementary Number Theory
6 Conjugacy Invariants
Part II: The Topology of Degeneration of Riemann Surfaces
7 Topological Monodromy
8 Blowing Down Is a Topological Operation
9 Singular Open
Book
ISBN:9783642225345
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2030
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9783642220036:ONLINE Show nearby items on shelf
Title:Algebraic Topology of Finite Topological Spaces and Applications [electronic resource]
Author(s): Jonathan A Barmak
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makesfinite spaces a usefu l tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillens conjecture on the poset of p-subgroups ofa finite group and the Andrews-Curtis conjec ture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It isintended for topologists and combinatorialists, but it is also recom mended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology
Note:Springer eBooks
Contents:1 Preliminaries
2 Basic topological properties of finite spaces
3 Minimal finite models
4 Simple homotopy types and finite spaces
5 Strong homotopy types
6 Methods of reduction
7 h
regular complexes and quotients
8 Group actions and a conjecture of Quillen
9 Reduced lattices
10 Fixed points and the Lefschetz number
11 The Andrews
Curtis conjecture
ISBN:9783642220036
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2032
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Combinatorics , Discrete groups , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9783642195921:ONLINE Show nearby items on shelf
Title:Random Walks and Diffusions on Graphs and Databases [electronic resource] : An Introduction
Author(s): Philippe Blanchard
Dimitri Volchenkov
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precisequantitative descripti on of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on suchgraphs. The methods based on random walks and di ffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a numberof applications such diverse as electric resistance networks, estimat ion of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks
Note:Springer eBooks
Contents:Introduction to Permutations, Markov Chains, and Partitions
Worth Another Binary Relation: Graphs
Permutations Sieved Through Adjacency: Garph Autormorphisms
Exploring Undirected Graphs by Random Walks
Embedding of Graphs in Probabilistic Euclidean Space
Random Walks and Electric Resistance Networks
Random Walks and Diffusions on Directed Graphs and Interacting Networks
Structural Analysis of Networks and Databases
When Feedbacks Matter: Epidemics, Synchronization, and Self
Regulation in Complex Networks
Critical Phenomena on Large Graphs With Regular Subgraphs
Gl
ISBN:9783642195921
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Series in Synergetics, 0172-7389 : v10
Series:Physics and Astronomy (Springer-11651)
Keywords: Data structures (Computer science) , Cell aggregation Mathematics , Engineering
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Call number:SPRINGER-2011-9783642156373:ONLINE Show nearby items on shelf
Title:The Mathematics of Knots [electronic resource] Theory and Application
Author(s): Markus Banagl
Denis Vogel
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursuedareas of mathematical kn ot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented numerous illustrations support the text. The book will be of great interest toresearchers in topology, geometry, and mathemat ical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands
Note:Springer eBooks
Contents:Preface
1 Knots, Singular Embeddings, and Monodromy
2 Lower Bounds on Virtual Crossing Number and Minimal Surface Genus
3 A Survey of Twisted Alexander Polynomials
4 On Two Categorifications of the Arrow Polynomial for Virtual Knots
5 An Adelic Extension of the Jones Polynomial
6 Legendrian Grid Number One Knots and Augmentations of their Differential Algebras
7 Embeddings of Four
Valent Framed Graphs into 2
Surfaces
8 Geometric Topology and Field Theory on 3
Manifolds
9 From Goeritz Matrices to Quasi
Alternating Links
10 An Overview of Property 2R
11 DNA, Knot
ISBN:9783642156373
Series:e-books
Series:SpringerLink (Online service)
Series:Contributions in Mathematical and Computational Sciences : v1
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Physiology Mathematics , Global differential geometry , Topology , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9783642111020:ONLINE Show nearby items on shelf
Title:Differential Topology [electronic resource]
Author(s): Vinicio Villani
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:A. Banyaga: On the group of diffeomorphisms preserving an exact symplectic.- G.A. Fredricks: Some remarks on Cauchy-Riemann structures.- A. Haefliger: Differentiable Cohomology.- J.N. Mather: On the homology of Haefligersclassifying space.- P. Michor : Manifolds of differentiable maps.- V. Poenaru: Some remarks on low-dimensional topology and immersion theory.- F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S est nulle.- G. Wallet:Invariant de Godbillon-Vey et diffomorphismes commu tants
Note:Springer eBooks
Contents:A. Banyaga: On the group of diffeomorphisms preserving an exact symplectic
G.A. Fredricks: Some remarks on Cauchy
Riemann structures
A. Haefliger: Differentiable Cohomology
J.N. Mather: On the homology of Haefligers classifying space
P. Michor: Manifolds of differentiable maps
V. Poenaru: Some remarks on low
dimensional topology and immersion theory
F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S est nulle
G. Wallet: Invariant de Godbillon
Vey et diffomorphismes commutants
ISBN:9783642111020
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v73
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9783642109881:ONLINE Show nearby items on shelf
Title:Topologia differenziale [electronic resource]
Author(s): E Vesentini
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:J. Cerf: Invariants des paires despaces. Applications la topologie differentielle.- A. Hfliger: Varits feuilletes.- M.A. Kervaire: La mthode de Pontryagin pour la classification des applications sur une sphre.- S.Smale: Stable manifolds for differen tial equations and diffeomorphisms
Note:Springer eBooks
Contents:J. Cerf: Invariants des paires despaces. Applications la topologie differentielle
A. Hfliger: Varits feuilletes
M.A. Kervaire: La mthode de Pontryagin pour la classification des applications sur une sphre
S. Smale: Stable manifolds for differential equations and diffeomorphisms
ISBN:9783642109881
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v26
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9783540693925:ONLINE Show nearby items on shelf
Title:Geometry of Algebraic Curves [electronic resource] : Volume II with a contribution by Joseph Daniel Harris
Author(s): Enrico Arbarello
Maurizio Cornalba
Phillip A Griffiths
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of theGeometry of Algebraic Cur ves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending ofalgebro-geometric, complex analytic and topological/combi natorial methods. It treats important topics such as Teichmller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful andcomprehensive presentation of the material will be of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as volume 267 of the same series
Note:Springer eBooks
Contents:Preface
Guide to the Reader
Chapter IX. The Hilbert Scheme
Chapter X. Nodal curves
Chapter XI. Elementary deformation theory and some applications
Chapter XII. The moduli space of stable curves
Chapter XIII. Line bundles on moduli
Chapter XIV. The projectivity of the moduli space of stable curves
Chapter XV. The Teichmller point of view
Chapter XVI. Smooth Galois covers of moduli spaces
Chapter XVII. Cycles on the moduli spaces of stable curves
Chapter XVIII. Cellular decomposition of moduli spaces
Chapter XIX. First consequences of the cellular decomposit
ISBN:9783540693925
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v268
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Functions of complex variables , Differential equations, partial , Combinatorics , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9783034801041:ONLINE Show nearby items on shelf
Title:Symplectic Invariants and Hamiltonian Dynamics [electronic resource]
Author(s): Helmut Hofer
Eduard Zehnder
Date:2011
Publisher:Basel : Springer Basel
Size:1 online resource
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Note:The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature ofsymplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has establishedglobal periodic phenomena in Hamiltonian sy stems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants arethe main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplecticdiffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology. The exposition is self-contained andaddressed to researchers and students from the graduate level onwards. ------ All the chapters have a nice introduction with the historic development of the subject and with a perfect description of the state of the art. The mainideas are brightly exposed throughout the book. () This book, written by two experienced researchers, will certainly fill in a gap in the theory of symplectic topology. The authors have taken part in the development of such a theoryby themselves or by their collaboration with other outstanding people in the area. (Zentralblatt MATH) This book is a beautiful introduction to one outlook on the exci ting new developments of the last ten to fifteen years insymplectic geometry, or symplectic topology, as certain aspects of the subject are lately called. () The authors are obvious masters
Note:Springer eBooks
Contents:1 Introduction
2 Symplectic capacities
3 Existence of a capacity
4 Existence of closed characteristics
5 Compactly supported symplectic mappings in R2n
6 The Arnold conjecture, Floer homology and symplectic homology
Appendix
Index
Bibliography
ISBN:9783034801041
Series:e-books
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Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9781461411055:ONLINE Show nearby items on shelf
Title:An Invitation to Morse Theory [electronic resource]
Author(s): Liviu Nicolaescu
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part containsthe foundations of M orse theory. The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. Thisis the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations,and will be of interest to graduate students as well as research ers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Some features of thesecond edition include added applications, such as Morse theory and the curvature of knot s, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter onMorse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first editi on
Note:Springer eBooks
Contents:Preface
Notations and Conventions
1 Morse Functions
2 The Topology of Morse Functions
3 Applications
4 Morse
Smale Flows and Whitney Stratifications
5 Basics of Complex Morse Theory
6 Exercises and Solutions
References
Index
ISBN:9781461411055
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9781441979407:ONLINE Show nearby items on shelf
Title:Introduction to Topological Manifolds [electronic resource]
Author(s): John M Lee
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry,algebraic topology, and re lated fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. Although this second edition has the same basicstructure as the first edition, it has been extensivel y revised and clarified not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicialcomplexes in Chapter 5) expanded treatments of manifolds with boundary, local comp actness, group actions, and proper maps and a new section on paracompactness. This text is designed to be used for an introductory graduate course onthe geometry and topology of manifolds. It should be accessible to any student who has completed a solid u ndergraduate degree in mathematics. The authors book Introduction to Smooth Manifolds is meant to act as a sequel to thisbook
Note:Springer eBooks
Contents:Preface
1 Introduction
2 Topological Spaces
3 New Spaces from Old
4 Connectedness and Compactness
5 Cell Complexes
6 Compact Surfaces
7 Homotopy and the Fundamental Group
8 The Circle
9 Some Group Theory
10 The Seifert
Van Kampen Theorem
11 Covering Maps
12 Group Actions and Covering Maps
13 Homology
Appendix A: Review of Set Theory
Appendix B: Review of Metric Spaces
Appendix C: Review of Group Theory
References
Notation Index
Subject Index
ISBN:9781441979407
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v202
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9781441974426:ONLINE Show nearby items on shelf
Title:A Cp-Theory Problem Book [electronic resource] Topological and Function Spaces
Author(s): Vladimir V Tkachuk
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:The theory of function spaces endowed with the topology of pointwise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology.Cp-theory has an import ant role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-containedintroduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modernresearch. Key features include: - A unique problem-based introduction to t he theory of function spaces. - Detailed solutions to each of the presented problems and exercises. - A comprehensive bibliography reflecting thestate-of-the-art in modern Cp-theory. - Numerous open problems and directions for further research. This volum e can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialistsstudying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research
Note:Springer eBooks
Contents:Preface
Introduction
1.1. Basic notions of topology and function spaces Bibliographic notes
1.2. Solutions of problems 1.0011.500
1.3. Bonus results: some hidden statements
1.4. Open problems
1.5. Bibliography
1.6. List of special symbols
1.7. Index
ISBN:9781441974426
Series:e-books
Series:SpringerLink (Online service)
Series:Problem Books in Mathematics, 0941-3502
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9781441974006:ONLINE Show nearby items on shelf
Title:An Introduction to Manifolds [electronic resource]
Author(s): Loring W Tu
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classicalmechanics, general relativity , and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By theend of the book the reader should be able to comput e, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessaryfor further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for aone-semester graduate or advanced undergraduate course, as well as by students engaged in sel f-study. The requisite point-set topology is included in an appendix of twenty-five pages other appendices review facts from real analysisand linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal un dergraduate prerequisites, An Introduction to Manifolds is also an excellent foundation for the author'spublication with Raoul Bott, Differential Forms in Algebraic Topology.
Note:Springer eBooks
Contents:Preface to the Second Edition
Preface to the First Edition
Chapter 1. Euclidean Spaces
Chapter 2. Manifolds
Chapter 3. The Tangent Space
Chapter 4. Lie Groups and Lie Algebras
Chapter 5. Differential Forms
Chapter 6. Integration
Chapter 7. De Rham Theory
Appendices
A. Point
Set Topology
B. The Inverse Function Theorem on R(N) and Related Results
C. Existence of a Partition of Unity in General
D. Linear Algebra
E. Quaternions and the Symplectic Group
Solutions to Selected Exercises
Hints and Solutions to Selected End
of
Section Problems
List of Sym
ISBN:9781441974006
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9781441972361:ONLINE Show nearby items on shelf
Title:Simplicial Structures in Topology [electronic resource]
Author(s): Davide L Ferrario
Renzo A Piccinini
Date:2011
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The lastchapter of the book is devoted to homotopy groups, which are used in a short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henri Poincar (singularhomology is not discussed). Illustrative examples th roughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book.Researchers and professionals interested in topology and applications of mathemat ics will also find this book useful
Note:Springer eBooks
Contents:Preface
Fundamental Concepts
Simplicial Complexes
Homology of Polyhedra
Cohonology
Triangulable Manifolds
Homotopy Groups
Bibliography
Index
ISBN:9781441972361
Series:e-books
Series:SpringerLink (Online service)
Series:CMS Books in Mathematics, Ouvrages de mathmatiques de la SMC, 1613-5237
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9783642125898:ONLINE Show nearby items on shelf
Title:Intersection Spaces, Spatial Homology Truncation, and String Theory [electronic resource]
Author(s): Markus Banagl
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Intersection cohomology assigns groups which satisfy a generalized form of Poincar duality over the rationals to a stratified singular space. The present monograph introduces a method that assigns to certain classes ofstratified spaces cell complexes , called intersection spaces, whose ordinary rational homology satisfies generalized Poincar duality. The cornerstone of the method is a process of spatial homology truncation, whose functorialityproperties are analyzed in detail. The material on truncati on is autonomous and may be of independent interest to homotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possessesalgebraic features such as perversity-internal cup-products and cohomology operation s that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerningmassless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed
Note:Springer eBooks
ISBN:9783642125898
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1997
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topology , Algebraic topology , Cell aggregation Mathematics , Mathematical physics
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Call number:SPRINGER-2010-9781848829398:ONLINE Show nearby items on shelf
Title:Topics in Physical Mathematics [electronic resource]
Author(s): Kishore Marathe
Date:2010
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
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Note:The roots of physical mathematics can be traced back to the very beginning of man's attempts to understand nature. Indeed, mathematics and physics were part of what was called natural philosophy. Rapid growth of thephysical sciences, aided by technol ogical progress and increasing abstraction in mathematical research, caused a separation of the sciences and mathematics in the 20th century. Physicists methods were often rejected bymathematicians as imprecise, and mathematicians approach to physical the ories was not understood by the physicists. However, two fundamental physical theories, relativity and quantum theory, influenced new developments in geometry,functional analysis and group theory. The relation of Yang-Mills theory to the theory of connect ions in a fiber bundle discovered in the early 1980s has paid rich dividends to the geometric topology of low dimensional manifolds. Aimedat a wide audience, this self-contained book includes a detailed background from both mathematics and theoretical phy sics to enable a deeper understanding of the role that physical theories play in mathematics. Whilst the fieldcontinues to expand rapidly, it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader to their next point of exploration in this vast and exciting landscape
Note:Springer eBooks
Contents:Algebra
Topology
Manifolds
Bundles and Connections
Characteristic Classes
Theory of Fields, I: Classical
Theory of Fields, II: Quantum and Topological
YangMillsHiggs Fields
4
Manifold Invariants
3
Manifold Invariants
Knot and Link Invariants
ISBN:9781848829398
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Field theory (Physics) , Global analysis , Global differential geometry , Topology , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9780817649593:ONLINE Show nearby items on shelf
Title:Riemannian Geometry of Contact and Symplectic Manifolds [electronic resource]
Author(s): David E Blair
Date:2010
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
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Note:This second edition, divided into fourteen chapters, presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides manyillustrative examples for the reader. Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. New principal topics includea complex geodesic flow and the accompanying g eometry of the projectivized holomorphic tangent bundle and a complex version of the special directions discussed in Chapter 11 for the real case. Both of these topics make use of tienneGhys's attractive notion of a holomorphic Anosov flow. Researchers, m athematicians, and graduate students in contact and symplectic manifold theory and in Riemannian geometry will benefit from this work. A basic course in Riemanniangeometry is a prerequisite. Reviews from the First Edition: The book . . . can be used eithe r as an introduction to the subject or as a reference for students and researchers . . . [it] gives a clear and complete account of the mainideas . . . and studies a vast amount of related subjects such as integral sub-manifolds, symplectic structure of t angent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics.Mathematical Reviews this is a pleasant and useful book and all geometers will profit [from] reading it. They can use it for advanced courses, for thesis topics as well as for references. Beginners will find in it an attractive[table of] contents and useful ideas for pursuing their studies. Memoriile Sectiilor Stiintifice
Note:Springer eBooks
Contents:Preface
1. Symplectic Manifolds
2. Principal bundles
3. Contact Manifolds
4. Associated Metrics
5. Integral Submanifolds and Contact Transformations
6. Sasakian and Cosymplectic Manifolds
7. Curvature of Contact Metric Manifolds
8. Submanifolds of Khler and Sasakian Manifolds
9. Tangent Bundles and Tangent Sphere Bundles
10. Curvature Functionals and Spaces of Associated Metrics
11. Negative Xi
sectional Curvature
12. Complex Contact Manifolds
13. Additional Topics in Complex Geometry
14. 3
Sasakian Manifolds
Bibliography
Subjec
ISBN:9780817649593
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v203
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9780817649388:ONLINE Show nearby items on shelf
Title:Representation Theory and Complex Geometry [electronic resource]
Author(s): Neil Chriss
Victor Ginzburg
Date:2010
Edition:1st
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:This classic monograph provides an overview of modern advances in representation theory from a geometric standpoint. A geometrically-oriented treatment of the subject is very timely and has long been desired, especially since thediscovery of D-module s in the early 1980s and the quiver approach to quantum groups in the early 1990s. The techniques developed are quite general and can be successfully applied to other areas such as quantum groups, affine Liegroups, and quantum field theory. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. The book is largelyself-contained. . . . There is a nice introduction to symplectic geometry and a cha rming exposition of equivariant K-theory. Both are enlivened by examples related to groups. . . . An attractive feature is the attempt to convey someinformal 'wisdom' rather than only the precise definitions. As a number of results is due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory. . . it hasalready proved successful in introducing a new generation to the subject. --- Bulletin of the American Mathematical Society Th e authors have tried to help readers by adopting an informal and easily accessible style. . . . The book willprovide a guide to those who wish to penetrate into subject-matter which, so far, was only accessible in difficult papers. . . . The book is quite suitable as a basis for an advanced course or a seminar, devoted to the material of oneof the chapters of the book. --- Mededelingen van het Wiskundig Genootschap Represents an important and very interesting addition to the literature. --- Mathematical R eviews
Note:Springer eBooks
Contents:Preface
Chapter 0. Introduction
Chapter 1. Symplectic Geometry
Chapter 2. Mosaic
Chapter 3. Complex Semisimple Groups
Chapter 4. Springer Theory
Chapter 5. Equivariant K
Theory
Chapter 6. Flag Varieties, K
Theory, and Harmonic Polynomials
Chapter 7. Hecke Algebras and K
Theory
Chapter 8. Representations of Convolution Algebras
Bibliography
ISBN:9780817649388
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9780817649135:ONLINE Show nearby items on shelf
Title:Hyperbolic Manifolds and Discrete Groups [electronic resource]
Author(s): Michael Kapovich
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is onThurstons hyperbolization t heorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to thehyperbolization theorem as well as rich discussions on related t opics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich setof examples, numerous exercises, and an extensive bibliography and index, Hyperbolic M anifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairlyself-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem,this is an important book which had to be written some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolizationtheorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. -- -Zentralbatt MATH This book can act as source material for a postgraduatecourse and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide
Note:Springer eBooks
Contents:Preface
Three
dimensional Topology
Thurston Norm
Geometry of the Hyperbolic Space
Kleinian Groups
Teichmller Theory of Riemann Surfaces
Introduction to the Orbifold Theory
Complex Projective Structures
Sociology of Kleinian Groups
Ultralimits of Metric Spaces
Introduction to Group Actions on Trees
Laminations, Foliations and Trees
Rips Theory
Brooks' Theorem and Circle Packings
Pleated Surfaces and Ends of Hyperbolic Manifolds
Outline of the Proof of the Hyperbolization Theorem
Reduction to The Bounded Image Theorem
The Bounded Image Theorem
ISBN:9780817649135
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Geometry , Topology , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9780387789637:ONLINE Show nearby items on shelf
Title:Topics in Hyperplane Arrangements, Polytopes and Box-Splines [electronic resource]
Author(s): Corrado De Concini
Claudio Procesi
Date:2010
Edition:1
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Several mathematical areas that have been developed independently over the last 30 years are brought together revolving around the computation of the number of integral points in suitable families of polytopes. The problem isformulated here in terms of partition functions and multivariate splines. In its simplest form, the problem is to compute the number of ways a given nonnegative integer can be expressed as the sum of h fixed positive integers. Thisgoes back to ancient times and was investigated b y Euler, Sylvester among others in more recent times also in the higher dimensional case of vectors. The book treats several topics in a non-systematic way to show and compare a varietyof approaches to the subject. No book on the material is available in the existing literature. Key topics and features include: - Numerical analysis treatments relating this problem to the theory of box splines - Study of regularfunctions on hyperplane and toric arrangements via D-modules - Residue formulae for partition fu nctions and multivariate splines - Wonderful completion of the complement of hyperplane arrangements - Theory and properties of the Tuttepolynomial of a matroid and of zonotopes Graduate students as well as researchers in algebra, combinatorics and numeri cal analysis, will benefit from Topics in Hyperplane Arrangements, Polytopes, and Box Splines
Note:Springer eBooks
Contents:Introduction
I Preliminaries. 1 Polytopes. 2 Hyperplane Arrangements. 3 Fourier and Laplace Transforms. 4 Modules Over the Weyl Algebra. 5 Differential and Difference Equations. 6 Approximation Theory I
II The Differentiable Case. 7 Splines. 8 Rx as a D
Module. 9 The function Tx. 10 Cohomology. 11 Differential Equations
III The Discrete Case. 12 Partition Functions. 13 Toric Arrangements. 14 Cohomology of Toric Arrangements. 15 Difference Equations. 16 Applications. 17 Approximation Theory II
IV The Wonderful Model. 18 Minimal Models
ISBN:9780387789637
Series:e-books
Series:SpringerLink (Online service)
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Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Topological Groups , Differential Equations , Cell aggregation Mathematics
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Call number:SPRINGER-2009-9783642052057:ONLINE Show nearby items on shelf
Title:Vector fields on Singular Varieties [electronic resource]
Author(s): Jean-Paul Brasselet
Jos Seade
Tatsuo Suwa
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincar-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It isnatural to ask what is the good notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting withthe pioneering work of M.-H. Schwartz and R. MacPhers on. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of themonograph
Note:Springer eBooks
ISBN:9783642052057
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1987
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Differentiable dynamical systems , Global analysis , Differential equations, partial , Cell aggregation Mathematics
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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
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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-2009-9783540893066:ONLINE Show nearby items on shelf
Title:Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds [electronic resource]
Author(s): Rainer Weissauer
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:The geometry of modular curves and the structure of their cohomology groups have been a rich source for various number-theoretical applications over the last decades. Similar applications may be expected from the arithmetic ofhigher dimensional modul ar varieties. For Siegel modular threefolds some basic results on their cohomology groups are derived in this book from considering topological trace formulas
Note:Springer eBooks
Contents:1 An Application of the Hard Lefschetz Theorem
2 CAP
Localization
3 The Ramanujan Conjecture for Genus two Siegel modular Forms
4 Character Identities and Galois Representations related to the group GSp(4)
5 Endoscopy for GSp(4)
6 A special Case of the Fundamental Lemma I
7 A special Case of the Fundamental Lemma II
8 The Langlands
Shelstad transfer factor
9 Fundamental lemma (twisted case)
10 Reduction to unit elements
11 Appendix on Galois cohomology
12 Appendix on double cosets
ISBN:9783540893066
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1968
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Number theory , Cell aggregation Mathematics
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Call number:SPRINGER-2009-9783540857990:ONLINE Show nearby items on shelf
Title:Optimal Urban Networks via Mass Transportation [electronic resource]
Author(s): Giuseppe Buttazzo
Aldo Pratelli
Eugene Stepanov
Sergio Solimini
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) areknown, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, who goes where optimization are considered. These models can also beadapted for the optimization of other types o f networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology ofthe network to be constructed is known a priori
Note:Springer eBooks
Contents:Problem setting
Optimal connected networks
Relaxed problem and existence of solutions
Topological properties of optimal sets
Optimal sets and geodesics in the two
dimensional case
ISBN:9783540857990
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1961
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Mathematical optimization , Operations research , Cell aggregation Mathematics
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Call number:SPRINGER-2009-9781848009400:ONLINE Show nearby items on shelf
Title:A Course in Formal Languages, Automata and Groups [electronic resource]
Author(s): Ian M Chiswell
Date:2009
Publisher:London : Springer London
Size:1 online resource
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Note:Based on the authors lecture notes for an MSc course, this text combines formal language and automata theory and group theory, a thriving research area that has developed extensively over the last twenty-five years. The aim ofthe first three chapters is to give a rigorous proof that various notions of recursively enumerable language are equivalent. Chapter One begins with languages defined by Chomsky grammars and the idea of machine recognition, contains adiscussion of Turing Machines, and includes w ork on finite state automata and the languages they recognise. The following chapters then focus on topics such as recursive functions and predicates recursively enumerable sets of naturalnumbers and the group-theoretic connections of language theory, inc luding a brief introduction to automatic groups. Highlights include: A comprehensive study of context-free languages and pushdown automata in Chapter Four, inparticular a clear and complete account of the connection between LR(k) languages and determinist ic context-free languages. A self-contained discussion of the significant Muller-Schupp result on context-free groups. Enriched withprecise definitions, clear and succinct proofs and worked examples, the book is aimed primarily at postgraduate students in mathematics but will also be of great interest to researchers in mathematics and computer science who want tolearn more about the interplay between group theory and formal languages. A solutions manual is available to instructors via www.springer.com
Note:Springer eBooks
Contents:Preface
Contents
1. Grammars and Machine Recognition
2. Recursive Functions
3. Recursively Enumerable Sets and Languages
4. Context
free language
5. Connections with Group Theory
A. Results and Proofs Omitted in the Text
B. The Halting Problem and Universal Turing Machines
C. Cantor's Diagonal Argument
D. Solutions to Selected Exercises
References
Index
ISBN:9781848009400
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Algebra , Group theory , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2009-9781848009134:ONLINE Show nearby items on shelf
Title:A Topological Aperitif [electronic resource]
Author(s): David Jordan
Stephen Huggett
Date:2009
Publisher:London : Springer London
Size:1 online resource
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Note:This is a book of elementary geometric topology, in which geometry, frequently illustrated, guides calculation. The book starts with a wealth of examples, often subtle, of how to be mathematically certain whether two objects arethe same from the poin t of view of topology. After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. More refined tools are developed in a chapter on winding number,and an appendix gives a glimpse of knot the ory. Moreover, in this revised edition, a new section gives a geometrical description of part of the Classification Theorem for surfaces. Several striking new pictures show how given a spherewith any number of ordinary handles and at least one Klein handl e, all the ordinary handles can be converted into Klein handles. Numerous examples and exercises make this a useful textbook for a first undergraduate course in topology,providing a firm geometrical foundation for further study. For much of the book the p rerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the Aperitif. distinguished by clear and wonderfulexposition and laden with informal motivation, visual aids, cool (and beautifully rendered) picturesThis is a te rrific book and I recommend it very highly. MAA Online Aperitif conjures up exactly the right impression of thisbook. The high ratio of illustrations to text makes it a quick read and its engaging style and subject matter whet the tastebuds for a range of possible main courses. Mathematical Gazette A Topological Aperitif provides amarvellous introduction to the subject, with many different tastes of ideas. Professor Sir Roger Penrose OM FRS, Mathematical Institute, Oxford, UK
Note:Springer eBooks
Contents:Foreword (written by Roger Penrose)
Homeomorphic Sets
Topological Properties
Equivalent Subsets
Surfaces and Spaces
Polyhedra
Winding Number
Appendix A: Continuity
Appendix B: Knots
Appendix C: History
Appendix D: Solutions
Bibliography
Index
ISBN:9781848009134
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Cell aggregation Mathematics
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Call number:SPRINGER-2008-9783764388829:ONLINE Show nearby items on shelf
Title:Dimension and Recurrence in Hyperbolic Dynamics [electronic resource]
Author(s): Luis Barreira
Date:2008
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the richinterplay of four mai n areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. More than half ofthe material appears here for the first time in book form, describing many recent developments in the area such as topics on irregular sets, variational principles, applications to number theory, measures of maximal dimension,multifractal nonrigidity, and quantitative recurrence. All the results ar e included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained and directed to researchers as well asgraduate students that wish to have a global view of the theory together with a working knowled ge of its main techniques. It will also be useful as as basis for graduate courses in dimension theory of dynamical systems, multifractalanalysis, and pointwise dimension and recurrence in hyperbolic dynamics
Note:Springer eBooks
Contents:Preface
Introduction
Basic Notions
I. Dimension Theory
Dimension Theory and Thermodynamic Formalism
Repellers and Hyperbolic Sets
Measures of Maximal Dimension
II. Multifractal Analysis: Core Theory
Multifractal Analysis of Equilibrium Measures
General Concept of Multifractal Analysis
Dimension of Irregular Sets
Variational Principles in Multifractal Analysis
III. Multifractal Analysis: Further Developments
Multidimensional Spectra and Number Theory
Multifractal Rigidity
Hyperbolic Sets: Past and Future
IV. Hyperbolicity and Recurrence
Pointwi
ISBN:9783764388829
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v272
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differentiable dynamical systems , Cell aggregation Mathematics
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Call number:SPRINGER-2008-9783540782797:ONLINE Show nearby items on shelf
Title:Symplectic 4-Manifolds and Algebraic Surfaces [electronic resource] : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy September 210, 2003
Author(s): Denis Auroux
Marco Manetti
Paul Seidel
Bernd Siebert
Ivan Smith
Fabrizio Catanese
Gang Tian
Date:2008
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Springer eBooks
ISBN:9783540782797
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1938
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory , Differential equations, partial , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2008-9783540776956:ONLINE Show nearby items on shelf
Title:Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms [electronic resource]
Author(s): Rufus Bowen
Jean-Ren Chazottes
Date:2008
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: Rufus Bowen has left us a masterpiece ofmathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have beenproved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems.
Note:Springer eBooks
Contents:Preface to the 2nd edition by David Ruelle
0. Introduction
1.Gibbs measures
A.Gibbs measures
B.Ruelle's Perron
Frobenius Theorem
C.Construction of Gibbs measures
D.Variational principle
E.Further properties
References
2.General thermodynamic formalism
A.Entropy
B.Pressure
C.Variational principle
D.Equilibrium states
References
3.Axiom A diffeomorphisms
A.Definition
B. Spectral decomposition
C.Markov partitions
D.Symbolic dynamics
References
4.Ergodic theory of Axiom A diffeomorphisms
A.Equilibrium states for basic sets
B.The
ISBN:9783540776956
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v470
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Distribution (Probability theory) , Cell aggregation Mathematics
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Call number:SPRINGER-2008-9780387746562:ONLINE Show nearby items on shelf
Title:Lie Sphere Geometry [electronic resource] : With Applications to Submanifolds
Author(s): Thomas E Cecil
Date:2008
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamentalnotions of oriented co ntact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean submanifold theory is established via the Legendre map, which provides a powerful framework for the study ofsubmanifolds, especially those characterized by restri ctions on their curvature spheres. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclidesof Dupin. Completely new material on isoparametric hypersurfaces in sphere s and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicatesdirections for further research and wider application of the methods of Lie sphere geometry. Further key features of Lie Sphere Geometry 2/e: - Provides the reader with all the necessary background to reach the frontiers of research inthis area - Fills a gap in the literature no other thorough examination of Lie sphere geometry and its applications to subma nifold theory - Complete treatment of the cyclides of Dupin, including 11 computer-generated illustrations -Rigorous exposition driven by motivation and ample examples. Reviews from the first edition: The book under review sets out the basic material on L ie sphere geometry in modern notation, thus making it accessible to students andresearchers in differential geometry.....This is a carefully written, thorough, and very readable book. There is an excellent bibliography that not only provides pointers to p roofs that have been omitted, but gives appropriatereferences for the results presented. It should be useful to all geometers working in the theory of submanifolds. - P.J. Ryan, MathSciNet The book
Note:Springer eBooks
Contents:Preface
Introduction
Lie Sphere Geometry
Lie Sphere Transformations
Legendre Submanifolds
Dupin Submanifolds
Bibliography
Index
ISBN:9780387746562
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2008-9780387685489:ONLINE Show nearby items on shelf
Title:Braid Groups [electronic resource]
Author(s): Christian Kassel
Vladimir Turaev
Date:2008
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory ofbraids stems from their at tractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authorsthoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braidgroups, the Alexander--Conway and Jones link polynomials, connections wit h the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups. This book will serve graduatestudents, mathematicians, and theoretical physicists interested in low-dimensional topology and its co nnections with representation theory
Note:Springer eBooks
Contents:Braids and Braid Groups
Braids, Knots, and Links
Homological Representations of the Braid Groups
Symmetric Groups and IwahoriHecke Algebras
Representations of the IwahoriHecke Algebras
Garside Monoids and Braid Monoids
An Order on the Braid Groups
Presentations of SL(Z) and PSL(Z)
Fibrations and Homotopy Sequences
The BirmanMurakamiWenzl Algebras
Left Self
Distributive Sets
ISBN:9780387685489
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v247
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Algebra , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2008-9780387481012:ONLINE Show nearby items on shelf
Title:An Introduction to Manifolds [electronic resource]
Author(s): Loring W Tu
Date:2008
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classicalmechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By theend of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessaryfor further study of geometry and topology. The requisite point-set topolo gy is included in an appendix of twenty pages other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many ofthe exercises and problems. This work may be used as the text for a one-semester graduate or adva nced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, AnIntroduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology
Note:Springer eBooks
Contents:Euclidean Spaces
Smooth Functions on a Euclidean Space
Tangent Vectors in Rn as Derivations
Alternating k
Linear Functions
Differential Forms on Rn
Manifolds
Manifolds
Smooth Maps on a Manifold
Quotients
Lie Groups and Lie Algebras
The Tangent Space
Submanifolds
Categories and Functors
The Rank of a Smooth Map
The Tangent Bundle
Bump Functions and Partitions of Unity
Vector Fields
Lie Groups and Lie Algebras
Lie Groups
Lie Algebras
Differential Forms
Differential 1
Forms
Differential k
Forms
The Exterior Derivative
Integra
ISBN:9780387481012
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2007-9783764384784:ONLINE Show nearby items on shelf
Title:Positivity [electronic resource]
Author(s): Karim Boulabiar
Gerard Buskes
Abdelmajid Triki
Date:2007
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
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Note:This book contains nine well-organized survey articles by leading researchers in positivity, with a strong emphasis on functional analysis. It provides insight into the structure of classical spaces of continuous functions,f-algebras, and integral op erators, but also contains contributions to modern topics like vector measures, operator spaces, ordered tensor products, non-commutative Banach function spaces, and frames. Contributors: B. Banerjee, D.P.Blecher, K. Boulabiar, Q. Bu, G. Buskes, G.P. Curb era, M. Henriksen, A.G. Kusraev, J. Martnez, B. de Pagter, W.J. Ricker, A.R. Schep, A. Triki, A.W. Wickstead
Note:Springer eBooks
ISBN:9783764384784
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Mathematics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Global analysis (Mathematics) , Functional analysis , Operator theory , Cell aggregation Mathematics , Economics
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Call number:SPRINGER-2007-9783764381332:ONLINE Show nearby items on shelf
Title:An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem [electronic resource]
Author(s): Luca Capogna
Scott D Pauls
Donatella Danielli
Jeremy T Tyson
Date:2007
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysison metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessentialexample of a sub Riemannian structure is t he Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space,subelliptic PDE, jet spaces, and quantum mechanics. This book provid es an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state ofknowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian i soperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides anopportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginningresearchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area
Note:Springer eBooks
Contents:Preface
1. The Isoperimetric Problem
2. The Heisenberg Group
3. Horizontal Geometry of Submanifolds
4. Geometric Measure Theory
5. The Isoperimetric Inequality
6. The Isoperimetric Profile of the Heisenberg Group
7. Sharp Constants for Other Geometric Inequalities
Bibliography
Index
ISBN:9783764381332
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v259
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Differential equations, partial , Systems theory , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2007-9783764377762:ONLINE Show nearby items on shelf
Title:Real and Complex Singularities [electronic resource] : So Carlos Workshop 2004
Author(s): Jean-Paul Brasselet
Maria Aparecida Soares Ruas
Date:2007
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:The So Carlos Workshop on Real and Complex Singularities is the longest running workshop in singularities. It is held every two years and is a key international event for people working in the field. This volume contains paperspresented at the eighth workshop, held at the IML, Marseille, July 1923, 2004. The workshop offers the opportunity to establish the state of the art and to present new trends, new ideas and new results in all of the branches ofsingularities. This is reflected by the contributio ns in this book. The main topics discussed are equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes,classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, and applications of singularity theory to geometry of surfaces in low dimensionaleuclidean spaces, to differential equations and to bifurcation theory
Note:Springer eBooks
Contents:Celestial Integration, Stringy Invariants, and Chern
Schwartz
MacPherson Classes
Valuations Compatible with a Projection
Quelques Rsultats sur Certaines Fonctions Lieu Singulier de Dimension 1
Classification of Rational Unicuspidal Projective Curves whose Singularities Have one Puiseux Pair
Bounding from below the Degree of an Algebraic One
dimensional Foliation Having a Prescribed Algebraic Solution
Trajectory Singularities for a Class of Parallel Motions
Vertices and Inflexions of Plane Sections of Surfaces in ?3
Local Topology of Reducible Divisors
The Geometry
ISBN:9783764377762
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Mathematics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Geometry , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2007-9783540718079:ONLINE Show nearby items on shelf
Title:Punctured Torus Groups and 2-Bridge Knot Groups (I) [electronic resource]
Author(s): Hirotaka Akiyoshi
Makoto Sakuma
Masaaki Wada
Yasushi Yamashita
Date:2007
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory. Although Jorgensen's original work wasnot published in comple te form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology. In this monograph, we give an elementary andself-contained description of Jorgensen's theory wit h a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsiangroup evolves into complicated Kleinian groups
Note:Springer eBooks
Contents:Jorgensen's picture of quasifuchsian punctured torus groups
Fricke surfaces and PSL(2,C)
representations
Labeled representations and associated complexes
Chain rule and side parameter
Special examples
Reformulation of the main theorem and outline of the proof
Openness
Closedness
Algebraic roots and geometric roots
Appendix
References
Index
ISBN:9783540718079
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1909
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Functions of complex variables , Cell aggregation Mathematics
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Call number:SPRINGER-2007-9780817645830:ONLINE Show nearby items on shelf
Title:Metric Structures for Riemannian and Non-Riemannian Spaces [electronic resource]
Author(s): Mikhail Gromov
Date:2007
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
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Note:Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups andprobability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metrictheory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the GromovHausdorff distance between Riemannian manifolds. This distanceorganizes Riemannian manifolds of all possible topological types into a singl e connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya,Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced ne w invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degreesof maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosi s, stimulated by the LevyMilman concentration phenomenon, encompassing the law of large numbers for metricspaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which tur ned into the famous Green Book by Lafontaine and Pansu (1979). The present Englishtranslation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendicesby Gromov on Levy's inequality, by Pansu o n quasiconvex domains, by Katz on systoles ofRiemannian manifolds, and by Semmes overviewing analysis on metric spaces with measuresas well as an extensive bibliography and index round o
Note:Springer eBooks
Contents:Preface to the French Edition
Preface to the English Edition
Introduction: Metrics Everywhere
Length Structures: Path Metric Spaces
Degree and Dilatation
Metric Structures on Families of Metric Spaces
Convergence and Concentration of Metrics and Measures
Loewner Rediscovered
Manifolds with Bounded Ricci Curvature
Isoperimetric Inequalities and Amenability
Morse Theory and Minimal Models
Pinching and Collapse
Appendix A: Quasiconvex Domains in Rn
Appendix B: Metric Spaces and Mappings Seen at Many Scales
Appendix C: Paul Levy's Isoperimetric Inequalit
ISBN:9780817645830
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Global differential geometry , Distribution (Probability theory) , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2007-9780387495101:ONLINE Show nearby items on shelf
Title:An Invitation to Morse Theory [electronic resource]
Author(s): Liviu Nicolaescu
Date:2007
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This self-contained treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part containsthe foundations of M orse theory (over the reals). The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetztheory. This is the first textbook to inc lude topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations,and will be of interest to graduate students as well as research ers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Liviu Nicolaescu isAssociate Professor of Mathematics at University of Notre Dame
Note:Springer eBooks
Contents:Preface
Notations and conventions
Morse functions
The topology of Morse functions
Applications
Basics of complex Morse theory
Exercises and solutions
References
Index
ISBN:9780387495101
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Cell aggregation Mathematics
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Call number:SPRINGER-2006-9783764373887:ONLINE Show nearby items on shelf
Title:String Topology and Cyclic Homology [electronic resource]
Author(s): Ralph L Cohen
Kathryn Hess
Alexander A Voronov
Date:2006
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The subject of this book is string topology, Hochschild and cyclic homology. The first part consists of an excellent exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives acomplete and clear construc tion of an algebraic model for computing topological cyclic homology. The book provides many references for the reader wishing to learn more about the subject, to which it gives a perfect introduction. It istherefore suitable for both graduate students an d established researchers. It is certainly the best source of much information that was until now available only to specialists and covers material from the elementary bases to the mostrecent developments
Note:Springer eBooks
Contents:Foreword
Notes on String Topology (R.L. Cohen and A.A. Voronov)
Introduction
Intersection Theory in Loop Spaces
The Cacti Operad
String Topology as Field Theory
A Morse Theoretic Viewpoint
Brane Topology
Bibliography
An Algebraic Model for Mod 2 Topological Cyclic Homology (K. Hess)
Preface
Preliminaries
Free Loop Spaces
Homotopy Orbit Spaces
A Model for Mod 2 Toplological Cyclic Homology
Bibliography
ISBN:9783764373887
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 , Algebraic topology , Cell aggregation Mathematics , Mathematical physics
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Call number:SPRINGER-2006-9783540376811:ONLINE Show nearby items on shelf
Title:Mathematical Implications of Einstein-Weyl Causality [electronic resource]
Author(s): Hans-Jrgen Borchers
Rathindra Nath Sen
Date:2006
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 present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it?The authors propose a n axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one thatis locally a differentiable manifold. The m athematical level required of the reader is that of the graduate student in mathematical physics
Note:Springer eBooks
Contents:Introduction
Geometrical Structures on Space
Time
Light Rays and Light Cones
Local Structure and Topology
Homogeneity Properties
Order and Uniformizability
Spaces With Complete Light Rays
Consequences of Order Completeness
The Cushion Problem
Related Works
Concluding Remarks
ISBN:9783540376811
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v709
Series:Physics and Astronomy (Springer-11651)
Keywords: Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2006-9783540363606:ONLINE Show nearby items on shelf
Title:Singular Coverings of Toposes [electronic resource]
Author(s): Marta Bunge
Jonathon Funk
Date:2006
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The self-contained theory of certain singular coverings of toposes called complete spreads, that is presented in this volume, is a field of interest to topologists working in knot theory, as well as to various categorists. Itextends the complete spre ads in topology due to R. H. Fox (1957) but, unlike the classical theory, it emphasizes an unexpected connection with topos distributions in the sense of F. W. Lawvere (1983). The constructions, though oftenmotivated by classical theories, are sometimes q uite different from them. Special classes of distributions and of complete spreads, inspired respectively by functional analysis and topology, are studied. Among the former are theprobability distributions the branched coverings are singled out amongst th e latter. This volume may also be used as a textbook for an advanced one-year graduate course introducing topos theory with an emphasis on geometricapplications. Throughout the authors emphasize open problems. Several routine proofs are left as exercises, but also as exercises the reader will find open questions for possible future work in a variety of topics in mathematicsthat can profit from a categorical approach
Note:Springer eBooks
Contents:Introduction
Part I: Distributions and Complete Spreads
1.Lawvere Districutions on Toposes
2.Complete Spread Maps of Toposes
3.The Spread and Completeness Conditions
Part II: An Axiomatic Theory of Complete Spreads
4.Completion KZ
Monads
5.Complete Spreads as Discrete M
fibrations
6. Closed and Linear KZ
Monads
Part III: Aspects of Distributions and Complete Spreads
7.Lattice
Theoretic Aspects
8.Localic and Algebraic Aspects
9.Topological Aspects
Bibliography
Index
ISBN:9783540363606
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1890
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Cell aggregation Mathematics
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Call number:SPRINGER-2006-9783540334842:ONLINE Show nearby items on shelf
Title:Analytical and Numerical Approaches to Mathematical Relativity [electronic resource]
Author(s): Jrg Frauendiener
Domenico J.W Giulini
Volker Perlick
Date:2006
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Today, general relativity rates among the most accurately tested fundamental theories in all of physics. However, deficiencies in our mathematical and conceptual understanding still exist, and these partly hamper further progress.For this reason alon e, but no less important from the point of view that a theory-based prediction should be regarded as no better than one's own structural understanding of the underlying theory, one should undertake seriousinvestigations into the corresponding mathematical issues. This book contains a representative collection of surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There arefour contributions for each of the following mathematical areas: differen tial geometry and differential topology, analytical methods and differential equations, and numerical methods. This book addresses graduate students andspecialist researchers alike
Note:Springer eBooks
Contents:A Personal Perspective on Global Lorentzian Geometry
The Space of Null Geodesics (and a New Causal Boundary)
Some Variational Problems in Semi
Riemannian Geometry
On the Geometry of pp
Wave type Spacetimes
Concepts for Hyperbolicity and Relativistic Continuum Mechanics
Elliptic Systems
Mathematical Properties of Cosmological Models with Accelerated Expansion
The Poincar Structure and the Centre
of
Mass of Asymptotically Flat Spacetimes
Computer Simulation
a Tool For Mathematical Relativity
and Vice Versa
On Boundary Conditions for the Einstein Equations
Rece
ISBN:9783540334842
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v692
Series:Physics and Astronomy (Springer-11651)
Keywords: Global differential geometry , Cell aggregation Mathematics , Mathematical physics , Relativity (Physics)
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Call number:SPRINGER-2006-9783540279501:ONLINE Show nearby items on shelf
Title:Categories and Sheaves [electronic resource]
Author(s): Masaki Kashiwara
Pierre Schapira
Date:2006
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays. This book covers categories, homological algebraand sheaves in a system atic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond. The authors present the general theory ofcategories and functors, emphasising inductive a nd projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories andalso unbounded derived categories using transfinite induction and ac cessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies
Note:Springer eBooks
Contents:The Language of Categories
Limits
Filtrant Limits
Tensor Categories
Generators and Representability
Indization of Categories
Localization
Additive and Abelian Categories
?
accessible Objects and F
injective Objects
Triangulated Categories
Complexes in Additive Categories
Complexes in Abelian Categories
Derived Categories
Unbounded Derived Categories
Indization and Derivation of Abelian Categories
Grothendieck Topologies
Sheaves on Grothendieck Topologies
Abelian Sheaves
Stacks and Twisted Sheaves
ISBN:9783540279501
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v332
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Cell aggregation Mathematics
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Call number:SPRINGER-2006-9780387295558:ONLINE Show nearby items on shelf
Title:Non-Euclidean Geometries [electronic resource] : Jnos Bolyai Memorial Volume
Author(s): Andrs Prkopa
Emil Molnr
Date:2006
Publisher:Boston, MA : Springer US
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:From nothing I have created a new different world, wrote Jnos Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyaiand the co-discoverer, the Rus sian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume,which commemorates the 200th anniversary of the birth of Jnos Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life andworks of Jnos Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics polyhedra fractals hyperbolic, Riemannian and discrete geometry tilings visualization and applications in physics. AudienceThis book is intended for those who teach, study, and do research in geometry and history of mathematics. Cul tural historians, physicists, and computer scientists will also find it an important source of information
Note:Springer eBooks
Contents:History
The Revolution of Jnos Bolyai
Gauss and Non
Euclidean Geometry
Jnos Bolyais New Face
Axiomatical and Logical Aspects
Hyperbolic Geometry, Dimension
Free
An Absolute Property of Four Mutually Tangent Circles
Remembering Donald Coxeter
Axiomatizations of Hyperbolic and Absolute Geometries
Logical Axiomatizations of Space
Time. Samples from the Literature
Polyhedra, Volumes, Discrete Arrangements, Fractals
Structures in Hyperbolic Space
The Symmetry of Optimally Dense Packings
Flexible Octahedra in the Hyperbolic Space
Fractal Geometry on H
ISBN:9780387295558
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Its Applications : v581
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry , Mathematics_$xHistory , Cell aggregation Mathematics , Relativity (Physics)
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Call number:SPRINGER-2005-9783764373153:ONLINE Show nearby items on shelf
Title:The Novikov Conjecture [electronic resource] Geometry and Algebra
Author(s): Matthias Kreck
Wolfgang Lck
Date:2005
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-CobordismTheorem. Then an introductio n to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds aregiven. Finally, the most recent developments concer ning these conjectures are surveyed, including a detailed status report. The prerequisites consist of a solid knowledge of the basics about manifolds, vector bundles, (co-) homologyand characteristic classes
Note:Springer eBooks
Contents:Introduction
0. A Motivating Problem
1. Introduction to the Nopvikov and Borel Conjecture
2. Normal Bordism Groups
3. The Signature
4. The Signature Theorem and the Novikov Conjecture
5. The Projective Class Group and the Whitehead Group
6. Whitehead Torsion
7. The Statement and Consequences of the s
Cobordism Theorem
8. Sketch of the Proof of the s
Cobordism Theorem
9. From the Novikov Conjecture to Surgery
10. Surgery Below the Middle Dimension I: An Example
11. Surgery Below the Middle Dimension II: Systematically
12. Surgery in the Middle Dimension I
ISBN:9783764373153
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2005-9783540315414:ONLINE Show nearby items on shelf
Title:Hamiltonian Dynamics. Theory and Applications [electronic resource] : Lectures given at the C.I.M.E.-E.M.S. Summer School held in Cetraro, Italy, July 1-10, 1999
Author(s): Giancarlo Benettin
Jacques Henrard
Sergei Kuksin
Date:2005
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems,such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants and the phenomena related to stability over exponentially long times ofNekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation
Note:Springer eBooks
Contents:A. Giorgilli: Preface
G. Benettin: Physical Applications of Nekhoroshev Theorem and Exponential Estimates
J. Henrard: The Adiabatic Invariant Theory and Applications
S. Kuksin: Lectures on Hamiltonian Methods in Nonlinear PDEs
ISBN:9783540315414
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, Fondazione C.I.M.E., Firenze, 1617-9692 : v1861
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Differential equations, partial , Cell aggregation Mathematics , Thermodynamics
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Call number:SPRINGER-2005-9783540315315:ONLINE Show nearby items on shelf
Title:Invariant Manifolds for Physical and Chemical Kinetics [electronic resource]
Author(s): Alexander Gorban
Ilya Karlin
Date:2005
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:By bringing together various ideas and methods for extracting the slow manifolds the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. Aunifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation andhydrodynamics to the Fokker-Planck equatio ns of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, andexact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and modelreduction, it will also be valuable to PhD students and researchers in applied mathematics, p hysics and various fields of engineering
Note:Springer eBooks
Contents:Introduction
The Source of Examples
Invariance Equation in the Differential Form
Film Extension of the Dynamics: Slowness as Stability
Entropy, Quasi
Equilibrium and Projector Field
Newton Method with Incomplete Linearization
Quasi
chemical Representation
Hydrodynamics from Grad's Equations: Exact Solutions
Relaxation Methods
Method of Invariant Grids
Method of Natural Projector
Geometry of Irreversibility: The Film of Nonequilibrium States
Slow Invariant Manifolds for Open Systems
Estimation of Dimension of Attractors
Accuracy Estimation and Post
Proc
ISBN:9783540315315
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v660
Series:Physics and Astronomy (Springer-11651)
Keywords: Chemistry, Physical organic , Cell aggregation Mathematics , Mathematical physics , Quantum computing , Statistical physics , Thermodynamics
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Call number:SPRINGER-2005-9783540315223:ONLINE Show nearby items on shelf
Title:Geometric and Topological Methods for Quantum Field Theory [electronic resource]
Author(s): Hernn Ocampo
Sylvie Paycha
Andrs Vargas
Date:2005
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is byChristine Lescop on knot inv ariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of RaimarWulkenhaar on Euclidean quantum field theory from a sta tistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on stringcompactification with unbroken supersymmetry. The authors show that this requ irement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theoryproof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommuta tive geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start withintroductory material before presenting more advanced results. Each chapter is self-contained and can be read independently
Note:Springer eBooks
Contents:Knot Invariants and Configuration Space Integrals (Christine Lescop)
Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces (Raimar Wulkenhaar)
Introduction to String Compactification (Anamaria Font, Stefan Theisen)
Index Theorems and Noncommutative Topology (Thierry Fack)
ISBN:9783540315223
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v668
Series:Physics and Astronomy (Springer-11651)
Keywords: Global differential geometry , Cell aggregation Mathematics , Mathematical physics , Quantum theory
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Call number:SPRINGER-2005-9780817644246:ONLINE Show nearby items on shelf
Title:Complex, Contact and Symmetric Manifolds [electronic resource] : In Honor of L. Vanhecke
Author(s): Oldich Kowalski
Emilio Musso
Domenico Perrone
Date:2005
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume contains research and survey articles by well known and respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his manyfruitful and inspiring cont ributions to these fields. The papers, all written with the necessary introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics andcurvature, contact and symplectic geometry, compl ex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the keystrengths of these articles is their appeal to non-specialists, as well as re searchers and differential geometers. Contributors: D.E. Blair E. Boeckx A.A. Borisenko G. Calvaruso V. Corts P. de Bartolomeis J.C. Daz-Ramos M.Djoric C. Dunn M. Fernndez A. Fujiki E. Garca-Ro P.B. Gilkey O. Gil-Medrano L. Hervella O. Kowalski V. Muoz M. Pontecorvo A.M. Naveira T. Oguro L. Schfer K. Sekigawa C-L. Terng K. Tsukada Z. Vlek E.Wang and J.A. Wolf
Note:Springer eBooks
Contents:Preface
Acknowledgments
Authors' Addresses
List of Participants
D.E. Blair: Curvature of Contact Metric Manifolds
E. Boeckx: A case for curvature: the unit tangent bundle
A.A. Borisenko: Convex hypersurfaces in Hadamard manifolds
G. Calvaruso: Contact metric geometry of the unit tangent sphere bundle
V. Corts and L. Schfer: Topological
antitopological fusion equations, pluriharmonic maps and special Khler manifolds
P. de Bartolomeis: Z2 and Z
Deformation Theory for Holomorphic and Symplectic Manifolds
J.C. Daz
Ramos, E. Garca
Ro and L. Hervella: Total
ISBN:9780817644246
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v234
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Geometry , Global differential geometry , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2003-9783034880435:ONLINE Show nearby items on shelf
Title:Polymer and Cell Dynamics Multiscale Modeling and Numerical Simulations
Author(s):
Date:2003
Size:1 online resource (308 p.)
Note:10.1007/978-3-0348-8043-5
Contents:to Part I -- Molecular Dynamics Studies of Micelle and Capsid Self-assembly -- A Functional Study on Saposin B and C Using Experimentally Validated Models -- A Review of the Morph Server and the Macromolecular Motions Database: A
Standardized System for Analyzing and Visualizing Macromolecular Motions in a Database Framework -- to Part II -- Brownian Dynamics of Flexible Polymers in Flow -- A Microscopic Model for the Dynamics of Actin Filaments in Motility
Assays and Its Numerical Simulation -- Multiparticle Modeling of Actin-Myosin Networks: From Molecular Interactions to Cell Motility -- Analysis of Cell Motility Combining Cytomechanical Model Simulations and an Optical Flow Method --
Micropipet Aspiration of the Human Neutrophil -- Physical-object-oriented 3D Simulations of Cell Deformations and Migration -- to Part III -- Computational Modeling of Blood Clotting: Coagulation and Three-dimensional Platelet
Aggregation -- Space-and Time-resolved Simulations of Processes in Biofilm Systems on a Microscale -- On Selected Individual-based Approaches to the Dynamics in Multicellular Systems -- Individual-based Models of Cohort Migration in
Cell Cultures -- Interactive Movement, Aggregation, and Swarm Dynamics -- A Discrete-cell Model of Tissue-equivalent Compaction -- A Hybrid Discrete-continuum Technique for Individual-based Migration Models -- Application of the Hybrid
Discrete-continuum Technique -- List of contributors and workshop participants
ISBN:9783034880435
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Computer simulation , Biomathematics , Mathematics , Mathematical and Computational Biology , Simulation and Modeling
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Call number:SPRINGER-2001-9781475734843:ONLINE Show nearby items on shelf
Title:The Geometry of Biological Time
Author(s): Arthur T Winfree
Date:2001
Edition:Second Edition
Size:1 online resource (779 p.)
Note:10.1007/978-1-4757-3484-3
Contents:1. Circular Logic -- 2. Phase Singularities (Screwy Results of Circular Logic) -- 3. The Rules of the Ring -- 4. Ring Populations -- 5. Getting off the Ring -- 6. Attracting Cycles and Isochrons -- 7. Measuring the Trajectories of a
Circadian Clock -- 8. Populations of Attracting-Cycle Oscillators -- 9. Excitable Kinetics and Excitable Media -- 10. The Varieties of Phaseless Experience: In which the Geometrical Orderliness of Rhythmic Organization Breaks Down in
Diverse Ways -- 11. The Firefly Machine -- 12. Energy Metabolism in Cells -- 13. The Malonic Acid Reagent (“Sodium Geometrate”) -- 14. Electrical Rhythmicity and Excitability in Cell Membranes -- 15. The Aggregation of Slime Mold
Amoebae -- 16. Numerical Organizing Centers -- 17. Electrical Singular Filaments in the Heart Wall -- 18. Pattern Formation in the Fungi -- 19. Circadian Rhythms in General -- 20. The Circadian Clocks of Insect Eclosion -- 21. The
Flower of Kalanchoë -- 22. The Cell Mitotic Cycle -- 23. The Female Cycle 650 A: Women, Hormones, and Eggs -- Index of Author Citations and Publications -- Index of Subjects
ISBN:9781475734843
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Interdisciplinary Applied Mathematics: 12
Keywords: Mathematics , Mathematical analysis , Analysis (Mathematics) , Applied mathematics , Engineering mathematics , Biomathematics , Mathematics , Applications of Mathematics , Mathematical and Computational Biology , Analysis
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Call number:SPRINGER-1997-9783034889162:ONLINE Show nearby items on shelf
Title:Dynamics of Cell and Tissue Motion
Author(s):
Date:1997
Size:1 online resource (336 p.)
Note:10.1007/978-3-0348-8916-2
Contents:I Motile Dynamics at the Cellular Level — Cytoplasmic Motion and Cell Shape — -- I.1 Embryonic Mesoderm Cells and Larval Keratocytes from Xenopus: Structure and Motility of Single Cells -- I.2 Periodicity in Shape Changes of Human
Epidermal Keratinocytes -- I.3 Self-organized F-Actin Autowaves Govern Pseudopodium Projection and the Non-random Locomotion of Dictyostelium Amoebae -- I.4 Mathematical Analysis of Cell Shape -- I.5 Protrusion, Retraction and the
Efficiency of Cell Locomotion -- I.6 Microscopic Image Classification Based on Descriptor Analysis -- I.7 A Dynamical Model of Cell Division -- I.8 Shape Behavior of Closed Layered Membranes and Cytokinesis -- I.9 Protrusion-Retraction
Dynamics of an Annular Lamellipodial Seam -- I.10 Auto-oscillatory Processes and Feedback Mechanisms in Physarum Plasmodium Motility -- I.11 Origin of Actin-induced Locomotion of Listeria -- I.12 Models for the Formation of Oriented
F-actin Structures in the Cytoskeleton -- II Dynamics of Cell Interaction with the Environment -- II.1 Cell-Substratum Interactions of Amoeba proteus: Old and New Open Questions -- II.2 Imaging Traction Stresses -- II.3 Chemotaxis and
Chemokinesis of Dictyostelium Amoebae: Different Accumulation Mechanisms Induced by Temporal Signals and Spatial -- II.4 Receptor-mediated Models for Leukocyte Chemotaxis -- II.5 A Model for Cell Migration by Contact Guidance -- II.6
Derivation of a Cell Migration Transport Equation from an Underlying Random Walk Model -- II.7 A Continuum Model for the Role of Fibroblast Contact Guidance in Wound Contraction -- II.8 Wound Healing and Tumour Growth — Relations and
Differences — -- III Dynamics of Cell-Cell Interactions — Collective Motion and Aggregation — -- III.1 Models for Spatio-angular Self-organization in Cell Biology -- III.2 Aggregation Induced by Diffusing and Nondiffusing Media --
III.3 Models of Dictyostelium discoideum Aggregation -- III.4 A Cellular Automata Approach to the Modelling of Cell-Cell Interactions -- IV Dynamics within Tissues — Morphogenesis and Plant Movement — -- IV.1 Morphogenetic Dynamics in
Tissues: Expectations of Developmental and Cell Biologists -- IV.2 Mechanical Stresses in Animal Development: Patterns and Morphogenetical Role -- IV.3 Mechanisms for Branching Morphogenesis of the Lung -- IV.4 Tissue Stresses in Plant
Organs: Their Origin and Importance for Movements -- IV.5 Self-Organization and the Formation of Patterns in Plants -- IV.6 The Mathematics of Plate Bending -- IV.7 Mechanical Forces and Signal Transduction in Growth and Bending of
Plant Roots -- IV.8 Growth Field and Cell Displacement within the Root Apex -- IV.9 The Stationary State of Epithelial Tissues -- References -- Group Picture -- Addresses
ISBN:9783034889162
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Mathematics , Mathematics, general
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Call number:SPRINGER-1985-9783642932878:ONLINE Show nearby items on shelf
Title:Mathematics in Biology and Medicine Proceedings of an International Conference held in Bari, Italy, July 18–22, 1983
Author(s):
Date:1985
Size:1 online resource (528 p.)
Note:10.1007/978-3-642-93287-8
Contents:I. — Population Genetics and Ecology -- Invited Papers -- The role of diffusion in mathematical population biology: Skellam revisited -- The dynamics of structured populations: some examples -- Mathematical problems in the description
of age structured populations -- Contributed Papers -- Models for mutual attraction and aggregation of motile individuals -- A problem on invariant manifolds arising in population genetics -- On a mathematical problem arising in cell
population biology -- The external memory of intertidal molluscs:a theoretical study of trail-following -- Stationary distributions for populations subject to random catastrophes -- A nonlinear diffusion equation in phytoplankton
dynamics with self—shading effects -- A model of aphid population with age structure -- On two-population models with switching depletion -- On some nonlinear diffusion models in population dynamics -- Reduction of the gene Flow of a
“neutral” linked gene due to the partial sterility of heterozygotes for a chromosome mutation -- Predator-mediated coexistence of competing species in a Volterra model -- On a nonlinear problem arising from interaction of algae with
light -- II. — Epidemics -- Invited Papers -- Congenital rubella syndrome (C.R.S.): models of disease control by vaccination -- A simulation model for the control of helminth diseases by chemotherapy -- Models for endemic diseases --
Stochastic epidemics as point processes -- Contributed Papers -- A computer simulation program for the assessment of multistate epidemiological models of infectious diseases -- Mathematical model of hepatitis B -- Models of the
interaction of host genotypes and infectious disease -- On the general epidemic model in discrete time -- Control of virus transmission in age-structured populations -- Parameter estimation and validation for an epidemic model -- Local
stability in epidemic models for heterogeneous populations -- III. — Resource Management -- Invited Papers -- Bayesian methods in ecology and resource management -- Contributed Papers -- Stochastic differential equation models of
fisheries in an uncertain world: extinction probabilities, optimal fishing effort, and parameter estimation -- IV. — Physiology and Medicine -- Invited Papers -- Experiment designs identification of simple and complex models of
endocrine-metabolic systems -- A mathematical model for cardiac electric sources and related potential fields -- Mathematical analysis of immobilized enzyme systems -- Contributed Papers -- Modeling controls and variability of the cell
cycle -- The phase resetting characteristics of endogenously active neurones -- Theory of DNA superhelicity -- Determination of DNA synthesis rate in cell populations with locally exponential S-phase influx -- A numerical study for a
cell system -- Experimental validation of a mathematical procedure for the analysis of flow cytometric data -- A stochastic model for describing the space-time evolution of the extreme values of cardiac potentials on the chest surface
-- Statistical analysis of the coding capacity of complementary DNA strands -- Mass transport across multimembrane systems: a general analysis -- Time hierarchy in oscillating metabolic systems -- Modeling of the interaction between
ligands and cell membrane receptors in the presence of exogenous electric fields -- Balance of growth models of cell populations: the significance of simple mathematical considerations -- The age structure of populations of cells
reproducing by asymmetric division -- Numerical simulation of reentry of the activation wave in the heart hiss bundle -- Hopf bifurcation and the repetitive activity of excitable cells -- Nonlinear evolution equations with a
convolution term involved in some neurophysiological models -- Investigation of rapid metabolic reactions in whole organs by multiple pulse Labelling -- Cross-linking of identical particles by multiple ligand-types -- Enumeration of
RNA secondary structures by complexity -- Growth of cell populations -- V. — Compartmental Analysis -- Invited Papers -- A staging process with applications in biology and medicine -- On the use of residence time moments in the
statistical analysis of age-dependent stochastic compartmental systems -- An algorithm for reconstruction of count rate curves from total counts -- Contributed Papers -- On identifiability of linear compartmental systems: some results
obtained by means of structural properties of the associated graph -- Compartmental vs, noncompartmental modeling of ketone body kinetics -- Identifiability of compartmental models: on characterization of two extremal types of
input-output experiments -- VI. — General Mathematical Methods -- Invited Papers -- Estimation techniques for transport equations -- Stability of delay differential equations with applications in biology and medicine -- Existence of
quasi-solutions of systems of nonlinear elliptic BVP’s suggested by biochemical reactions -- Diffusion approximations and first passage time problems in population biology and neurobiology -- Contributed Papers -- The role of
exchangeability in biology, genetics and medicine -- Cyclic chemical systems: an asymptotic stability criterion -- On existence, uniqueness and attractivity of stationary solutions to some quasilinear parabolic systems -- Asymptotic
estimates for principal eigenvalues -- Remarks on the connection between positive feedback and instability in regard to model selection in population biology -- Lyapunov methods for a wide class of stochastic models in biology --
Existence and uniqueness for a non linear Cauchy problem of hyperbolic type -- Catastrophe theory in biology -- S-system analysis of biological systems
ISBN:9783642932878
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Biomathematics: 57
Keywords: Mathematics , Algebra , Applied mathematics , Engineering mathematics , Biomathematics , Mathematics , Applications of Mathematics , Algebra , Mathematical and Computational Biology
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Call number:SPRINGER-1985-9783642521157:ONLINE Show nearby items on shelf
Title:Branching Processes Applied to Cell Surface Aggregation Phenomena
Author(s): Catherine A Macken
Date:1985
Size:1 online resource (124 p.)
Note:10.1007/978-3-642-52115-7
Contents:1. Introduction -- 2. Branching Processes Applied to the Aggregation of f-Valent Particles -- 3. Multitype Branching Processes -- 4. Aggregate Size Distribution on a Cell Surface -- 5. Gelation and Infinite-Sized Trees -- 6. Post-Gel
Relations -- 7. Conclusions and Extensions -- List of Symbols
ISBN:9783642521157
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Biomathematics: 58
Keywords: Mathematics , Algebra , Applied mathematics , Engineering mathematics , Biomathematics , Mathematics , Applications of Mathematics , Algebra , Mathematical and Computational Biology
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Call number:SPRINGER-1984-9783642455896:ONLINE Show nearby items on shelf
Title:Modelling of Patterns in Space and Time Proceedings of a Workshop held by the Sonderforschungsbereich 123 at Heidelberg July 4–8, 1983
Author(s):
Date:1984
Size:1 online resource (410 p.)
Note:10.1007/978-3-642-45589-6
Contents:Contraction patterns in a viscous polymer system -- Formation and evolution of spatial structures in chemotactic bacterial systems -- Pattern formation in directional solidification: the nonlinear evolution of cellular melt/solid
interfaces -- Evolution of 3-D chemical waves in the BZ reaction medium -- Patterns of bifurcations in plane layers and spherical shells -- Chemotactic collapse in two dimensions -- Singular bifurcation in reaction-diffusion systems --
How chemical structure determines spatial structure in flame profiles -- An age-dependent population model with applications to microbial growth processes -- Cell traction and the generation of anatomical structure -- A hysteresis
model for bacterial growth patterns -- Chaos in simple three- and four-variable chemical systems -- Spatial structures induced by chemical reactions at interfaces: survey of some possible models and computerized pattern analysis --
Dynamic patterns in excitable media -- Head regeneration in hydra: biological studies and a model -- Pattern formation in aspect -- Chemotaxis and cell aggregation -- Turing structures, periodic and chaotic regimes in coupled cells --
Digits, segments, somites — the superposition of sequential and periodic structures -- Spatial pattern formation in thin layers of NADH-solutions -- Pattern formation in precipitation processes -- On a mechanical model for
morphogenesis: mesenchymal patterns -- Every multi-mode singularly perturbed solution recovers its stability — from a global bifurcation view point -- A mechanochemical model for plasmodial oscillations in physarum -- Genomic control
of global features in morphogenesis -- Patterns of starvation in a distributed predator-prey system -- Global branches of one dimensional stationary solutions to Chemotaxis systems and stability -- Analytical and topological methods
for reaction-diffusion equations -- Branching processes with interaction as models of cellular pattern formation -- Periodic growth phenomena in spatially organized microbial systems
ISBN:9783642455896
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Biomathematics: 55
Keywords: Life sciences , Algebra , Applied mathematics , Engineering mathematics , Biomathematics , Life Sciences , Life Sciences, general , Applications of Mathematics , Algebra , Mathematical and Computational Biology
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Call number:SPRINGER-1980-9783662224922:ONLINE Show nearby items on shelf
Title:The Geometry of Biological Time
Author(s): Arthur T Winfree
Date:1980
Size:1 online resource (530 p.)
Note:10.1007/978-3-662-22492-2
Contents:1. Circular Logic -- 2. Phase Singularities (Screwy Results of Circular Logic) -- 3. The Rules of the Ring -- 4. Ring Populations -- 5. Getting off the Ring -- 6. Attracting Cycles and Isochrons -- 7. Measuring the Trajectories of a
Circadian Clock -- 8. Populations of Attractor Cycle Oscillators -- 9. Excitable Kinetics and Excitable Media -- 10. The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in
Diverse Ways -- 11. The Firefly Machine -- 12. Energy Metabolism in Cells -- 13. The Malonic Acid Reagent (“Sodium Geometrate”) -- 14. Electrical Rhythmicity and Excitability in Cell Membranes -- 15. The Aggregation of Slime Mold
Amoebae -- 16. Growth and Regeneration -- 17. Arthropod Cuticle -- 18. Pattern Formation in the Fungi -- 19. Orcadian Rhythms in General -- 20. The Circadian Clocks of Insect Eclosion -- 21. The Flower of Kalanchoe -- 22. The Cell
Mitotic Cycle -- 23. The Female Cycle -- References -- Index of Names -- Index of Subjects
ISBN:9783662224922
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Biomathematics , Mathematics , Mathematical and Computational Biology
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