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Call number: | 9783319393391:ONLINE Show nearby items on shelf |
Title: | Singularities in Geometry, Topology, Foliations and Dynamics A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014 |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (XVII, 231 p. 15 illus., 10 illus. in color p.) |
Contents: | Extending the action of Schottky groups on the complex anti-de Sitter space to the projective space -- Puiseux Parametric Equations via the Amoeba of the Discriminant -- Some open questions on arithmetic Zariski pairs -- Logarithmic |
vector fields and the Severi strata in the discriminant -- Classification of Isolated Polar Weighted Homogeneous Singularities -- Rational and iterated maps, degeneracy loci, and the generalized Riemann-Hurwitz formula -- On singular | |
varieties with smooth subvarieties -- On Polars of Plane Branches -- Singular Intersections of Quadrics I -- A New Conjecture, a New Invariant, and a New Non-splitting Result -- Lipschitz geometry does not determine embedded | |
topological type -- Projective transverse structures for some foliations -- Chern classes and transversality for singular spaces | |
ISBN: | 9783319393391 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Algebraic geometry , Global analysis (Mathematics) , Manifolds (Mathematics) , Functions of complex variables , Mathematics , Several Complex Variables and Analytic Spaces , Algebraic Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | 9783319297347:ONLINE Show nearby items on shelf |
Title: | Geometrodynamics of Gauge Fields On the Geometry of Yang-Mills and Gravitational Gauge Theories |
Author(s): |
Eckehard W Mielke |
Date: | 2017 |
Edition: | 2nd ed. 2017 |
Size: | 1 online resource (XVII, 373 p. 18 illus., 8 illus. in color p.) |
Contents: | Preface -- 1 Historical background -- 2 Geometry of gauge fields -- 3 Maxwell and Yang-Mills theory -- 4 Gravitation as a gauge theory -- 5 Einstein-Cartan theory -- 6 Teleparallelism -- 7 Yang’s theory of gravity -- 8 BRST |
quantization of gravity -- 9 Gravitational instantons -- 10 Three-dimensional gravity -- 11 Spinor bundles -- 12 Chiral anomalies -- 13 Topological SL(5R) gauge invariant action -- 14 Geometrodynamics and its extensions -- 15 Color | |
Geometrodynamics -- 16 Geometrodynamical model of quark confinement?- Appendix A Notation and mathematical terms -- Appendix B Calculus of exterior forms -- Appendix C Lie groups | |
ISBN: | 9783319297347 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Physics , Mathematical physics , Gravitation , Elementary particles (Physics) , Quantum field theory , Physics , Classical and Quantum Gravitation, Relativity Theory , Mathematical Physics , Elementary Particles, Quantum Field Theory |
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Call number: | SPRINGER-2016-9783658106331:ONLINE Show nearby items on shelf |
Title: | Manifolds, Sheaves, and Cohomology |
Author(s): |
Torsten Wedhorn |
Date: | 2016 |
Size: | 1 online resource (354 p.) |
Note: | 10.1007/978-3-658-10633-1 |
Contents: | Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohom ology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis |
ISBN: | 9783658106331 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Topological groups , Lie groups , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Category Theory, Homological Algebra , Topological Groups, Lie Groups , Differential Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319397801:ONLINE Show nearby items on shelf |
Title: | Extensions of Positive Definite Functions Applications and Their Harmonic Analysis |
Author(s): |
Palle Jorgensen |
Date: | 2016 |
Size: | 1 online resource (9 p.) |
Note: | 10.1007/978-3-319-39780-1 |
ISBN: | 9783319397801 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2160 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Fourier analysis , Functional analysis , Probabilities , Mathematical physics , Mathematics , Abstract Harmonic Analysis , Topological Groups, Lie Groups , Fourier Analysis , Functional Analysis , Mathematical Physics , Probability Theory and Stochastic Processes |
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Call number: | SPRINGER-2016-9783319392868:ONLINE Show nearby items on shelf |
Title: | Operator Algebras and Applications The Abel Symposium 2015 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (2 p.) |
Note: | 10.1007/978-3-319-39286-8 |
Contents: | C*-tensor categories and subfactors for totally disconnected groups: Y. Arano and S. Vaes -- Decomposable approximations revisited: N.P. Brown, J.R. Carrión and S. White -- Exotic crossed products: A. Buss, S. Echterhoff, and R. Willett -- On Hong and Szymanski’s description of the primitive-ideal space of a graph algebra: T. M. Carlsen and A. Sims -- Commutator inequalities via Schur products: E. Christensen -- C*-algebras associated with algebraic actions: J. Cuntz -- A new look at C*-simplicit y and the unique trace property of a group: U. Haagerup -- Equilibrium states on graph algebras: A. an Huef and I. Raeburn -- Semigroup C_-algebras: X. Li -- Topological full groups of étale groupoids: H. Matui -- Towards a classification of compact quan tum groups of Lie type: S. Neshveyev and M. Yamashita -- A homology theory for Smale spaces: a summary: I.F. Putnam -- On the positive eigenvalues and eigenvectors of a non-negative matrix: K. Thomsen -- Classification of graph algebras: a |
selective survey: M. Tomforde -- QDQ vs. UCT: W. Winter | |
ISBN: | 9783319392868 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Abel Symposia: 12 |
Keywords: | Mathematics , K-theory , Dynamics , Ergodic theory , Functional analysis , Mathematical physics , Mathematics , Functional Analysis , Dynamical Systems and Ergodic Theory , K-Theory , Mathematical Physics |
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Call number: | SPRINGER-2016-9783319304519:ONLINE Show nearby items on shelf |
Title: | Symmetries in Graphs, Maps, and Polytopes 5th SIGMAP Workshop, West Malvern, UK, July 2014 |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (332 p.) |
Note: | 10.1007/978-3-319-30451-9 |
ISBN: | 9783319304519 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 159 |
Keywords: | Mathematics , Algebra , Field theory (Physics) , Topological groups , Lie groups , Graph theory , Mathematics , Graph Theory , Field Theory and Polynomials , Topological Groups, Lie Groups |
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Call number: | SPRINGER-2016-9783319295589:ONLINE Show nearby items on shelf |
Title: | Quantization on Nilpotent Lie Groups |
Author(s): |
Veronique Fischer |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (557 p.) |
Note: | 10.1007/978-3-319-29558-9 |
Contents: | Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-d ifferential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index |
ISBN: | 9783319295589 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics: 314 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Mathematical physics , Mathematics , Topological Groups, Lie Groups , Abstract Harmonic Analysis , Functional Analysis , Mathematical Physics |
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Call number: | SPRINGER-2014-9789462390249:ONLINE Show nearby items on shelf |
Title: | Recent Progress in General Topology III [electronic resource] |
Author(s): |
K.P Hart J van Mill P Simon |
Date: | 2014 |
Publisher: | Paris : Atlantis Press : Imprint: Atlantis Press |
Size: | 1 online resource |
Note: | The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland,1992 and 2002). The boo k was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in2002. The following areas experienced signifi cant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems |
Contents: | Topological Homogeneity |
Some Recent Progress Concerning Topology of Fractals | |
A biased view of topology as a tool in functional analysis | |
Large scale versus small scale | |
Descriptive aspects of Rosenthal compacta | |
Minimality conditions in topological groups | |
Set | |
Theoretic update on Topology | |
Topics in Dimension Theory | |
Representations of dynamical systems on Banach spaces | |
Generalized metrizable spaces | |
Permanence in Coarse Geometry | |
Selections and Hyperspaces | |
Continuum Theory | |
Almost disjoint families and topology | |
Some Topics in Geometric Topology II | |
Topologic | |
ISBN: | 9789462390249 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functional analysis , Logic, Symbolic and mathematical , Topology |
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Call number: | SPRINGER-2014-9788132215998:ONLINE Show nearby items on shelf |
Title: | Basic Modern Algebra with Applications [electronic resource] |
Author(s): |
Mahima Ranjan Adhikari Avishek Adhikari |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a waythat it encourages ind ependent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. Inaddition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theoryto structure theory of rings and homological algebra. Algebraic as pects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraictopology, category theory, algebraic geometry, algebraic number theory, cryptography and theo retical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, withthe help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, example s, exercises and historical notes represents a valuable and unique resource |
Contents: | Prerequisites: Basics of Set Theory and Integers |
Groups: Introductory Concepts | |
Actions of Groups, Topological Groups and semigroups | |
Rings: Introductory Concepts | |
Ideals of Rings: Introductory concepts | |
Factorization in Integral Domains and in Polynomial Rings | |
Rings with Chain Conditions | |
Vector Spaces | |
Modules | |
Algebraic Aspects of Number Theory | |
Algebraic Numbers | |
Introduction to Mathematical Cryptography | |
Appendix A: Some Aspects of Semirings | |
Appendix B: Category Theory | |
Appendix C: A Brief Historical Note | |
ISBN: | 9788132215998 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Number theory |
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Call number: | SPRINGER-2014-9783642553615:ONLINE Show nearby items on shelf |
Title: | Algebra, Geometry and Mathematical Physics [electronic resource] : AGMP, Mulhouse, France, October 2011 |
Author(s): |
Abdenacer Makhlouf Eugen Paal Sergei D Silvestrov Alexander Stolin |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetriesand conservation laws and mathematical physics and applications, the book covers deformation theory and quantization Hom-algebras and n-ary algebraic structures Hopf algebra, integrable systems and related math structures jet theoryand Weil bundles Lie theory and applications non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures ofLie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry andapplications in physics and beyond. The book benefits a broad audience of researchers a nd advanced students |
Contents: | Part I Algebra |
Part II Geometry | |
Part III Dynamical Symmetries and Conservation Laws | |
Part IV Mathematical Physics and Applications | |
ISBN: | 9783642553615 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v85 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global differential geometry , Engineering mathematics |
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Call number: | SPRINGER-2014-9783319078427:ONLINE Show nearby items on shelf |
Title: | Probability on Compact Lie Groups [electronic resource] |
Author(s): |
David Applebaum |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applicationsin statistics and engineering (par ticularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topicspresented are: the study of measures via the non-commutative F ourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. Theemphasis on compact (rather than general) Lie groups helps readers to get acquaint ed with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance ofthese groups for applications. The book is primarily aimed at researchers working in probability, stochast ic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists,statisticians and engineers who are working on related applications. A background in first year graduate level measure theoreti c probability and functional analysis is essential a background in Lie groups and representation theory iscertainly helpful but the first two chapters also offer orientation in these subjects |
Contents: | Introduction |
1.Lie Groups | |
2.Representations, Peter | |
Weyl Theory and Weights | |
3.Analysis on Compact Lie Groups | |
4.Probability Measures on Compact Lie Groups | |
5.Convolution Semigroups of Measures | |
6.Deconvolution Density Estimation | |
Appendices | |
Index | |
Bibliography | |
ISBN: | 9783319078427 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Probability Theory and Stochastic Modelling, 2199-3130 : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Harmonic analysis , Fourier analysis , Functional analysis , Distribution (Probability theory) |
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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-2014-9783319052243:ONLINE Show nearby items on shelf |
Title: | Descriptive Topology and Functional Analysis [electronic resource] : In Honour of Jerzy Kakols 60th Birthday |
Author(s): |
Juan Carlos Ferrando Manuel Lpez-Pellicer |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topologicalAbelian groups, linear top ological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapterpresents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area |
Contents: | 1Some aspects in the Mathematical work of Jerzy Kakol |
2Weak barrelledness vs. P | |
spaces | |
3On the topology of the sets of the real projections of the zeros ofexponential polynomials | |
4The density character of the space Cp(X) | |
5Compactness and distances to spaces of continuous functions andFrchet spaces | |
6Two classes of metrizable spaces lc | |
invariant | |
7Characteristics of the Mackey topology for abelian topologicalgroups | |
8Bowens Entropy for Endomorphisms of Totally Bounded Abelian | |
9On preserved and unpreserved extreme pointsGroups | |
10Cantor set | |
ISBN: | 9783319052243 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v80 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functional analysis , Operator theory , Topology |
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Call number: | SPRINGER-2014-9783319020457:ONLINE Show nearby items on shelf |
Title: | Locally Convex Spaces [electronic resource] |
Author(s): |
M. Scott Osborne |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convextopological vector spaces, is i ntended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convexspaces, which is why this is an important topic in function al analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varyingdifficulty. Key topics covered include point set topology, topological vector space s, the HahnBanach theorem, seminorms and Frchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach spacetheory typically taught in a beginning graduate real analysis course |
Contents: | 1 Topological Groups |
2 Topological Vector Spaces | |
3 Locally Convex Spaces | |
4 The Classics | |
5 Dual Spaces | |
6 Duals of Fr chet Spaces | |
A Topological Oddities | |
B Closed Graphs in Topological Groups | |
C The Other KreinSmulian Theorem | |
D Further Hints for Selected Exercises | |
Bibliography | |
Index | |
ISBN: | 9783319020457 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Graduate Texts in Mathematics, 0072-5285 : v269 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functional analysis |
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Call number: | SPRINGER-2014-9783319020365:ONLINE Show nearby items on shelf |
Title: | Contact and Symplectic Topology [electronic resource] |
Author(s): |
Frdric Bourgeois Vincent Colin Andrs Stipsicz |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new researchfield worldwide. The inten se activity of many European research groups in this field is reflected by the ESF Research Networking Programme Contact And Symplectic Topology (CAST). The lectures of the Summer School in Nantes (June2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which havedeveloped in an amazing speed in the recent past. These topics include 3- dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embeddedcontact homology, and flexibility results for Stein manifolds |
Contents: | Mathematical contributions from V.I. Arnold |
Topological methods in 3 | |
dimensional contact geometry | |
A short introduction to Fukaya categories | |
Open books and Lefschetz pencils in contact geometry | |
Introduction to contact topology in higher dimensions | |
Bordered Heegaard Floer homology | |
Stein structures: existence and flexibility | |
Embedded contact homology, cobordism maps, and applications | |
Knot contact homology and applications | |
ISBN: | 9783319020365 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Bolyai Society Mathematical Studies, 1217-4696 : v26 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Geometry , Mathematical physics |
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Call number: | SPRINGER-2014-9781493909384:ONLINE Show nearby items on shelf |
Title: | Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics [electronic resource] |
Author(s): |
Mahir Can Zhenheng Li Benjamin Steinberg Qiang Wang |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: v structure andrepresentation theory of reducti ve algebraic monoids v monoid schemes and applications of monoids v monoids related to Lie theory v equivariant embeddings of algebraic groups v constructions and properties of monoids fromalgebraic combinatorics v endomorphism monoids induced from vector bundles v HodgeNewton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics,while the remaining contributions are research articles containing previously unpublished result s, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and LexRenner showing that the algebraic semigroups are strongly -regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics, and the theory of algebraic groupembeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings, and alge braic combinatorics merged under the umbrella of algebraic monoids |
Contents: | On Algebraic Semi groups and Monoids (M. Brion) |
Algebraic Semi groups are Strongly | |
regular (M. Brion, L. E. Renner) | |
Rees Theorem and Quotients in Linear Algebraic Semi groups (M. S. Putcha) | |
Representations of Reductive Normal Algebraic Monoids (S. Doty) | |
On Linear Hodge Newton Decomposition for Reductive Monoids (S. Varma) | |
The Structure of Affine Algebraic Monoids in Terms of Kernel Data (W. Huang) | |
Algebraic Monoids and Renner Monoids (Z. Li, Z. Li, Y. Cao) | |
Conjugacy Decomposition of Canonical and Dual Canonical Monoids (R. K. Therkelsen) | |
The Endomorphisms Monoid of a | |
ISBN: | 9781493909384 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Fields Institute Communications, 1069-5265 : v71 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Topological Groups , Combinatorics |
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Call number: | SPRINGER-2014-9781493907489:ONLINE Show nearby items on shelf |
Title: | The Compressed Word Problem for Groups [electronic resource] |
Author(s): |
Markus Lohrey |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups.The authorpresents thenecessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontierofcurrent research which makes the book especially ap pealing for students looking for a currently active research topic at theintersection of group theory and computer science. The word problem introduced in 1910 by Max Dehnisone of the most important decision problems in group theory. For many groups, high ly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithmsfor word problems, has been developed, by representing long words over group generators in a compressed f orm using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressedword problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups |
Contents: | 1. Preliminaries from Theoretical Computer Science |
2. Preliminaries from Combinatorial Group Theory | |
3. Algorithms on Compressed Words | |
4. The Compressed Word Problem | |
5. The Compressed Word Problem in Graph Products | |
6. The Compressed Word Problem in HNN | |
Extensions | |
7.Outlook | |
References | |
Index | |
ISBN: | 9781493907489 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Topological Groups , Global analysis (Mathematics) |
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Call number: | SPRINGER-2014-9781461491613:ONLINE Show nearby items on shelf |
Title: | Nonlinear Maps and their Applications [electronic resource] : Selected Contributions from the NOMA 2011 International Workshop |
Author(s): |
Clara Grcio Daniele Fournier-Prunaret Tetsushi Ueta Yoshifumi Nishio |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | In the field of Dynamical Systems, nonlinear iterative processes play an important role. Nonlinear mappings can be found as immediate models for many systems from different scientific areas, such as engineering, economics,biology, or can also be obta ined via numerical methods permitting to solve non-linear differential equations. In both cases, the understanding of specific dynamical behaviors and phenomena is of the greatest interest for scientists.This volume contains papers that were presented at the International Workshop on Nonlinear Maps and their Applications (NOMA 2011) held in vora, Portugal, on September 15-16, 2011. This kind of collaborative effort is of paramountimportance in promoting communication among the various groups that work in dynamical systems and networks in their research theoretical studies as well as for applications. This volume is suitable for graduate students as well asresearchers in the field |
Contents: | J. P. Almeida A. A. Pinto D. A. Rand, Renormalization of circlediffeomorphism sequences and Markov sequences |
F. Balibrea M. V. Caballero, Examples of Lyapunov exponents in two dimensional systems | |
R. A. da Costa S. N. Dorogovtsev A.V. Goltsev J. F. F. Mendes, Characteristics of the explosive percolation transition | |
E. S. Roberts A. Annibale A. C. C. Coolen, Controlled Markovian dynamics of graphs: unbiased generation of random graphs with prescribed topological properties | |
G. Bettencourt, A case leading to rationalist of the drift | |
L. S. Efremova, Remarks on the nonwanderi | |
ISBN: | 9781461491613 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v57 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9789400753457:ONLINE Show nearby items on shelf |
Title: | Differential Geometry and Mathematical Physics [electronic resource] : Part I. Manifolds, Lie Groups and Hamiltonian Systems |
Author(s): |
Gerd Rudolph Matthias Schmidt |
Date: | 2013 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Starting from an undergraduate level, this book systematically develops the basics of Calculus on manifolds, vector bundles, vector fields and differential forms, Lie groups and Lie group actions, Linear symplecticalgebra and symplectic geometry, Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. Thesecond and third items constitute the link between abstr act calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class andcaustics. The book guides the reader from elementary differential geometry to advan ced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematicaltextbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact |
Note: | Springer eBooks |
Contents: | 1 Differentiable manifolds |
2 Vector bundles | |
3 Vector fields | |
4 Differential forms | |
5 Lie groups | |
6 Lie group actions | |
7 Linear symplectic algebra | |
8 Symplectic geometry | |
9 Hamiltonian systems | |
10 Symmetries | |
11 Integrability | |
12 Hamilton | |
Jacobi theory | |
References | |
ISBN: | 9789400753457 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Topological Groups , Global analysis , Global differential geometry , Mathematical physics , Mechanics |
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Call number: | SPRINGER-2013-9788847028418:ONLINE Show nearby items on shelf |
Title: | Geometric Properties for Parabolic and Elliptic PDE's [electronic resource] |
Author(s): |
Rolando Magnanini Shigeru Sakaguchi Angelo Alvino |
Date: | 2013 |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understoodquite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad andwell-established research area, with contributions tha t often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name afew. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulatingfuture developments and perspectives in this very active area of research |
Note: | Springer eBooks |
Contents: | Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations |
Elvise Berchio, A family of Hardy | |
Rellich type inequalities involving the L2 | |
norm of the Hessian matrices | |
Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains | |
Lorenzo Brasco and Rolando Magnanini, The heart of a convex set | |
Giulio Ciraolo, A viscosity equation for minimizers of a class of very degenerate elliptic functionals | |
Adele Ferone, Kato's inequality in the half space: an alternative proof and relative i | |
ISBN: | 9788847028418 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer INdAM Series, 2281-518X : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Discrete groups , Global differential geometry , Mathematical optimization |
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Call number: | SPRINGER-2013-9784431542704:ONLINE Show nearby items on shelf |
Title: | Lie Theory and Its Applications in Physics [electronic resource] : IX International Workshop |
Author(s): |
Vladimir Dobrev |
Date: | 2013 |
Publisher: | Tokyo : Springer Japan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to asystem yields in general so me notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantumgroups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples ofthese new trends are presented in this volume, based on contributions fr om the Workshop Lie Theory and Its Applications in Physics held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience ofmathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theo ry |
Note: | Springer eBooks |
ISBN: | 9784431542704 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v36 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Geometry |
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Call number: | SPRINGER-2013-9783642362163:ONLINE Show nearby items on shelf |
Title: | Clifford Algebras and Lie Theory [electronic resource] |
Author(s): |
Eckhard Meinrenken |
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 provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results onsymmetric bilinear form s and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes apresentation of Petraccis proof of the PoincarBirk hoffWitt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lietheory include Duflos theorem for the case of quadratic Lie algebras, multiplets of rep resentations, and Dirac induction. The last part of the book is an account of Kostants structure theory of the Clifford algebra over asemisimple Lie algebra. It describes his Clifford algebra analogue of the HopfKoszulSamelson theorem, and explains his fa scinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principalsl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Cliffor d theory, relevant for students and researchers in mathematics andphysics |
Note: | Springer eBooks |
Contents: | Preface |
Conventions | |
List of Symbols | |
1 Symmetric bilinear forms | |
2 Clifford algebras | |
3 The spin representation | |
4 Covariant and contravariant spinors | |
5 Enveloping algebras | |
6 Weil algebras | |
7 Quantum Weil algebras | |
8 Applications to reductive Lie algebras | |
9 D(g k) as a geometric Dirac operator | |
10 The HopfKoszulSamelson Theorem | |
11 The Clifford algebra of a reductive Lie algebra | |
A Graded and filtered super spaces | |
B Reductive Lie algebras | |
C Background on Lie groups | |
References | |
Index | |
ISBN: | 9783642362163 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v58 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global differential geometry , Mathematical physics |
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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-2013-9783642310904:ONLINE Show nearby items on shelf |
Title: | Poisson Structures [electronic resource] |
Author(s): |
Camille Laurent-Gengoux Anne Pichereau Pol Vanhaecke |
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: | Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of thesecontexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to theproblem in nearly all cases. Poisson Structu res is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures.The first part coverssolid foundations,the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications ofPoisson structures (integrable systems and deformation quantization). The clear structure of th e book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researcherswhoare interested in anintroduction to the many facets and applications of Poisson structures |
Note: | Springer eBooks |
Contents: | Part I Theoretical Background:1.Poisson Structures: Basic Definitions |
2.Poisson Structures: Basic Constructions | |
3.Multi | |
Derivations and Khler Forms | |
4.Poisson (Co)Homology | |
5.Reduction | |
Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds | |
7.Linear Poisson Structures and Lie Algebras | |
8.Higher Degree Poisson Structures | |
9.Poisson Structures in Dimensions Two and Three | |
10.R | |
Brackets and r | |
Brackets | |
11.PoissonLie Groups | |
Part III Applications:12.Liouville Integrable Systems | |
13.Deformation Quantization | |
A Multilinear Algebra | |
B Real | |
ISBN: | 9783642310904 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v347 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global analysis (Mathematics) , Global differential geometry |
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Call number: | SPRINGER-2013-9783642309946:ONLINE Show nearby items on shelf |
Title: | Linear Algebra and Geometry [electronic resource] |
Author(s): |
Igor R Shafarevich Alexey O Remizov |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements ofmatrix theory and continue s with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but areusually not covered in such courses: exterior alge bras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitelygenerated periodic modules (similar to Jordan normal forms of linear opera tors). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equationsand differential geometry, as well as from mechanics and physics |
Note: | Springer eBooks |
Contents: | Preface |
Preliminaries | |
1. Linear Equations | |
2. Matrices and Determinants | |
3. Vector Spaces | |
4. Linear Transformations of a Vector Space to Itself | |
5. Jordan Normal Form | |
6. Quadratic and Bilinear Forms | |
7. Euclidean Spaces | |
8. Affine Spaces | |
9. Projective Spaces | |
10. The Exterior Product and Exterior Algebras | |
11. Quadrics | |
12. Hyperbolic Geometry | |
13. Groups, Rings, and Modules | |
14. Elements of Representation Theory | |
Historical Note | |
References | |
Index | |
ISBN: | 9783642309946 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Matrix theory , Geometry |
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Call number: | SPRINGER-2013-9783642307096:ONLINE Show nearby items on shelf |
Title: | Variational, Topological, and Partial Order Methods with Their Applications [electronic resource] |
Author(s): |
Zhitao Zhang |
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: | Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry,measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been usedextensively to solve existence of solutions for ellipt ic equations, wave equations, Schrdinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This bookis useful for researchers and graduate students in the field of nonlinear fu nctional analysis. Chapter 1 contains preliminaries. In Chapter 2, three kinds of operators are introduced: increasing operators, decreasing operators, andmixed monotone operators. In Chapter 3, the minimax methods are presented and in Chapter 4, the auth or uses bifurcation and critical point theory to study structures of the solutions of elliptic equations. Chapter 5 is concerned with aclass of MongeAmpre equations. In Chapter 6, the superlinear system of Hammerstein integral equations and applications i s studied. Chapter 7 is devoted to the DancerFucik spectrum. In Chapter 8, some results on sign-changingsolutions are introduced. In Chapter 9, a local minimizer problem of a functional in differential topology is studied. Chapter 10 focuses on a class of nonlocal Kirchhoff elliptic problems via different methods. In Chapter 11, thefocus is on free boundary problems, Schrdinger systems from BoseEinstein condensate and competing systems with many species |
Note: | Springer eBooks |
Contents: | 1 Preliminaries |
Sobolev spaces and embedding theorems | |
Critical point | |
Cone and partial order | |
Brouwer Degree | |
Compact map and Leray | |
Schauder Degree | |
Fredholm operators | |
Fixed point index | |
Banach's Contract Theorem, Implicit Functions Theorem | |
Krein | |
Rutman theorem | |
Bifurcation theory | |
Rearrangements of sets and functions | |
Genus and Category | |
Maximum principles and symmetry of solution | |
Comparison theorems | |
2 Cone and Partial Order Methods | |
Increasing operators | |
Decreasing operators | |
Mixed monotone operators | |
Applications of mixed monotone operators | |
Fur | |
ISBN: | 9783642307096 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, 1389-2177 : v29 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Title: | Rational Points and Arithmetic of Fundamental Groups [electronic resource] : Evidence for the Section Conjecture |
Author(s): |
Jakob Stix |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of itsfundamental group. Whi le the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only oneagainst rational points on curves. This monogr aph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and thelocal-to-global approach is studied in detail. The monograph concl udes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birationalanalogue in lieu of the fundamental group extension |
Note: | Springer eBooks |
Contents: | Part I Foundations of Sections |
1 Continuous Non | |
abelian H1 with Profinite Coefficients | |
2 The Fundamental Groupoid | |
3 Basic Geometric Operations in Terms of Sections | |
4 The Space of Sections as a Topological Space | |
5 Evaluation of Units | |
6 Cycle Classes in Anabelian Geometry | |
7 Injectivity in the Section Conjecture | |
Part II Basic Arithmetic of Sections | |
7 Injectivity in the Section Conjecture | |
8 Reduction of Sections | |
9 The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers | |
Part III On the Passage from Local to Global | |
10 Local Obstructions | |
ISBN: | 9783642306747 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2054 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Number theory |
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Call number: | SPRINGER-2013-9783319002576:ONLINE Show nearby items on shelf |
Title: | The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups [electronic resource] |
Author(s): |
Daciberg Lima Goncalves John Guaschi |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
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Note: | This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks animportant step in th e computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysisof their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups.This manuscript will serve as a reference for the study of bra id groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra |
Note: | Springer eBooks |
Contents: | Introduction and statement of the main results |
Virtually cyclic groups: generalities, reduction and the mapping class group | |
Realisation of the elements of V1(n) and V2(n) in Bn(S2) | |
Appendix: The subgroups of the binary polyhedral groups | |
References. | |
ISBN: | 9783319002576 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Algebraic topology |
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Title: | Pseudo-Differential Operators, Generalized Functions and Asymptotics [electronic resource] |
Author(s): |
Shahla Molahajloo Stevan Pilipovi Joachim Toft M. W Wong |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume consists of twenty peer-reviewed papers from the special sessions on pseudodifferential operators and on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples FriendshipUniversity of Russia in Moscow on August 2227, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifoldswith edges, heat kernels and Green functions of sub-Lapla cians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, L^p-boundedness of pseudo-differential operators on thetorus, and pseudo-differential operators related to time-frequency analysis. The s econd group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlineardifferential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differ ential equations. This second group of papers is related to the third collection of papers via the setting ofColombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volumecontains the synergi es of the three areas treatedand is a useful complement toitspredecessorspublished in the same series |
Note: | Springer eBooks |
Contents: | Preface |
Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds | |
The Singular Functions of Branching Edge Asymptotics | |
The Heat Kernel and Green Function of the Sub | |
Laplacian on the Heisenberg Group | |
Metaplectic Equivalence of the Hierarchical Twisted Laplacian | |
The Heat Kernel and Green Function of a Sub | |
Laplacian on the Hierarchical Heisenberg Group | |
Lp | |
Bounds for Pseudo | |
Differential Operators on the Torus | |
Multiplication Properties in Gelfand | |
Shilov Pseudo | |
Differential Calculus | |
Operator Invariance | |
Initial Value Problems in the Time | |
Frequency Do | |
ISBN: | 9783034805858 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v231 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034804813:ONLINE Show nearby items on shelf |
Title: | Complex Kleinian Groups [electronic resource] |
Author(s): |
Angel Cano Juan Pablo Navarrete Jos Seade |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph lays down the foundations of the theory of complex Kleinian groups, a newborn area of mathematics whose origin can be traced back to the work of Riemann, Poincar, Picard and many others. Kleinian groupsare, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions,there is a dichotomy: Should we look at conformal automorp hisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In thefirst case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition in the second, about an area of mathematics that is still in its infancy, and this is the focus ofstudy in this monograph. It brings together several important areas of mathematics, e.g. classical Kleini an group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Acknowledgments | |
1 A glance of the classical theory | |
2 Complex hyperbolic geometry | |
3 Complex Kleinian groups | |
4 Geometry and dynamics of automorphisms of P2C | |
5 Kleinian groups with a control group | |
6 The limit set in dimension two | |
7 On the dynamics of discrete subgroups of PU(n,1) | |
8 Projective orbifolds and dynamics in dimension two | |
9 Complex Schottky groups | |
10 Kleinian groups and twistor theory | |
Bibliography | |
Index. | |
ISBN: | 9783034804813 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v303 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Differentiable dynamical systems , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461487814:ONLINE Show nearby items on shelf |
Title: | Ricci Flow for Shape Analysis and Surface Registration [electronic resource] : Theories, Algorithms and Applications |
Author(s): |
Wei Zeng Xianfeng David Gu |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Ricci Flow for Shape Analysis and Surface Registration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate calculus, readers can deduce all themajor theorems in surfac e Ricci flow by themselves. The authors adapttheRicci flow theory to practical computational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricciflow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network. Due to minimal pre-requisites, this bookis accessible toengineersand medicalexperts, including educators,researchers, students and industry engineerswhohave an interest insolvingreal problems related to shape analysis and surface registration. |
Note: | Springer eBooks |
Contents: | 1. Introduction |
2. Computational | |
3.Computational Geometry | |
4. Differential Geometry of Surface | |
5. Riemann Surface | |
6. Ricci Flow | |
7. Topological Algorithms | |
8. Harmonic Maps | |
9. Discrete Ricci Flow | |
10. Shape Analysis | |
11. Surface Diffeomorphism | |
12. Medical Imaging Applications | |
13. Computer Vision Applications | |
14. Computer Graphics Applications | |
15. Network Applications. | |
ISBN: | 9781461487814 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Computer science Mathematics , Geometry , Discrete groups |
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Call number: | SPRINGER-2013-9781461480242:ONLINE Show nearby items on shelf |
Title: | Lie Groups [electronic resource] |
Author(s): |
Daniel Bump |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range ofmaterial to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests.This second edition has substantial new material, including improved discussions ofunderlying principles, streamlining of some pro ofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the PeterWeyl theorem, Lie algebra, conjugacy of maximal tori, the Weylgroup, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flagvarieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics tha t are treated are symmetric function theory, the representation theory of the symmetric group, FrobeniusSchur duality andGL(n)GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatoric s of tableaux, Gelfand pairs, Hecke algebras, the philosophy of cusp forms and thecohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations |
Note: | Springer eBooks |
Contents: | Part I: Compact Topological Groups |
1 Haar Measure | |
2 Schur Orthogonality | |
3 Compact Operators | |
4 The PeterWeyl Theorem | |
Part II: Compact Lie Groups | |
5 Lie Subgroups of GL(n,C) | |
6 Vector Fields | |
7 Left | |
Invariant Vector Fields | |
8 The Exponential Map | |
9 Tensors and Universal Properties | |
10 The Universal Enveloping Algebra | |
11 Extension of Scalars | |
12 Representations of sl(2,C) | |
13 The Universal Cover | |
14 The Local Frobenius Theorem | |
15 Tori | |
16 Geodesics and Maximal Tori | |
17 The Weyl Integration Formula | |
18 The Root System | |
19 Examples of Root Systems | |
ISBN: | 9781461480242 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v225 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups |
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Call number: | SPRINGER-2013-9781461479727:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis on Symmetric SpacesEuclidean Space, the Sphere, and the Poincar Upper Half-Plane [electronic resource] |
Author(s): |
Audrey Terras |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar upper half plane. This book is intended for beginning graduate students inmathematics or researchers in phy sics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, andengineering. Many corrections, new topics, and updates have be en incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T.Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question Can y ou hear the shape of a drum?, Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maasswaveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summationformula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon tr ansform, non-Euclidean geometry on the Poincar upper half plane H or unit disc andapplications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg tra ce formula and its applications in spectral theory as wellas number theory |
Note: | Springer eBooks |
Contents: | Chapter1 Flat Space. Fourier Analysis on R^m |
1.1 Distributions or Generalized Functions | |
1.2 Fourier Integrals | |
1.3 Fourier Series and the Poisson Summation Formula | |
1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions | |
1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyls Criterion for Uniform Distribution | |
Chapter2 A Compact Symmetric Space | |
The Sphere | |
2.1 Fourier Analysis on the Sphere | |
2.2 O(3) and R^3. The Radon Transform | |
Chapter 3 The Poincar Upper Half | |
Plane | |
3.1 Hyperbolic Geometry | |
3.2 Harmonic Analysis on H | |
3.3 Fundamental Domains for | |
ISBN: | 9781461479727 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Topological Groups , Harmonic analysis , Fourier analysis , Functions of complex variables , Functions, special |
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Call number: | SPRINGER-2013-9781461473008:ONLINE Show nearby items on shelf |
Title: | An Introduction to Quasisymmetric Schur Functions [electronic resource] Hopf Algebras, Quasisymmetric Functions, and Young Composition Tableaux |
Author(s): |
Kurt Luoto Stefan Mykytiuk Stephanie van Willigenburg |
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: | An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is to provide a reference text for the basic theoryof Hopf algebras, in particular the Hopf algebras of symmetric, quasisymmetric and noncommutative symmetric functions and connections between them. The second goal is to give a survey of results with respect to an exciting new basis ofthe Hopf algebra of quasisymmetric functi ons, whose combinatorics is analogous to that of the renowned Schur functions |
Note: | Springer eBooks |
Contents: | 1. Introduction |
2. Classical combinatorial concepts | |
3. Hopf algebras | |
4. Compsition tableaux and further combinatorial concepts | |
5. Quasisymmetric Schur functions | |
References | |
Index | |
ISBN: | 9781461473008 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Algorithms , Combinatorics |
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Call number: | SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf |
Title: | Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday |
Author(s): |
Alan Huckleberry Ivan Penkov Gregg Zuckerman |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted |
Note: | Springer eBooks |
Contents: | Preface |
Real group orbits on flag manifolds | |
Complex connections with trivial holonomy | |
Indefinite harmonic theory and harmonic spinors | |
Twistor theory and the harmonic hull | |
Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets | |
Propagation of the multiplicity | |
freeness property for holomorphic vector bundles | |
Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains | |
Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf | |
Weakly harmonic Maa forms and the princi | |
ISBN: | 9781461471936 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v306 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Functional analysis |
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Call number: | SPRINGER-2013-9781461471165:ONLINE Show nearby items on shelf |
Title: | Quantum Theory for Mathematicians [electronic resource] |
Author(s): |
Brian C Hall |
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: | Springer eBooks |
ISBN: | 9781461471165 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v267 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functional analysis , Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2013-9781461469568:ONLINE Show nearby items on shelf |
Title: | Measure Theory [electronic resource] : Second Edition |
Author(s): |
Donald L Cohn |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Intended as a self-contained introduction to measure theory, this textbook also includesa comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haarmeasures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and theexistence of liftings. Measure Theory provides a soli d background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. Theprerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review ofessential background material. The author aims to present a straightforward treatment of thepart of measure theory necessary for analysis and probability' assuming only basic knowledge of analysis and topol ogy...Each chapter includes numerous well-chosen exercises, varying from very routine practice problems to importantextensions and developments of the theory for the difficult ones there are helpful hints. It is the reviewer's opinion that the author has succeeded in his aim. In spite of its lack of new results, the selection and presentation ofmaterials makes this a useful book for an introduction to measure and integration theory. Mathematical Reviews (Review of the First Edition) The book is a compreh ensive and clearly written textbook on measure andintegration...The book contains appendices on set theory, algebra, calculus and topology in Euclidean spaces, topological and metric spaces, and the Bochner integral. Each section of the book contains a nu mber of exercises.zbMATH (Review of the First Edition) |
Note: | Springer eBooks |
Contents: | 1. Measures |
Algebras and sigma | |
algebras | |
Measures | |
Outer measures | |
Lebesgue measure | |
Completeness and regularity | |
Dynkin classes | |
2. Functions and Integrals | |
Measurable functions | |
Properties that hold almost everywhere | |
The integral | |
Limit theorems | |
The Riemann integral | |
Measurable functions again, complex | |
valued functions, and image measures | |
3. Convergence | |
Modes of Convergence | |
Normed spaces | |
Definition of L^p and L^p | |
Properties of L^p and L | |
p | |
Dual spaces | |
4. Signed and Complex Measures | |
Signed and complex measures | |
Absolute continuity | |
Singu | |
ISBN: | 9781461469568 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Birkhuser Advanced Texts Basler Lehrbcher, 1019-6242 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9781461464068:ONLINE Show nearby items on shelf |
Title: | Asymptotic Geometric Analysis [electronic resource] : Proceedings of the Fall 2010 Fields Institute Thematic Program |
Author(s): |
Monika Ludwig Vitali D Milman Vladimir Pestov Nicole Tomczak-Jaegermann |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as thedimension tends to inf inity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in theFall of 2010 continued an established traditi on of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces *Concentration of measure and isoperimetric inequalities, optimal transport ation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Randommatrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working ina wide range of mathematical sciencesin particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science |
Note: | Springer eBooks |
Contents: | Preface |
The Variance Conjecture on Some Polytopes (D. Alonso Gutirrez, J. Bastero) | |
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures (D. Bartosova) | |
On the Lyapounov Exponents of Schrodinger Operators Associated with the Standard Map (J. Bourgain) | |
Overgroups of the Automorphism Group of the Rado Graph (P. Cameron, C. Laflamme, M. Pouzet, S. Tarzi, R. Woodrow) | |
On a Stability Property of the Generalized Spherical Radon Transform (D. Faifman) | |
Banach Representations and Affine Compactification of Dynamical Systems (E. Glasner, M. Megrelishvili) | |
F | |
ISBN: | 9781461464068 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fields Institute Communications, 1069-5265 : v68 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functional analysis , Operator theory , Discrete groups , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9781461458883:ONLINE Show nearby items on shelf |
Title: | Drinfeld Moduli Schemes and Automorphic Forms [electronic resource] : The Theory of Elliptic Modules with Applications |
Author(s): |
Yuval Z Flicker |
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: | Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the authors original work establishing the correspondence between ell-adic rank r Galois representations andautomorphic representations of GL( r) over a function field, in the local case, and,in the global case, under a restriction at a single place. It develops Drinfelds theory of elliptic modules, their moduli schemes and coveringschemes, the simple trace formula, the fixed point formula, as w ell as the congruence relations and a simpleconverse theorem, not yet published anywhere. This version, based on a recent course taught by the author at TheOhioState University, is updated with references to research that has extended and developed the or iginal work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as avaluable resource to facilitate anentrance to this fascinating area of mathematics |
Note: | Springer eBooks |
Contents: | Elliptic Moduli |
Hecke Correspondences | |
Trace Formulae | |
Higher Recipropcity Laws. | |
ISBN: | 9781461458883 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Number theory |
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Call number: | SPRINGER-2013-9781461453925:ONLINE Show nearby items on shelf |
Title: | Interpolation and Sidon Sets for Compact Groups [electronic resource] |
Author(s): |
Colin C Graham Kathryn E Hare |
Date: | 2013 |
Publisher: | Boston, MA : Springer US : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Understanding special sets of integers was classically of interest to Hadamard, Zygmund and others, and continues to be of interest today. This book is a modern treatment of the subject of interpolation and Sidon sets. It is aunique book, aimed at bo th new and experienced researchers. In particular, this is the only book in Englishwhich featuresa complete treatment of the Pisier-Bourgain results on Sidon sets, many of which were originally in French, inhard to access publications. Applications of the P-B results, due to Pisier, Bourgain, Ramsey, and the authors are included.The book introduces the reader to a wealth of methods important in mathematics today: topological,probabilistic, algebraic, combinatoric and analytic. It prepares students to perf orm research in the area and provides both exercises and open problems. The book also provides direction to the literature for topics it does not fullycover. The book is self-contained, with appendices covering results that are required, but not necessari ly in the pre-requisite background of a student ready to choose an area for research in harmonic analysis |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Hadamard Sets | |
$\epsilon$ | |
Kronecker sets | |
Sidon sets: Introduction and decomposition properties | |
Characterizations of $I_0$ sets | |
Proportional characterizations of Sidon sets | |
Decompositions of $I_0$ sets | |
Sizes of thin sets | |
Sets of zero discrete harmonic density | |
Related results | |
Open problems | |
Appendices (Groups, Probability, Combinatoric results,...) | |
Bibliography | |
Author index | |
Subject index | |
Index of notation | |
ISBN: | 9781461453925 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | CMS Books in Mathematics, Ouvrages de mathmatiques de la SMC, 1613-5237 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Functional analysis |
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Call number: | SPRINGER-2013-9781461450580:ONLINE Show nearby items on shelf |
Title: | Uniform Spaces and Measures [electronic resource] |
Author(s): |
Jan Pachl |
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: | Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures -- a need that became more critical when uniform measures recently reemerged in new results inabstract harmonic analysis. Until now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations. Uniform measures arefunctionals on the space of bounded uniformly continuo us functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in topological measure theory, probabilitytheory, and abstract harmonic analysis. They offer a natural framework for resu lts about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. Thisbook can serve as a reference for the theory of uniform measures. It includes a self-contained develop ment of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It also includes severalnew results, and presents diverse results from many sources organized in a logical whole. The content is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis, and containsa number of exercises with hints to solutions as well as several open problems with suggestions for further research |
Note: | Springer eBooks |
Contents: | Prerequisites |
1. Uniformities and Topologies | |
2. Induced Uniform Structures | |
3. Uniform Structures on Semigroups | |
4. Some Notable Classes of Uniform Spaces | |
5. Measures on Complete Metric Spaces | |
6. Uniform Measures | |
7. Uniform Measures as Measures | |
8. Instances of Uniform Measures | |
9. Direct Product and Convolution | |
10. Free Uniform Measures | |
11. Approximation of Probability Distributions | |
12. Measurable Functionals | |
Hints to Excercises | |
References | |
Notation Index | |
Author Index | |
Subject Index | |
ISBN: | 9781461450580 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fields Institute Monographs, 1069-5273 : v30 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Functions of complex variables |
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Call number: | SPRINGER-2013-9781441979100:ONLINE Show nearby items on shelf |
Title: | A Course in Topological Combinatorics [electronic resource] |
Author(s): |
Mark Longueville |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years withgrowing applications i n math, computer science, and other applied areas. Topological combinatorics is concerned with solutions to combinatorial problems by applying topological tools. In most cases these solutions are very elegant andthe connection between combinatorics and to pology often arises as an unexpected surprise. The textbook covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discretegeometry. The text contains a large number of figures that suppo rt the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given, and each chapter ends with a series of exercises. Theextensive appendix makes the book completely self-contained. The textbook is well sui ted for advanced undergraduate or beginning graduate mathematics students. Previous knowledge in topology or graph theory is helpful but notnecessary. The text may be used as a basis for a one- or two-semester course as well as a supplementary text for a topology or combinatorics class |
Note: | Springer eBooks |
Contents: | Preface |
List of Symbols and Typical Notation | |
1 Fair | |
Division Problems | |
2 Graph | |
Coloring Problems | |
3 Evasiveness of Graph Properties | |
4 Embedding and Mapping Problems | |
A Basic Concepts from Graph Theory | |
B Crash Course in Topology | |
C Partially Ordered Sets, Order Complexes, and Their Topology | |
D Groups and Group Actions | |
E Some Results and Applications from Smith Theory | |
References | |
Index | |
ISBN: | 9781441979100 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Combinatorics , Discrete groups |
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Call number: | SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf |
Title: | New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number |
Author(s): |
Garret Sobczyk |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s |
Note: | Springer eBooks |
Contents: | 1 Modular Number Systems |
2 Complex and Hyperbolic Numbers | |
3 Geometric Algebra | |
4 Vector Spaces and Matrices | |
5 Outer Product and Determinants | |
6 Systems of Linear Equations | |
7 Linear Transformations on R^n | |
8 Structure of a Linear Operator | |
9 Linear and Bilinear Forms | |
10 Hermitian Inner Product Spaces | |
11 Geometry of Moving Planes | |
12 Representations of the Symmetric Group | |
13 Calculus on m | |
Surfaces | |
14 Differential Geometry of Curves | |
15 Differential Geometry of k | |
Surfaces | |
16 Mappings Between Surfaces | |
17 Non | |
Euclidean and Projective Geometries | |
18 Lie Gr | |
ISBN: | 9780817683856 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2013-9780817683641:ONLINE Show nearby items on shelf |
Title: | Configurations from a Graphical Viewpoint [electronic resource] |
Author(s): |
Toma Pisanski Brigitte Servatius |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. Inthis self-contained tex tbook, algebraic graph theory is used to introduce groups topological graph theory is used to explore surfaces and geometric graph theory is implemented to analyze incidence geometries. After a preview ofconfigurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied.Geometric aspects, some historical remarks, references, and applicationsof classicalconfigurationsappear in the last chapter. With over two hundred illustrations, challenging exercises at t he end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint iswell suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicia ns and researchers |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Graphs | |
Groups, Actions, and Symmetry | |
Maps | |
Combinatorial Configurations | |
Geometric Configurations | |
Index | |
Bibliography | |
ISBN: | 9780817683641 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Birkhuser Advanced Texts Basler Lehrbcher |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Combinatorics , Geometry , Topology |
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Call number: | SPRINGER-2012-9783642227172:ONLINE Show nearby items on shelf |
Title: | The Schrdinger-Virasoro Algebra [electronic resource] Mathematical structure and dynamical Schrdinger symmetries |
Author(s): |
Jrmie Unterberger Claude Roger |
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 monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structurethe Schrdinger-Virasoro algebra. Just as Poincar invariance or conformal (Virasoro) invarianceplay a key role in understanding , respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study ofsome models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Liealgebra touches upon topics as various as statistical physics, vertex algebras, Po isson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and thespectral theory of Schrdinger operators. |
Note: | Springer eBooks |
Contents: | Introduction |
Geometric Definitions of SV | |
Basic Algebraic and Geometric Features | |
Coadjoint Representaion | |
Induced Representations and Verma Modules | |
Coinduced Representations | |
Vertex Representations | |
Cohomology, Extensions and Deformations | |
Action of sv on Schrdinger and Dirac Operators | |
Monodromy of Schrdinger Operators | |
Poisson Structures and Schrdinger Operators | |
Supersymmetric Extensions of sv | |
Appendix to chapter 6 | |
Appendix to chapter 11 | |
Index | |
ISBN: | 9783642227172 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Algebra , Topological Groups , Mathematical physics |
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Call number: | SPRINGER-2012-9783642227165:ONLINE Show nearby items on shelf |
Title: | The Schringer-Virasoro Algebra [electronic resource] |
Author(s): |
Jie Unterberger Claude Roger |
Date: | 2012 |
Publisher: | Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Monograph |
Note: | Springer 2012 Physics and Astronomy eBook collection |
Note: | Springer e-book platform |
ISBN: | 9783642227165 |
Series: | Texts and Monographs in Physics |
Series: | e-books |
Keywords: | Mathematical Methods in Physics , Topological Groups, Lie Groups , Mathematical Physics , Category Theory, Homological Algebra , Statistical Physics, Dynamical Systems and Complexity |
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Call number: | SPRINGER-2012-9783642225970:ONLINE Show nearby items on shelf |
Title: | Topics in Noncommutative Algebra [electronic resource] : The Theorem of Campbell, Baker, Hausdorff and Dynkin |
Author(s): |
Andrea Bonfiglioli Roberta Fulci |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, NumericalAnalysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: 1) fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra ornot) to understand and apply the statements and numero us corollaries of the main result 2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view andnotation 3) provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincar, Pascal, Campbell, Baker, Hausdorff and Dynkin 4) give an outlook on theapplications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) 5 ) quickly enable the reader, through a description of the state-of-art and open problems, to understand the modernliterature concerning a theorem which, though having its roots in the beginning of the20th century, has not ceased to provide new problems an d applications. The book assumes some undergraduate-level knowledge of algebra and analysis,but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool fo r beginners in Algebra |
Note: | Springer eBooks |
Contents: | 1 Historical Overview |
Part I Algebraic Proofs of the CBHD Theorem | |
2 Background Algebra | |
3 The Main Proof of the CBHD Theorem | |
4 Some Short Proofs of the CBHD Theorem | |
5 Convergence and Associativity for the CBHD Theorem | |
6 CBHD, PBW and the Free Lie Algebras | |
Part II Proofs of the Algebraic Prerequisites | |
7 Proofs of the Algebraic Prerequisites | |
8 Construction of Free Lie Algebras | |
9 Formal Power Series in One Indeterminate | |
10 Symmetric Algebra | |
ISBN: | 9783642225970 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2034 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global differential geometry |
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Call number: | SPRINGER-2012-9783034801546:ONLINE Show nearby items on shelf |
Title: | Frames and Locales [electronic resource] : Topology without points |
Author(s): |
Jorge Picado Ale Pultr |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the 1920s offered an expression of the geometric intuition of arealistic place (spot, gr ain) of non-trivial extent. Imitating the behaviour of open sets and their relationsled to a new approach to topology flourishing since the end of the 1950s. It has proved to be beneficial in manyrespects. Neglecting points, only little information was lo st, while deeper insights have been gained moreover, many results previously dependent onchoice principles became constructive. The result is often a smoother, rather than amore entangled, theory. No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book formfor the first time or is presented from new points of view. Two appendices provide an introduction to s ome requisite concepts from order and category theories |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
I. Spaces and lattices of open sets | |
II. Frames and locales. Spectra | |
III. Sublocales | |
IV. Structure of localic morphisms. The categories Loc and Frm | |
V. Separation axioms | |
VI. More on sublocales | |
VII. Compactness and local compactness | |
VIII. (Symmetric) uniformity and nearness | |
IX. Paracompactness | |
X. More about completion | |
XI. Metric frames | |
XII. Entourages, non | |
symmetric uniformity | |
XIII. Connectedness | |
XIV. The frame of reals and real functions | |
XV. Localic groups | |
Appendix I: Posets | |
Appendix II: Categories | |
Bibliography | |
Index | |
ISBN: | 9783034801546 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topology |
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Call number: | SPRINGER-2012-9781447122944:ONLINE Show nearby items on shelf |
Title: | Syzygies and Homotopy Theory [electronic resource] |
Author(s): |
F.E.A Johnson |
Date: | 2012 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivialfundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematicrehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. Theinnovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation these are confronted in the second, practical, part of the book. Inparticular, the second part of the book considers how the theory works out in detail for the specific e xamples Fn F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms ofthe more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potentialapplications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of inte rest to researchers and also to graduate students with a background in algebra andalgebraic topology |
Note: | Springer eBooks |
Contents: | Preliminaries |
The restricted linear group | |
The calculus of corners and squares | |
Extensions of modules | |
The derived module category | |
Finiteness conditions | |
The Swan mapping | |
Classification of algebraic complexes | |
Rings with stably free cancellation | |
Group rings of cyclic groups | |
Group rings of dihedral groups | |
Group rings of quaternionic groups | |
Parametrizing W1 (Z) : generic case | |
Parametrizing W1 (Z) : singular case | |
Generalized Swan modules | |
Parametrizing W1 (Z) : G = C F | |
Conclusion | |
ISBN: | 9781447122944 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications, 1572-5553 : v17 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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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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