Complex analysis, complex variables Books
RAND Air Force Capability Development Planning:
Book Synopsis
£17.59
Mathematical Society of Japan Moduli Spaces And Arithmetic Geometry
Book SynopsisSince its birth algebraic geometry has been closely related to and deeply motivated by number theory. Particularly the modern study of moduli spaces and arithmetic geometry have many important techniques and ideas in common. With this close relation in mind, the RIMS conference Moduli Spaces and Arithmetic Geometry was held at Kyoto University during September 8-15, 2004 as the 13th International Research Institute of the Mathematical Society of Japan. This volume is the outcome of this conference and consists of thirteen papers by invited speakers, including C Soulé, A Beauville and C Faber, and participants. All papers, with two exceptions by C Voisin and Yoshinori Namikawa, treat moduli problem and/or arithmetic geometry. Algebraic curves, Abelian varieties, algebraic vector bundles, connections and D-modules are the subjects of those moduli papers. Arakelov geometry and rigid geometry are studied in arithmetic papers. In the two exceptions, integral Hodge classes on Calabi-Yau threefolds and symplectic resolutions of nilpotent orbits are studied.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North AmericaTable of ContentsModuli spaces of twisted sheaves on a projective variety by K. Yoshioka Appendix. Proof of Caldararu's conjecture by D. Huybrechts and P. Stellari On integral Hodge classes on uniruled or Calabi-Yau threefolds by C. Voisin Birational geometry of symplectic resolutions of nilpotent orbits by Y. Namikawa The moduli stack of rank-two Gieseker bundles with fixed determinant on a nodal curve by T. Abe Vector bundles on curves and theta functions by A. Beauville On the finiteness of abelian varieties with bounded modular height by A. Moriwaki Moduli of regular holonomic $\mathcal{D}_X$-modules with natural parabolic stability by N. Nitsure The cohomology groups of stable quasi-abelian schemes and degenerations associated with the $E_8$-lattice by I. Nakamura and K. Sugawara Semi-stable extensions on arithmetic surfaces by C. Soule On the cusp form motives in genus 1 and level 1 by C. Consani and C. Faber Polarized K3 surfaces of genus thirteen by S. Mukai Rigid geometry and applications by K. Fujiwara and F. Kato Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painleve equation of type VI, part II by M. Inaba, K. Iwasaki, and M. Saito.
£80.75
Mathematical Society of Japan Potential Theory In Matsue - Proceedings Of The
Book SynopsisThis volume collects, in written form, eight plenary lectures and twenty-five selected contributions from invited and contributed lectures delivered at the International Workshop on Potential Theory 2004. The workshop was held at Shimane University, Matsue, Japan, from 23 to 28 August, 2004. The topic of the workshop was Potential Theory and its related fields. There were stimulus talks from classical potential theory to pluri-potential theory and probabilistic potential theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America
£81.70
Mathematical Society of Japan Singularities In Geometry And Topology 2004
Book SynopsisThis volume constitutes the proceedings of the third Franco-Japanese symposium on singularities, held in Sapporo in September 2004. It contains not only research papers on the most advanced topics in the field, but also some survey articles which give broad scopes in some areas of the subject. All the articles are carefully refereed for correctness and readability.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North AmericaTable of ContentsCobordism of fibered knots and related topics by V. Blanloeil and O. Saeki Proportionality of indices of 1-forms on singular varieties by J.-P. Brasselet, J. Seade, and T. Suwa Motivic sheaves and intersection cohomology by M. Hanamura On hyperbolic perturbations of algebraic links and small Mahler measure by E. Hironaka Stably hyperbolic polynomials by V. P. Kostov On weighted-degrees for algebraic local cohomologies associated with semiquasihomogeneous singularities by Y. Nakamura and S. Tajima The geometry of continued fractions and the topology of surface singularities by P. Popescu-Pampu Exemples de fonctions de Artin de germes d'espaces analytiques by G. Rond Perverse sheaves and Milnor fibers over singular varieties by K. Takeuchi On Horn-Kapranov uniformisation of the discriminantal loci by S. Tanabe Duality of Euler data for affine varieties by M. Tibuar Algebre graduee associee a une valuation de $K[x]$ by M. Vaquie Plane curve singularities whose Milnor and Tjurina numbers differ by three by M. Watari Characteristic classes of (pro)algebraic varieties by S. Yokura.
£80.75
World Scientific Publishing Co Pte Ltd Zeta Regularization Techniques With Applications
Book SynopsisThis book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.Table of ContentsPart 1 The Riemann Zeta function: Riemann, Hurwitz, Epstein, Selberg and related zeta functions; analytic continuation - practical uses for series summation; asymptotic expansion of "zeta". Part 2 Zeta-function regularization of sums over known spectrum: the zeta-function regularization theorem; multiple zeta-functions with arbitrary exponents. Part 3 Zeta-function regularization when the spectrum is not known: zeta-function vs heat-kernel regularization; small-"t" asymptotic expansion of the heat-kernel. Part 4 The Casimir effect in flat space-time with compact spatial part: simply connected compact manifold with constant curvature; the Selberg trace formula for compact hyperbolic manifolds. Part 5 Finite temperature effects for theories defined on compact hyperbolic manifolds: basic formalism for the finite-temperature effective potential; the finite-temperature thermodynamic potential for manifolds with a compact spatial part. Part 6 Properties of the chemical potential in higher-dimensional manifolds: the flat-manifold case; the constant non-zero curvature case. Part 7 Strings at non-zero temperature and 2d gravity: free energy for the Bosonic string; vacuum energy for Torus compactified strings. Part 8 Membranes at non-zero temperatures: supermembrane free energy; free energy for the compactified supermembranes and modular invariance; and others.
£95.00
World Scientific Publishing Co Pte Ltd Semi-classical Analysis For Nonlinear Schrodinger
Book SynopsisThese lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated.These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided.Table of ContentsWKB Analysis: Preliminary Analysis; Weak Nonlinearity; Modulated Energy Functionals; Point-wise Description; Some Instability Phenomena; Caustic Crossing: The Case of Focal Points: Caustic Crossing: Formal Analysis; Focal Point without External Potential; Focal Point with a Potential; Some Ideas for Supercritical Cases.
£80.75
World Scientific Publishing Co Pte Ltd Approximation By Complex Bernstein And
Book SynopsisThe monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein—Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados.The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented.Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.Table of ContentsBernstein-Type Operators of One Complex Variable: Auxiliary Results in Complex Analysis; Bernstein Polynomials; Iterates of Bernstein Polynomials; Generalized Voronovskaja Theorems for Bernstein Polynomials; Butzer's Linear Combination of Bernstein Polynomials; q-Bernstein Polynomials; Bernstein-Stancu Polynomials; Bernstein-Kantorovich Type Polynomials; Favard-Szasz-Mirakjan Operators; Baskakov Operators; Balazs-Szabados Operators; Bibliographical Notes and Open Problems; Bernstein-Type Operators of Several Complex Variables: Introduction; Bernstein Polynomials; Favard-Szasz-Mirakjan Operators; Baskakov Operators; Bibliographical Notes and Open Problems; Complex Convolutions: Linear Polynomial Convolutions; Linear Non-Polynomial Convolutions; Nonlinear Complex Convolutions; Bibliographical Notes and Open Problems; Appendices: Related Topics: Bernstein Polynomials of Quaternion Variable; Approximation of Vector-Valued Functions; Strong Approximation by Complex Taylor Series; Bibliographical Notes and Open Problems.
£100.70
Society for Industrial & Applied Mathematics,U.S. Mastering Frequency Domain Techniques for the
Book SynopsisIn many dynamical systems, time delays arise because of the time it takes to measure system states, perceive and evaluate events, formulate decisions, and act on those decisions. The presence of delays may lead to undesirable outcomes; without an engineered design, the dynamics may underperform, oscillate, and even become unstable. How to study the stability of dynamical systems influenced by time delays is a fundamental question. Related issues include how much time delay the system can withstand without becoming unstable and how to change system parameters to render improved dynamic characteristics, utilize or tune the delay itself to improve dynamical behavior, and assess the stability and speed of response of the dynamics. Mastering Frequency Domain Techniques for the Stability Analysis of LTI Time Delay Systems addresses these questions for linear time-invariant (LTI) systems with an eigenvalue-based approach built upon frequency domain techniques. Readers will find key results from the literature, including all subtopics for those interested in deeper exploration. The book presents step-by-step demonstrations of all implementations—including those that require special care in mathematics and numerical implementation—from the simpler, more intuitive ones in the introductory chapters to the more complex ones found in the later chapters. Maple and MATLAB code is available from the author’s website.This multipurpose book is intended for graduate students, instructors, and researchers working in control engineering, robotics, mechatronics, network control systems, human-in-the-loop systems, human-machine systems, remote control and tele-operation, transportation systems, energy systems, and process control, as well as for those working in applied mathematics, systems biology, and physics. It can be used as a primary text in courses on stability and control of time delay systems and as a supplementary text in courses in the above listed domains.
£64.60
Springer International Publishing Fundamentals of Fourier Analysis
Book SynopsisThis self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables.
£999.99
Springer International Publishing AG Metrical and Dynamical Aspects in Complex
Book SynopsisThe central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.Table of Contents1. Invariant Distances.- 2. Dynamics in Several Complex Variables.- 3. Gromov Hyperbolic Spaces and Applications to Complex Analysis.- 4. Gromov Hyperbolicity of Bounded Convex Domains.- 5. Quasi-conformal Mappings.- 6. Carleson Measures and Toeplitz Operators. References.
£999.99
Princeton University Press The Real Fatou Conjecture
Book SynopsisIn 1920, Pierre Fatou expressed the conjecture that - except for special cases - all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This book provides a proof of the Real Fatou Conjecture. It includes a self-contained and complete version of the argument.Table of Contents1Review of Concepts31.1Theory of Quadratic Polynomials31.2Dense Hyperbolicity61.3Steps of the Proof of Dense Hyperbolicity122Quasiconformal Gluing252.1Extendibility and Distortion262.2Saturated Maps302.3Gluing of Saturated Maps353Polynomial-Like Property453.1Domains in the Complex Plane453.2Cutting Times474Linear Growth of Moduli674.1Box Maps and Separation Symbols674.2Conformal Roughness874.3Growth of the Separation Index1005Quasiconformal Techniques1095.1Initial Inducing1095.2Quasiconformal Pull-back1205.3Gluing Quasiconformal Maps1295.4Regularity of Saturated Maps1335.5Straightening Theorem139Bibliography143Index147
£999.99
Princeton University Press Rigid Local Systems
Book SynopsisThe author introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise.Trade Review"It is clear that this book presents highly important new views and results on the classical theory of complex linear differential equations."--Zentralblatt fur MathematikTable of Contents* First results on rigid local systems * The theory of middle concolution * Fourier Transform and rigidity * Middle concolution: dependence on parameters * Structure of rigid local systems * Existence algorithms for rigids * Diophantine aspects of rigidity * rigids
£999.99
Princeton University Press Complex Ball Quotients and Line Arrangements in
Book SynopsisThis book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. Paula Tretkoff emphasizes those finite covers that are free quotients of the complex two-dimensional ball. Tretkoff also includes background on the classical Gauss hypergeometric function of oneTrade Review"A very welcome addition to the literature and is recommended for anyone interested in the theory under discussion."--Daniel Greb, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*Introduction, pg. 1*Chapter One. Topological Invariants and Differential Geometry, pg. 6*Chapter Two. Riemann Surfaces, Coverings, and Hypergeometric Functions, pg. 23*Chapter Three. Complex Surfaces and Coverings, pg. 47*Chapter Four. Algebraic Surfaces and the Miyaoka-Yau Inequality, pg. 65*Chapter Five. Line Arrangements in P2(C) and Their Finite Covers, pg. 85*Chapter Six. Existence of Ball Quotients Covering Line Arrangements, pg. 126*Chapter Seven. Appell Hypergeometric Functions, pg. 167*Appendix A. Torsion-Free Subgroups of Finite Index by Hans-Christoph Im Hof, pg. 189*Appendix B. Kummer Coverings, pg. 197*Bibliography, pg. 205*Index, pg. 213
£60.00
Princeton University Press Advances in Analysis
Book SynopsisPrinceton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. This volume gathers papers from internationally renowned mathematicians, many of whom have been Stein's students.Table of ContentsPreface ix Chapter 1 Selected Theorems by Eli Stein 1 Charles Fefferman Chapter 2 Eli's Impact: A Case Study 35 Charles Fefferman Chapter 3 On Oscillatory Integral Operators in Higher Dimensions 47 Jean Bourgain Chapter 4 Holder Regularity for Generalized Master Equations with Rough Kernels 63 Luis Caffarelli and Luis Silvestre Chapter 5 Extremizers of a Radon Transform Inequality 84 Michael Christ Chapter 6 Should We Solve Plateau's Problem Again? 108 Guy David Chapter 7 Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups: Singular Radon Transforms 146 Alexandru D. Ionescu, Akos Magyar, and Stephen Wainger Chapter 8 Internal DLA for Cylinders 189 David Jerison, Lionel Levine, and Scott Sheffield Chapter 9 The Energy Critical Wave Equation in 3D 215 Carlos Kenig Chapter 10 On the Bounded L2 Curvature Conjecture 224 Sergiu Klainerman Chapter 11 On Div-Curl for Higher Order 245 Loredana Lanzani and Andrew S. Raich Chapter 12 Square Functions and Maximal Operators Associated with Radial Fourier Multipliers 273 Sanghyuk Lee, Keith M. Rogers, and Andreas Seeger Chapter 13 Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in 3, and Newton Polyhedra 303 Detlef Muller Chapter 14 Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length 346 Camil Muscalu, Terence Tao, and Christoph Thiele Chapter 15 Diagonal Estimates for Bergman Kernels in Monomial-Type Domains 402 Alexander Nagel and Malabika Pramanik Chapter 16 On the Singularities of the Pluricomplex Green's Function 419 D. H. Phong and Jacob Sturm Chapter 17 Smoothness of Spectral Multipliers and Convolution Kernels in Nilpotent Gelfand Pairs 436 Fulvio Ricci Chapter 18 On Eigenfunction Restriction Estimates and L4-Bounds for Compact Surfaces with Nonpositive Curvature 447 Christopher D. Sogge and Steve Zelditch List of Contributors 463 Index 465
£90.00
Princeton University Press Topics in Quaternion Linear Algebra
Book SynopsisQuaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quateTrade ReviewOne of Choice's Outstanding Academic Titles for 2015 "Rodman fills a void in the monographic literature with this work."--Choice "The book is self-contained and well organized... Full and detailed proofs are supplied. Another exciting point is the presence of many open problems throughout the book."--Gisele C. Ducati, MatchSciNetTable of Contents*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. xi*Chapter One. Introduction, pg. 1*Chapter Two. The algebra of quaternions, pg. 9*Chapter Three. Vector spaces and matrices: Basic theory, pg. 28*Chapter Four. Symmetric matrices and congruence, pg. 64*Chapter Five. Invariant subspaces and Jordan form, pg. 83*Chapter Six. Invariant neutral and semidefinite subspaces, pg. 131*Chapter Seven. Smith form and Kronecker canonical form, pg. 153*Chapter Eight. Pencils of hermitian matrices, pg. 172*Chapter Nine. Skewhermitian and mixed pencils, pg. 194*Chapter Ten. Indefinite inner products: Conjugation, pg. 228*Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution, pg. 261*Chapter Twelve. Mixed matrix pencils: Nonstandard involutions, pg. 279*Chapter Thirteen. Indefinite inner products: Nonstandard involution, pg. 300*Chapter Fourteen. Matrix equations, pg. 328*Chapter Fifteen. Appendix: Real and complex canonical forms, pg. 339*Bibliography, pg. 353*Index, pg. 361
£73.80
Taylor & Francis Inc Finite or Infinite Dimensional Complex Analysis
Book SynopsisThis volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.Table of ContentsModular space for complete intersection curve-singularities; quasinormability of vector valued sequence spaces; holomorphic mappings and cardinality; approximation numbers for polynomials; applications of Laguerre calculus to Dirichlet problem of the Heisenberg Laplacian; the Pisier-Schutt theorem for spaces of polynomials; canonical versus functional extensions of holomorphic functions; on convergence of trigonometric interpolation for periodic analytic functions; on the double series expansion with harmonic components; extension of pluriharmonic functions in locally convex spaces; regeneration in complex, quaternionic and Clifford analysis; Schauder decompositions of weighted spaces of holomorphic functions; spaces of Banach-valued holomorphic functions in the polydisk in connection with their boundary values; univalent C4 mappings on the unit ball in C; the growth theorem of biholomorphic mappings on a Banach space; stability of solutions for singular integral equations for two classes in locally convex spaces; the Nevanlinna's first main theorem for holomorphic Hermitian line bundles; on distortion theorem for N-set quasiconformal mappings; monodromy of a holomorphic family of Riemann surfaces - a remark on monodromy of a holomorphic family of Riemann surfaces induced by a Kodaira surface and the Nielsen-Thurston-Bers classification of surface automorphisms; characterisations of holomorphy of domains through validity of theorem A, B or Oka's principle; envelope of biregularity and F-convexity in Clifford analysis; on a representative domain in a matrix space; a new approximation of tree Navier-Stokes equations; generalisation du produit de Blaschke dans le Bidisque Unite; P-spaces. (Part contents).
£275.50
John Wiley & Sons Inc Global Dynamics
Book SynopsisA world model: economies, trade, migration, security and development aid. This bookprovides the analytical capability to understand and explore the dynamics of globalisation. It is anchored in economic input-output models of over 200 countries and their relationships through trade, migration, security and development aid. The tools of complexity science are brought to bear and mathematical and computer models are developed both for the elements and for an integrated whole. Models are developed at a variety of scales ranging from the global and international trade through a European model of inter-sub-regional migration to piracy in the Gulf and the London riots of 2011. The models embrace the changing technology of international shipping, the impacts of migration on economic development along with changing patterns of military expenditure and development aid. A unique contribution is the level of spatial disaggregation which presents each of 200+ countries and their muTable of ContentsNotes on Contributors xiii Acknowledgements xvii Part I GLOBAL DYNAMICS AND THE TOOLS OF COMPLEXITY SCIENCE 1 Global Dynamics and the Tools of Complexity Science 3Alan Wilson Reference 7 Part II TRADE AND ECONOMIC DEVELOPMENT 2 The Global Trade System and Its Evolution 11Simone Caschili and Francesca Medda 2.1 The Evolution of the Shipping and Ports’ System 11 2.2 Analyses of the Cargo Ship Network 12 2.3 A Complex Adaptive Systems (CASs) Perspective 15 2.4 Conclusions: The Benefits of a Systems Perspective 20 References 21 Appendix 23 A.1 Complexity Science and Complex Adaptive Systems: Key Characteristics 23 A.1.1 Four Properties 24 A.1.2 Three Mechanisms 25 3 An Interdependent Multi-layer Model for Trade 26Simone Caschili, Francesca Medda, and Alan Wilson 3.1 Introduction 26 3.2 The Interdependent Multi-layer Model: Vertical Integration 27 3.3 Model Layers 30 3.3.1 Economic Layer 30 3.3.2 Social and Cultural Layer (Socio-cultural) 33 3.3.3 Physical Layer 34 3.4 The Workings of the Model 34 3.5 Model Calibration 35 3.6 Result 1: Steady State 39 3.7 Result 2: Estimation and Propagation of Shocks in the IMM 42 3.8 Discussion and Conclusions 48 References 48 4 A Global Inter-country Economic Model Based on Linked Input–Output Models 51Robert G. Levy, Thomas P. Oléron Evans, and Alan Wilson 4.1 Introduction 51 4.2 Existing Global Economic Models 52 4.3 Description of the Model 53 4.3.1 Outline 53 4.3.2 Introduction to Input–Output Tables 53 4.3.3 A Single Country Model 55 4.3.4 An International Trade Model 57 4.3.5 Setting Model Coefficients from Data 58 4.4 Solving the Model 58 4.4.1 The Leontief Equation 58 4.4.2 The Drawbacks of Mathematical Elegance 59 4.4.3 Algorithm for an Iterative Solution 59 4.5 Analysis 61 4.5.1 Introduction 61 4.5.2 Simple Modelling Approaches 61 4.5.3 A Unified Network Approach 64 4.5.4 Comparison with a Multi-region Input–Output Model 67 4.6 Conclusions 67 Acknowledgements 69 References 69 Appendix 71 A.1 Modelling the ‘Rest of the World’ 71 A.2 Services Trade Data 71 A.2.1 Importing Own Exports 72 A.2.2 The Rest of the World for Sectors 72 Part III MIGRATION 5 Global Migration Modelling: A Review of Key Policy Needs and Research Centres 75Adam Dennett and Pablo Mateos 5.1 Introduction 75 5.2 Policy and Migration Research 76 5.2.1 Key Policy Issues in Contemporary Migration Research 76 5.2.2 Linking Policy Issues to Modelling Challenges 81 5.2.3 Policy-related Research Questions for Modellers 82 5.2.4 Other International Migration Modelling Research 83 5.3 Conclusion 84 References 84 Appendix 87 A.1 United Kingdom 87 A.2 Rest of Europe 90 A.3 Rest of the World 94 6 Estimating Inter-regional Migration in Europe 97Adam Dennett and Alan Wilson 6.1 Introduction 97 6.2 The Spatial System and the Modelling Challenge 98 6.3 Biproportional Fitting Modelling Methodology 100 6.3.1 Model (i) 104 6.3.2 Model (ii) 105 6.3.3 Model (iii) 105 6.3.4 Model (iv) 108 6.3.5 Model (v) 109 6.3.6 Model (vi) 110 6.4 Model Parameter Calibration 110 6.5 Model Experiments 113 6.6 Results 118 6.7 Conclusions and Comments on the New Framework for Estimating Inter-regional, Inter-country Migration Flows in Europe 121 References 123 7 Estimating an Annual Time Series of Global Migration Flows – An Alternative Methodology for Using Migrant Stock Data 125Adam Dennett 7.1 Introduction 125 7.2 Methodology 129 7.2.1 Introduction 129 7.2.2 Calculating Migration Probabilities 129 7.2.3 Calculating Total Migrants in the Global System 130 7.2.4 Generating a Consistent Time Series of Migration Probabilities 133 7.2.5 Producing Annual Bilateral Estimates 135 7.3 Results and Validation 135 7.3.1 Introduction 135 7.3.2 IMEM comparison 135 7.3.3 UN Flow Data Comparison 136 7.4 Discussion 138 7.5 Conclusions 140 References 140 Part IV SECURITY 8 Conflict Modelling: Spatial Interaction as Threat 145Peter Baudains and Alan Wilson 8.1 Introduction 145 8.2 Conflict Intensity: Space–Time Patterning of Events 146 8.3 Understanding Conflict Onset: Simulation-based Models 148 8.4 Forecasting Global Conflict Hotspots 150 8.5 A Spatial Model of Threat 150 8.6 Discussion: The Use of a Spatial Threat Measure in Models of Conflict 153 8.6.1 Threat in Models for Operational Decision-Making 153 8.6.2 Threat in a Model of Conflict Escalation 154 8.6.3 Threat in Modelling Global Military Expenditure 156 8.6.4 Summary 156 References 157 9 Riots 159Peter Baudains 9.1 Introduction 159 9.2 The 2011 Riots in London 160 9.2.1 Space–Time Interaction 162 9.2.2 Journey to Crime 164 9.2.3 Characteristics of Rioters 165 9.3 Data-Driven Modelling of Riot Diffusion 166 9.4 Statistical Modelling of Target Choice 169 9.5 A Generative Model of the Riots 171 9.6 Discussion 172 References 173 10 Rebellions 175Peter Baudains, Jyoti Belur, Alex Braithwaite, Elio Marchione and Shane D. Johnson 10.1 Introduction 175 10.2 Data 176 10.3 Hawkes model 177 10.4 Results 181 10.5 Discussion 183 References 185 11 Spatial Interaction as Threat: Modelling Maritime Piracy 187Elio Marchione and Alan Wilson 11.1 The Model 187 11.2 The Test Case 188 11.3 Uses of the Model 189 Reference 191 Appendix 192 A.1 Volume Field of Type k Ship 192 A.2 Volume Field of Naval Units 193 A.3 Pirates Ports and Mother Ships 193 12 Space–Time Modelling of Insurgency and Counterinsurgency in Iraq 195Alex Braithwaite and Shane Johnson 12.1 Introduction 195 12.2 Counterinsurgency in Iraq 196 12.3 Counterinsurgency Data 200 12.4 Diagnoses of Space, Time and Space–Time Distributions 202 12.4.1 Introduction 202 12.4.2 Spatial Distribution 202 12.4.3 Temporal Distribution 203 12.4.4 Space–Time Distribution 203 12.4.5 Univariate Knox Analysis 206 12.4.6 Bivariate Knox Analysis 208 12.5 Concluding Comments 210 References 212 13 International Information Flows, Government Response and the Contagion of Ethnic Conflict 214Janina Beiser 13.1 Introduction 214 13.2 Global Information Flows 216 13.3 The Effect of Information Flows on Armed Civil Conflict 220 13.4 The Effect of Information Flows on Government Repression 225 13.5 Conclusion 226 References 226 Appendix 229 Part V AID AND DEVELOPMENT 14 International Development Aid: A Complex System 233Belinda Wu 14.1 Introduction: A Complex Systems’ Perspective 233 14.2 The International Development Aid System: Definitions 234 14.3 Features of International Development Aid as a Complex System 235 14.3.1 Introduction 235 14.3.2 Non-linearity 235 14.3.3 Connectedness 237 14.3.4 Self-Adapting and Self-Organising 238 14.3.5 Emergence 238 14.4 Complexity and Approaches to Research 238 14.4.1 Organisations 238 14.4.2 The Range of Issues 239 14.4.3 Research Approaches 240 14.4.4 The Complexity Science Approach 242 14.5 The Assessment of the Effectiveness of International Development Aid 242 14.5.1 Whether Aid Can Be Effective 242 14.5.2 Complexity in the Measurement of Aid Effectiveness 244 14.5.3 Complexity in Methods/Standards of Measurement of Aid Effectiveness 245 14.5.4 Standardising Aid Effectiveness 246 14.6 Relationships and Interactions 248 14.6.1 Relationships between Donor and Recipient Countries 248 14.6.2 Relationships between Aid and Other Systems 249 14.7 Conclusions 251 References 252 15 Model Building for the Complex System of International Development Aid 257Belinda Wu, Sean Hanna and Alan Wilson 15.1 Introduction 257 15.2 Data Collection 258 15.2.1 Introduction 258 15.2.2 Aid Data 258 15.2.3 Trade Data 260 15.2.4 Security Data 261 15.2.5 Migration Data 261 15.2.6 Geographical Data 261 15.2.7 Data Selected 262 15.3 Model Building 263 15.3.1 Modelling Approach 263 15.3.2 Alesina and Dollar Model 263 15.3.3 Our Models 264 15.3.4 Model B: Introducing Donor Interactions and Modification of the Model 267 15.3.5 Findings from Model B 267 15.3.6 Model C: Introducing Interactions with Trade System and Further Modification of the Model 267 15.3.7 Findings from Model C 268 15.4 Discussion and Future Work 268 References 269 16 Aid Allocation: A Complex Perspective 271Robert J. Downes and Steven R. Bishop 16.1 Aid Allocation Networks 271 16.1.1 Introduction 271 16.1.2 Why Networks? 272 16.1.3 Donor Motivation in Aid Allocation 273 16.2 Quantifying Aid via a Mathematical Model 273 16.2.1 Overview of Approach 273 16.2.2 Basic Set-Up 274 16.2.3 The Network of Nations 275 16.2.4 Preference Functions 275 16.2.5 Specifying the Preference Functions 275 16.2.6 Recipient Selection by Donors 276 16.3 Application of the Model 277 16.3.1 Introduction 277 16.3.2 Scenario 1. No Feedback 277 16.3.3 Scenario 2. Bandwagon Feedback 281 16.3.4 Scenario 3. Aid Effectiveness Feedback 283 16.3.5 Aid Usage Mechanism 284 16.3.6 Application 286 16.3.7 Conclusions 287 16.4 Remarks 287 Acknowledgements 288 References 288 Appendix 290 A.1 Common Functional Definitions 290 Part VI GLOBAL DYNAMICS: AN INTEGRATED MODEL AND POLICY CHALLENGES 17 An Integrated Model 293Robert G. Levy 17.1 Introduction 293 17.2 Adding Migration 294 17.2.1 Introduction 294 17.2.2 The Familiarity Effect 295 17.2.3 Consumption Similarity 301 17.2.4 Conclusions 304 17.3 Adding Aid 304 17.3.1 Introduction 304 17.3.2 Estimating ‘Exportness’ 305 17.3.3 Modelling Approach 306 17.3.4 Results 306 17.3.5 Conclusions 314 17.4 Adding Security 316 17.4.1 Introduction 316 17.4.2 Literature Review 316 17.4.3 Measures of Threat and the Global Dynamics Model 317 17.4.4 Trade during Changing Security Conditions 318 17.4.5 An Experiment of Increased Threat in the Global Dynamics Model 318 17.4.6 Conclusions 322 17.5 Concluding Comments 323 References 324 Index 327
£65.50
Springer Nature Switzerland AG Excursions in Harmonic Analysis, Volume 6: In
Book SynopsisJohn J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.Table of ContentsJohn Benedetto's mathematical work.- Absolute continuity and the Banach-Zaretsky Theorem.- Spectral Synthesis and H1(R).- Universal Upper Bound on the Blowup Rate of Nonlinear Schrodinger Equation with Rotation.- Almost Eigenvalues and Eigenvectors of Almost Mathieu Operators.- Spatio-spectral limiting on rendundant cubes: A case study.- A notion of optimal packings of subspaces with mix-rank and solutions.- Construction of Frames Using Calderon-Zygmund Operator Theory.- Equiangular frames and their duals.- Wavelet sets for crystallographic groups.- Discrete Translates in Function Spaces.- Local-to-global frames and applications to the dynamical sampling problem.- Signal analysis using Born-Jordan-type Distributions.- Sampling by averages and average splines on Dirichlet spaces and on combinatorial graphs.- Dynamical Sampling: a view from Control Theory.- Linear Multiscale Transforms Based on Even-Reversible Subdivision Operators.- Sparsity-Based MIMO Radars.- Robust width: A Characterization of uniformly stable and robust compressed sensing.- On best uniform affine approximants of convex or concave real valued functions from RK, Chebyshev equioscillation and graphics.- A Kaczmarz Algorithm for Solving Tree Based Distributed Systems of Equations.- Maximal function pooling with applications.
£98.99
Springer Nature Switzerland AG Geometric Aspects of Harmonic Analysis
Book SynopsisThis volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables.The work is addressed to researchers in the field.Table of Contents- An Extension Problem and Hardy Type Inequalities for the Grushin Operator. - Sharp Local Smoothing Estimates for Fourier Integral Operators. - On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective. - Potential Spaces on Lie Groups. - On Fourier Restriction for Finite-Type Perturbations of the Hyperbolic Paraboloid. - On Young’s Convolution Inequality for Heisenberg Groups. - Young’s Inequality Sharpened. - Strongly Singular Integrals on Stratified Groups. - Singular Brascamp–Lieb: A Survey. - On the Restriction of Laplace–Beltrami Eigenfunctions and Cantor-Type Sets. - Basis Properties of the Haar System in Limiting Besov Spaces. - Obstacle Problems Generated by the Estimates of Square Function. - Of Commutators and Jacobians. - On Regularity and Irregularity of Certain Holomorphic Singular Integral Operators.
£999.99
Springer International Publishing AG Birational Geometry, Kähler–Einstein Metrics and
Book SynopsisThis book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and PohangThe conferences were focused on the following two related problems:• existence of Kähler–Einstein metrics on Fano varieties• degenerations of Fano varietieson which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide.These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.Table of ContentsT. Abe, Classification of exceptional complements: elliptic curve case.- E. Ballico, E. Gasparim, F. Rubilar, B. Suzuki, LAGRANGIAN SKELETA, COLLARS AND DUALITY.- G. Belousov, CYLINDERS IN DEL PEZZO SURFACES OF DEGREE TWO.- M. Benzerga, FINITENESS OF REAL STRUCTURES ON KLT CALABI-YAU REGULAR SMOOTH PAIRS OF DIMENSION 2.- C. Birkar, ANTICANONICAL VOLUME OF FANO 4-FOLDS.- C. Boyer Christina Tonnesen-Friedman, CONSTANT SCALAR CURVATURE SASAKI METRICS AND PROJECTIVE BUNDLES.- G. Brown, J. Buczynski, A. Kasprzyk, TORIC SARKISOV LINKS.- I. Burban, DU VAL SINGULARITIES.- I. Cheltsov, H. Suess, K-POLYSTABILITY OF TWO SMOOTH FANO THREEFOLDS.- G. Codogni, Z. Patakfalvi, A NOTE ON FAMILIES OF K-SEMISTABLE LOG-FANO PAIRS.- T. Delcroix, THE YAU-TIAN-DONALDSON CONJECTURE FOR COHOMOGENEITY ONE MANIFOLDS.- A. Dubouloz, FIBRATIONS BY AFFINE LINES ON RATIONAL AFFINE SURFACES WITH IRREDUCIBLE BOUNDARIES.- K. Fujita, ON FANO THREEFOLDS OF DEGREE 22 AFTER CHELTSOV AND SHRAMOV.- K. Fujita, Y. Liu, H. Suess, K. Zhang, Z. Zhuang, ON THE CHELTSOV-RUBINSTEIN CONJECTURE.- S. Grishin, Ilya Karzhemanov, Ming-Chang Kang, RATIONALITY OF QUOTIENTS BY FINITE HEISENBERG GROUPS.- Y. Hashimoto.- J. Keller, QUOT-SCHEME LIMIT OF FUBINI–STUDY METRICS AND ITS APPLICATIONS TO BALANCED METRICS.- Z. Hu, EXISTENCE OF CANONICAL MODELS FOR KAWAMATA LOG TERMINAL PAIRS.- Y. Imagi, GENERALIZED THOMAS–YAU UNIQUENESS THEOREMS.- K. Jamieson, BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION 3.- D. Jeong.- J. Park, SIMPLY CONNECTED SASAKI-EINSTEIN 5-MANIFOLDS: OLD AND NEW.- C. Jiang, CHARACTERIZING Q-FANO THREEFOLDS WITH THE SMALLEST ANTI-CANONICAL VOLUME.- L. Katzarkov, Kyoung-Seog Lee, J. Svoboda, A. Petkov, INTERPRETATIONS OF SPECTRA.- Young-Hoon Kiem, Kyoung-Seog Lee, FANO VISITORS, FANO DIMENSION AND FANO ORBIFOLDS.- In-kyun Kim, N. Viswanathan, J. Won, ON SINGULAR DEL PEZZO HYPERSURFACES OF INDEX 3.- S. Kudryavtsev, Blow-ups of three-dimensional toric singularities.- N. Kurnosov, E. Yasinsky, AUTOMORPHISMS OF HYPERKAHLER MANIFOLDS AND GROUPS ACTING ON CAT(0) SPACES.- A. Laface, R. Quezada, ON GENERALIZED BUCHI SURFACES.- Chi Li, K-STABILITY AND FUJITA APPROXIMATION.- Y. Li, Zhenye Li, ON A CONJECTURE OF FULTON ON ISOTROPIC GRASSMANNIANS.- Y. Maeda, Y. Odaka, FANO SHIMURA VARIETIES WITH MOSTLY BRANCHED CUSP.- L. Makar-Limanov, ON LOCALLY NILPOTENT DERIVATIONS OF DANIELEWSKI DOMAINS.- D. Markouchevitch, A. Moreau, ACTION OF THE AUTOMORPHISM GROUP ON THE JACOBIAN OF KLEIN'S QUARTIC CURVE.- J. Martinez-Garcia, C. Spotti, SOME OBSERVATIONS ON THE DIMENSION OF FANO K-MODULI.- D. Witt Nystrom, OKOUNKOV BODIES AND THE KAHLER GEOMETRY OF PROJECTIVE MANIFOLDS.- J. Park, SINGULARITIES OF PLURI-FUNDAMENTAL DIVISORS ON GORENSTEIN FANO VARIETIES OF COINDEX.- J. Paulhus, A DATABASE OF GROUP ACTIONS ON RIEMANN SURFACES.- A. Petracci, A 1-DIMENSIONAL COMPONENT OF K-MODULI OF DEL PEZZO SURFACES.- T. De Piro, A NON-STANDARD BEZOUT THEOREM FOR CURVES.- Y. Prokhorov, EMBEDDINGS OF THE SYMMETRIC GROUPS TO THE SPACE CREMONA GROUP.- J. Ross, M. Toma, ON HODGE-RIEMANN COHOMOLOGY CLASSES.- Y. Rubinstein, ON LARGE DEVIATION PRINCIPLES AND THE MONGE–AMPERE EQUATION (FOLLOWING BERMAN, HULTGREN).- T. Sano, ON BIRATIONAL BOUNDEDNESS OF SOME CALABI-YAU HYPERSURFACES.- Y. Zarhin, ABELIAN VARIETIES, QUATERNION TRICK AND ENDOMORPHISMS.
£999.99
Springer International Publishing AG Mappings with Direct and Inverse Poletsky
Book SynopsisThe monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality.Table of ContentsGeneral definitions and notation.- Boundary behavior of mappings with Poletsky inequality.- Removability of singularities of generalized quasiisometries.- Normal families of generalized quasiisometries.- On boundary behavior of mappings with Poletsky inequality in terms of prime ends.- Local and boundary behavior of mappings on Riemannian manifolds.- Local and boundary behavior of maps in metric spaces.- On Sokhotski-Casorati-Weierstrass theorem on metric spaces.- On boundary extension of mappings in metric spaces in the terms of prime ends.- On the openness and discreteness of mappings with the inverse Poletsky inequality.- Equicontinuity and isolated singularities of mappings with the inverse Poletsky inequality.- Equicontinuity of families of mappings with the inverse Poletsky inequality in terms of prime ends.- Logarithmic H¨older continuous mappings and Beltrami equation.- On logarithmic H¨older continuity of mappings on the boundary.- The Poletsky and V¨ais¨al¨a inequalities for the mappings with (p;q)-distortion.- An analog of the V¨ais¨al¨a inequality for surfaces.- Modular inequalities on Riemannian surfaces.- On the local and boundary behavior of mappings of factor spaces.- References.- Index.
£999.99
Birkhauser Verlag AG Functions of OmegaBounded Type
Book SynopsisThe book gives the basic results of the theory of the spaces Ap? of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ? permitting any rate of growth of a function near the boundary of the domain.
£44.99
Birkhauser Verlag AG Visual Complex Functions: An Introduction with
Book SynopsisThis book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains.Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes.In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions.Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.Trade ReviewFrom the reviews:“This textbook is an introduction to the classical theory of functions of one complex variable. Its distinctive feature are the graphical representations of functions, being the most useful tool in teaching and generally in mathematics. … The self-sufficiency of the textbook and the broad range of graphical examples makes the book useful for students as well as teachers of mathematics. … the book can be warmly recommended both to experts and to a new generation of mathematicians.” (Stanislawa Kanas, Zentralblatt MATH, Vol. 1264, 2013)“Anyone who works with complex variables should read this book. … Visual Complex Functions is a beautiful and careful presentation of an entire advanced introduction to complex analysis based on phase portraits and, where appropriate, other kinds of computer-generated pictures. … My understanding of many ideas and phenomena deepened through reading this book.” (Lloyd N. Trefethen, SIAM Review, Vol. 55 (4), 2013)Table of ContentsPreface.- 1. Getting Acquainted.- 2. Complex Functions.- 3. Analytic Functions.- 4. Complex Calculus.- 5. Construction Principles.- 6. Conformal Mappings.- 7. Riemann Surfaces
£52.24
Springer Fachmedien Wiesbaden Die Lehre von den Kettenbrüchen: Band II:
Book SynopsisNunmehr kann ich auch den zweiten Teil meiner Lehre von den Kettenbrüchen, der den analytischen Kettenbrüchen gewidmet ist, als Band 11 in neuer Be arbeitung den Fachgenossen vorlegen. Ebenso wie bei dem im Jahr 1954 er schienenen Band I ging mein Bemühen dah~, den heutigen Stand der Wissen schaft in möglichst leicht verständlicher Weise darzustellen. Die leichte Ver ständlichkeit kann natürlich nicht bedeuten, daß der Leser das Buch wie einen Roman durcheilen kann. Wenn er aber die Technik der Differential-und Integral rechnung beherrscht, wenn er schon etwas von der Gammafunktion und von linearen Differentialgleichungen gehört hat und ein klein wenig Funktionen theorie weiß, kann er unschwer folgen; nur darf er, um in Einzelheiten ein zudringen, nicht die Mühe scheuen, gelegentlich Papier und Bleistift zur Hand zu nehmen und einfache Rechnungen nach gegebener Anweisung selbst durch zuführen. Es geht alles nach geläufigen Methoden. Der allgemeine Rahmen des Buches ist der alte geblieben; doch sind die sechs Kapitel mit weitgehend verändertem Inhalt gefüllt. Namentlich die ersten drei und auch die zweite Hälfte des vierten sind mannigfach umgestaltet und er weitert, während in den letzten zwei nur geringere Änderungen nötig und sogar Kürzungen möglich waren, um Raum für den neuen Stoff der früheren zu ge winnen. Überall in der Welt, besonders in der Neuen, ist in den letzten Dezennien ein reiches Material von neuen Kettenbruchtypen und neuen Erkenntnissen, vor allem in bezug auf Konvergenz, gewonnen worden, das gesichtet, geordnet und systematisch eingearbeitet werden mußte.Table of ContentsI. Transformation von Kettenbrüchen..- § 1. Rekapitulation.- § 2. Null als Teilzähler. — Äquivalente Kettenbrüche.- § 3. Kettenbrüche mit vorgegebenen Näherungsbrüchen.- § 4. Kontraktion und Extension.- § 5. Äquivalenz von Kettenbrüchen und Reihen.- § 6. Äquivalenz von Kettenbrüchen und Produkten.- § 7. Die Transformation von Bauer und Muir.- § 8. Weitere Anwendungen. Haupformel von Ramanujan.- II. Kriterien für Konvergenz und Divergenz..- § 9. Bedingte und unbedingte Konvergenz.- § 10. Allgemeine Kriterien von Broman, Stern und Scott-Wall.- § 11. Konvergenz bei positiven Elementen.- § 12. Konvergenz bei reellen Elementen.- § 13. Irrationalität gewisser Kettenbrüche.- § 14. Die Konvergenzkriterien von Pringsheim.- § 15. Die Konvergenzkriterien von van Vleck-Jensen und Hamburger-Mall-Wall.- § 16. Anwendung: Geltungsbereich der Ramanujan-Formel.- § 17. Einige neuere Kriterien. — Das Parabeltheorem.- § 18. Periodische Kettenbrüche.- § 19. Limitärperiodische Kettenbrüche.- § 20. Die Gleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % WG4bWaaSbaaSqaaiaaicdaaeqaaaGcbaGaamiEamaaBaaaleaacaaI % XaaabeaaaaGccqGH9aqpcaWGIbWaaSbaaSqaaiaaicdaaeqaaOGaey % 4kaSYaaSaaaeaadaabcaqaaiaadggadaWgaaWcbaGaaGymaaqabaaa % kiaawIa7aaqaamaaeeaabaGaamOyamaaBaaaleaacaaIXaaabeaaaO % Gaay5bSdaaaiabgUcaRmaalaaabaWaaqGaaeaacaWGHbWaaSbaaSqa % aiaaikdaaeqaaaGccaGLiWoaaeaadaabbaqaaiaadkgadaWgaaWcba % GaaGOmaaqabaaakiaawEa7aaaacqGHRaWkcqWIVlctaaa!4F24! $$ \frac{{{x_0}}}{{{x_1}}} = {b_0} + \frac{{\left. {{a_1}} \right|}}{{\left| {{b_1}} \right.}} + \frac{{\left. {{a_2}} \right|}}{{\left| {{b_2}} \right.}} + \cdots $$als Folge des Rekursionssystems % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa % aaleaacaWG2baabeaakiabg2da9iaadkgadaWgaaWcbaGaamODaaqa % baGccaWG4bWaaSbaaSqaaiaadAhacqGHRaWkcaaIXaaabeaakiabgU % caRiaadggadaWgaaWcbaGaamODaiabgUcaRiaaigdaaeqaaOGaamiE % amaaBaaaleaacaWG2bGaey4kaSIaaGOmaaqabaaaaa!4763! $$ {x_v} = {b_v}{x_{v + 1}} + {a_{v + 1}}{x_{v + 2}} $$.- III. Verschiedene Zuordnungen von Potenzreihen zu Kettenbrüchen..- § 21. Allgemeine C-Kettenbrüche.- § 22. Quadratwurzeln.- § 23. Regelmäßige C-Kettenbrüche.- § 24. Die Kettenbrüche von Gauß, Heine und damit verwandte.- § 25. Der assoziierte Kettenbruch.- § 26. Zusammenhang zwischen dem korrespondierenden und assoziierten Kettenbruch. — Einige Transformationen des korrespondierenden Kettenbruches.- § 27. Konvergenz und Divergenz.- § 28. Konvergenz der Kettenbrüche von Gauß, Heine usw.- § 29. Ein bemerkenswertes Divergenzphänomen.- § 30. J-Kettenbrüche und ihre Anwendung auf Polynome, deren Wurzeln negative reelle Teile haben.- § 31. Weitere Typen von Kettenbrüchen, denen man Potenzreihen zuordnen kann.- IV. Die Kettenbrüche von Stieltjes..- § 32. Der Integralbegriff von Stieltjes.- § 33. Der korrespondierende und assoziierte Kettenbruch eines Stieltjessehen Integrals.- § 34. Der Satz von Markoff.- § 35. Die Wurzeln der Näherungsnenner von G-, H- und S-Kettenbrüchen.- § 36. Das Grommersche Auswahltheorem.- § 37. Konvergenz und analytischer Charakter der S- und H-Kettenbrüche.- § 38. Die vollständige Konvergenz der G-Kettenbrüche.- § 39. Das Momentenproblem.- V. Die P adésehe Tafel..- § 40. Begriff der Padéschen Tafel.- § 41. Normale und anormale Tafel.- § 42. Die Exponentialfunktion.- § 43. Die Laguerresche Differentialgleichung.- § 44. Die Kettenbrüche der Padéschen Tafel.- § 45. Die Konvergenzfrage.- VI. Kettenbrüche, deren Elemente a, und b, rationale Funktionen von v sind..- § 46. Die Konvergenz dieser Kettenbrüche.- § 47. Zusammenhang mit Differentialgleichungen.- § 48. Die Kettenbrüche mit dem allgemeinen Glied % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada % abcaqaaiaadggadaWgaaWcbaGaamODaaqabaaakiaawIa7aaqaamaa % eeaabaGaamOyamaaBaaaleaacaWG2baabeaaaOGaay5bSdaaaiabg2 % da9maalaaabaWaaqGaaeaacaWGHbGaey4kaSIaamOyamaaBaaaleaa % caWG2baabeaaaOGaayjcSdaabaWaaqqaaeaacaWGJbGaey4kaSIaam % izamaaBaaaleaacaWG2baabeaaaOGaay5bSdaaaaaa!4961! $$ \frac{{\left. {{a_v}} \right|}}{{\left| {{b_v}} \right.}} = \frac{{\left. {a + {b_v}} \right|}}{{\left| {c + {d_v}} \right.}} $$.- § 49. Die Kettenbrüche mit dem allgemeinen Glied % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaada % abcaqaaiaadggadaWgaaWcbaGaamODaaqabaaakiaawIa7aaqaamaa % eeaabaGaamOyamaaBaaaleaacaWG2baabeaaaOGaay5bSdaaaiabg2 % da9maalaaabaWaaqGaaeaacaWGHbGaey4kaSIaamOyamaaBaaaleaa % caWG2baabeaakiabgUcaRiaadogacaWG2bWaaWbaaSqabeaacaaIYa % aaaaGccaGLiWoaaeaadaabbaqaaiaadsgacqGHRaWkcaWGLbGaamOD % aaGaay5bSdaaaaaa!4CE5! $$ \frac{{\left. {{a_v}} \right|}}{{\left| {{b_v}} \right.}} = \frac{{\left. {a + {b_v} + c{v^2}} \right|}}{{\left| {d + ev} \right.}} $$.- § 50. Die Methode von Cesàro.- § 51. Die Formel von Pincherle.- Literatur.- Verzeichnis der bemerkenswerten Formeln.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Complex Geometry: An Introduction
Book SynopsisEasily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)Trade ReviewFrom the reviews: "The book under review provides an introduction to the contemporary theory of compact complex manifolds, with a particular emphasis on Kähler manifolds in their various aspects and applications. As the author points out in the preface, the text is based on a two-semester course taught in 2001/2002 at the University of Cologne, Germany. Having been designed for third-year students, the aim of the course was to acquaint beginners in the field with some basic concepts, fundamental techniques, and important results in the theory of compact complex manifolds, without being neither too basic nor too sketchy. Also, as complex geometry has undergone tremendous developments during the past five decades, and become an indispensable framework in modern mathematical physics, the author has tried to teach the subject in such a way that would enable the students to understand the more recent developments in the field, too, up to some of the fascinating aspects of the stunning interplay between complex geometry and quantum field theory in theoretical physics. The present text, as an outgrowth of this special course in complex geometry, does evidently reflect these emphatic intentions of the author's in a masterly manner. Keeping the prerequisites from complex analysis and differential geometry to an absolute minimum, he provides a streamlined introduction to the theory of compact complex manifolds and Kählerian geometry, with many outlooks and applications, but without trying to be encyclopedic or panoramic. without trying to be encyclopedic or panoramic. As to the precise contents, the text consists of six chapters and two appendices. [...] The author has added two general appendices at the end of the book. Those aremeant to help the unexperienced reader to recall a few basic concepts and facts from differential geometry, Hodge theory on differentiable manifolds, sheaf theory, and sheaf cohomology. This very user-friendly service makes the entire introductory text more comfortable for less seasoned students, perhaps also for interested and mathematically less experienced physicists, although the author does not claim absolute self-containedness of the book. The entire text comes with a wealth of enlightening examples, historical remarks, comments and hints for further reading, outlooks to other directions of research, and numerous exercises after each section. The exercises are far from being bland and often quite demanding, but they should be mastered by ambitious and attentive readers, in the last resort after additional reading. Finally, there is a very rich bibliography of 118 references, also from the very recent research literature, which the author profusely refers to throughout the entire text. The whole exposition captivates by its clarity, profundity, versality, and didactical strategy, which lead the reader right to the more advanced literature in complex geometry as well as to the forefront of research in geometry and its applications to mathematical physics. No doubt, this book is an outstanding introduction to modern complex geometry." KIeinert (Berlin), Zentralblatt für Mathematik 1055 (2005) This is a very interesting and nice book. It provides a clear and deep introduction about complex geometry, namely the study of complex manifolds. These are differentiable manifolds endowed with the additional datum of a complex structure that is more rigid than the geometrical structures used in differential geometry. Complex geometry is on the crossroad of algebraic and differential geometry. Complex geometry is also becoming a stimulating and useful tool for theoretical physicists working in string theory and conformal field theory. The physicist, will be very glad to discover the interplay between complex geometry and supersymmetry and mirror symmetry. The book begins by explaining the local theory and all you need to understand the global structure of complex manifolds. Then we get an introduction to the complex manifolds as such, where the reader can progressively perceive the difference between real manifolds and complex ones. Then he gets an account of the theory of Kälher manifolds. And the physicist will be glad to find therein a first step on the road going from complex geometry to conformal field theory and supersymmetry. One chapter is dedicated to the study of holomorphic vector bundles (connections, curvature, Chern classes). In this context, the reader will clarify the relations between Riemannian and Kälher geometries. With all this stuff it is then possible to focus on some applications of cohomology. This leads to a nice introduction to the famous Hirzebruch-Riemann-Roch theorem and to Kodaira vanishing and embedding theorems. The last chapter of the book tackles the very important topics of deformations of complex structures. This chapter will be interesting especially for readers that are studying Calabi-Yau manifolds and mirror symmetries. The main text of the book is completed by two pedagogical appendices. One about Hodge theory and the other about sheaf cohomology. Thus this beautiful textbook will be very interesting for both pure mathematicians and theoretical physicists working in recent domains of field theory. It can be used by students or scientists for a first introduction in this field. It is always very accessible and the reader will find a detailed account of the basic concepts and many well-chosen exercises that illustrate the theory. Many illuminating examples help the reader in the understanding of all fundamental notions. I could certainly recommend this textbook to my students attending my lectures on differential geometry. Professor Dominique LAMBERT, University of Namur; Department « sciences, philosophies et sociétés » Rue de Bruxelles 61 B-5000 Namur Belgium "As complex geometry has undergone tremendous developments … the author has tried to teach the subject in such a way that would enable the students to understand the more recent developments in the field … . This very user-friendly … more comfortable for less seasoned students … . The entire text comes with a wealth of enlightening examples, historical remarks, comments and hints … . Finally, there is a very rich bibliography … . The whole exposition captivates by its clarity, profundity, versality, and didactical strategy … . an outstanding introduction to modern complex geometry." (Werner Kleinert, Zentralblatt Math, Vol. 1055, 2005) "The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. Appendices to various chapters allow an outlook to recent research directions." (L’Enseignment Mathematique, Vol. 50 (3-4), 2004) "This is the book that a generation of complex geometers will wish had existed when they first learned the subject, and that the next generation of geometers will surely use. … Inserted into the standard material are some excellent appendices to stimulate interest and further reading … . the reader learning the basic material is brought quickly and often to some fascinating areas of current research. Exercises introduce many examples … . The result is an excellent course in complex geometry." (Richard P. Thomas, Mathematical Reviews, 2005h) "The book is based on a year course on complex geometry and its interaction with Riemannian geometry. It prepares a basic ground for a study of complex geometry as well as for understanding ideas coming recently from string theory. … The book is a very good introduction to the subject and can be very useful both for mathematicians and mathematical physicists." (EMS Newsletter, June, 2005) "The book under review is a textbook, based on a 2-semester course to third year undergraduates in the University of Cologne. … In the UK I think the book would be regarded as more suitable for a masters’ level course for students well versed in standard complex analysis and differential geometry." (Peter Giblin, The Mathematical Gazette, Vol. 91 (520), 2007)Table of ContentsLocal Theory.- Complex Manifolds.- Kähler Manifolds.- Vector Bundles.- Applications of Cohomology.- Deformations of Complex Structures.
£61.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Analytische Stellenalgebren
Book SynopsisTable of ContentsI. Konvergente Potenzreihenalgebren.- § 0. Formale Potenzreihen.- 1. Potenzreihen. Ordnung.- 2. Substitutionshomomorphismen.- 3. Partielle Ableitungen. Kettenregel.- 4. Topologie der koeffizientenweisen Konvergenz.- § 1. Analytische k-Banachalgebren.- 0. Bewertungen.- 1. Definition der Bt.- 2. Partielle Ableitungen.- 3. Topologische Eigenschaften der Bt.- § 2. Weierstraßsche Formel und Weierstraßscher Vorbereitungssatz für Bt.- 1. Weierstraßsche Formel.- 2. Weierstraßscher Vorbereitungssatz.- § 3. Konvergente Potenzreihen.- 1. Definition konvergenter Potenzreihen.- 2. Analytische Homomorphismen.- 3. Partielle Ableitungen.- 4. Schwache Topologie und analytische Konvergenz.- § 4. Weierstraßsche Formel und Weierstraßscher Vorbereitungssatz für Kn.- 1. Weierstraßsche Formel und Vorbereitungssatz.- 2. Scherungen.- 3. Analytische Karten in Kn.- Supplement zu § 4. Der Stickelberger-Siegelsche Beweis des Vorbereitungssatzes.- 1. Der Stickelbergersche Beweis.- 2. Der Siegeische Beweis.- 3. Herleitung der Weierstraßschen Formel aus dem Vorbereitungssatz.- § 5. Algebraische Struktur des Ringes Kn.- 1. Weierstraßhomomorphismen und Weierstraßpolynome.- 2. Noethereigenschaft.- 3. Unbeschränktheit der Corangfunktion.- 4. Cartanscher Abgeschlossenheitssatz.- 5. Primfaktorzerlegung.- 6. Henselsches Lemma.- Supplement zu § 5. Noethersche Banachalgebren über ? und ?.- § 6. Die Folgentopologie des Kn.- 1. Finale Topologien.- 2. Folgentopologie auf Kn.- 3. Stetigkeit analytischer Homomorphismen.- § 7. Folgentopologien bei lokal-kompaktem Grundkörper.- 1. Produkttopologie. Silvasche Topologie.- 2. Produkttopologie von Silvatopologien.- 3. Ausgezeichnete Umgebungen. Charakterisierung konvergenter Folgen.- 4. Folgentopologie auf Kn.- 5. Erstes Abzählbarkeitsaxiom und Folgenabschluß.- § 8. Silvatopologie auf Vektorräumen und Algebren.- 1. Definitionen.- 2. Restklassenräume und Restklassenalgebren.- 3. Beschränkte Mengen.- 4. Silvasche Vektorräume und Silvasche Algebren.- 5. Kompakte Mengen.- 6. Lokale Konvexität.- 7. Ausblick.- II. Analytische k-Stellenalgebren.- § 0. Analytische k-Stellenalgebren und analytische Moduln.- 1. Die Kategorie U.- 2. Die Kategorie MA.- § 1. Topologie auf analytischen Stellenalgebren und analytischen Moduln.- 1. Schwache Topologie auf analytischen Stellenalgebren.- 2. Folgentopologie auf analytischen Stellenalgebren.- 3. Schwache Topologie und Folgentopologie auf analytischen Moduln.- § 2. Quasi-endliche und endliche Homomorphismen.- 1. Quasi-endliche Moduln.- 2. Quasi-endliche und endliche analytische Homomorphismen.- 3. Analytische Epimorphismen und analytische Erzeugendensysteme.- 4. Ganze Elemente und endliche Homomorphismen.- 5. Analytische k-Unterstellenalgebren.- 6. Invarianz der Modultopologie.- 7. Relativtopologie und strikte Homomorphismen.- § 3. Einbettungsdimension. Epimorphismen. Umkehrsatz.- 1. Cotangentialraum. Einbettungsdimension. Ableitung.- 2. Epimorphiekriterium.- 3. Jacobischer Umkehrsatz.- 4. Satz über implizite Funktionen.- 5. Einbettungsdimension und Epimorphismen.- § 4. Dimensionstheorie analytischer k-Stellerialgebren. Aktives Lemma.- 1. Aktive Elemente.- 2. Artinsche Algebren.- 3. Dimension.- 4. Aktives Lemma.- 5. Konstruktion aktiver Elemente.- 6. Konstruktion von Parametersystemen.- 7. Tiefe eines Ideals.- § 5. Dimension und endliche analytische Homomorphismen.- 1. Invarianz der Dimension.- 2. Endliche Monomorphismen. Osgoodsches Beispiel.- 3. Reguläre analytische k-Stellenalgebren.- § 6. Krullsche Dimension. Rein-dimensionale analytische Stellenalgebren.- 1. Primidealketten.- 2. Krullscher Hauptidealsatz.- 3. Rein-dimensionale analytische k-Stellenalgebren.- § 7. Endliche Erweiterungen analytischer Stellenalgebren. Normalisierung.- 1. Endliche Erweiterungen.- 2. Normalisierung reduzierter analytischer Stellenalgebren.- III. Weiterführende Theorie analytischer k-Stellenalgebren und analytischer Moduln.- § 1. Homologische Codimension (Profondeur).- 1. M-Sequenzen.- 2. Homologische Codimension. Maximale M-Sequenzen.- 3. Profondeur und endliche Homomorphismen.- 4. Cohen-Macaulay-Moduln.- 5. Unvermischtheit.- 6. Freie Moduln und Macaulay-Moduln.- 7. Beispiele von Macaulay-Moduln.- 8. Beispiele von nicht-Macaulayschen Ringen.- § 2. Homologische Dimension (Syzygientheorie).- 1. Minimale Epimorphismen.- 2. Minimale-freie Auflösungen.- 3. Syzygienmoduln.- 4. Homologische Dimension.- 5. Homologische Dimension und homologische Codimension. Syzygiensatz.- 6. Konstruktion von Hilbert-Auflösungen.- 7. Koszul-Komplexe.- § 3. Invariante analytische k-Unterstellenalgebren.- 1. Invariante Algebren zu endlichen Automorphismengruppen.- 2. Linearisierung.- 3. Beispiele. Zyklische Gruppen.- § 4. Derivations- und Differentialmoduln.- 1. Derivationen.- 2. Differentialmoduln.- 3. Existenz von Differentialmoduln.- 4. Eigenschaften der Differentialmoduln.- 5. Regularitätskriterium.- 6. Äußere Differentialformen über kn. Poincaré-Sequenz.- 7. Exaktheit der Poincaré-Sequenz.- § 5. Analytische Tensorprodukte.- 1. Definition und Existenz.- 2. Endlichkeit und Freiheit.- 3. Faseralgebren und endliche Homomorphismen.- 4. Das analytische Tensorprodukt analytischer Moduln.- 5. Invarianz unter endlichen Homomorphismen.- 6. Einbettungsdimension und Dimension.- 7. Normalität und Nullteilerfreiheit.- 8. Reduziertheit.- 9. Homologische Codimension.- 10. Differentialmoduln.- Anhang. Algebraische Hilfsmittel.- § 1. Ringe und Moduln.- 1. Idealpotenzen. Nilpotente Ideale.- 2. Primideale.- 3. Radikale. Reduzierte Ringe. Multiplikative Mengen.- 4. Torsionsmoduln. Quotientenmoduln.- 5. Rang und Corang.- 6. Noethersche Moduln.- 8. Zerlegungssatz von Lasker-Noether.- § 2. Endliche Moduln über noetherschen Stellenringen.- 2. Lemma von Nakayama.- 3. Krullscher Durchschnittsatz.- 4. Corang.- 5. Jacobirang.- 6. Einbettungsdimension.- 7. Freie Moduln.- § 3. Normale noethersche Integritätsringe.- 1. Ganze Elemente. Dedekindsches Lemma.- 2. Ganzer Abschluß. Normalisierung.- 3. Charakterisierung ganz-abgeschlossener Ringe.- 4. Hauptidealsatz.- 5. Minimale Primideale.- 6. Teilbarkeitstheorie.- § 4. Reduzierte und noethersche Ringe.- 1. Direkte Summen von Ringen.- 2. Epimorphiesatz.- 3. Reduzierte noethersche Ringe.- 4. Charakterisierung von Torsionsmoduln.- Literatur.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Abstract Harmonic Analysis: Volume II: Structure
Book SynopsisThis book is a continuation of Volume I of the same title [Grund lehren der mathematischen Wissenschaften, Band 115 ]. We constantly 1 1. The textbook Real and cite definitions and results from Volume abstract analysis by E. HEWITT and K. R. STROMBERG [Berlin · Gottin gen ·Heidelberg: Springer-Verlag 1965], which appeared between the publication of the two volumes of this work, contains many standard facts from analysis. We use this book as a convenient reference for such facts, and denote it in the text by RAAA. Most readers will have only occasional need actually to read in RAAA. Our goal in this volume is to present the most important parts of harmonic analysis on compact groups and on locally compact Abelian groups. We deal with general locally compact groups only where they are the natural setting for what we are considering, or where one or another group provides a useful counterexample. Readers who are interested only in compact groups may read as follows: § 27, Appendix D, §§ 28-30 [omitting subheads (30.6)-(30.60)ifdesired], (31.22)-(31.25), §§ 32, 34-38, 44. Readers who are interested only in locally compact Abelian groups may read as follows: §§ 31-33, 39-42, selected Mis cellaneous Theorems and Examples in §§34-38. For all readers, § 43 is interesting but optional. Obviously we have not been able to cover all of harmonic analysis.Table of ContentsSeven: Representations and duality of compact groups.- Eight: Fourier transforms.- Nine: Analysis on compact groups.- Ten: Spectral synthesis.- Eleven: Miscellany.- Appendix D: Tensor products and von Neumann norms.- Appendix E: Miscellaneous facts from functional analysis.- Addendum to Volume I.- Index of symbols.- Index of authors and terms.
£104.49
Springer Spektrum Grundkurs Funktionentheorie
Book SynopsisVorwort.- 1 Holomorphe Funktionen.- 2 Integration im Komplexen.- 3 Isolierte Singularitäten.- 4 Meromorphe Funktionen.- 5 Geometrische Funktionentheorie.- 6 Lösungen zu den Aufgaben.- Literaturverzeichnis.- Symbolverzeichnis.- Stichwortverzeichnis.
£32.29
Springer Verlag, Singapore Nevanlinna Theory
Book SynopsisThis book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from C to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.Table of ContentsPreface1. Nevanlinna Theory of One Variable (1)1.1 metrics of compact Rimann surfaces1.2 integral formula1.3 holomorphic maps over compact Riemann surfaces whose genus are greater than 21.4 holomorphic maps over Riemann sphreres1.5 Defect relation2. Schwarz--Kobayashi's Lemma2.1 Schwarz--Kobayashi's Lemma2.2 holomorphic maps over algebraic varieties (general type)2.3 hyperbolic measures3. Nevanlinna Theory of One Variable (2)3.1 holomorphic maps over Riemann shpres3.2 the first main theorem3.3 the second main theorem4. Nevanlinna Theory of Several Variables4.1 Biebelbach's example4.2 the first main theorem4.3 the second main theorem4.4 defect relation4.5 applicationsReferences
£999.99
Springer Verlag, Singapore Mathematical Analysis and Applications: MAA 2020,
Book SynopsisThis book collects original peer-reviewed contributions presented at the "International Conference on Mathematical Analysis and Applications (MAA 2020)" organized by the Department of Mathematics, National Institute of Technology Jamshedpur, India, from 2–4 November 2020. This book presents peer-reviewed research and survey papers in mathematical analysis that cover a broad range of areas including approximation theory, operator theory, fixed-point theory, function spaces, complex analysis, geometric and univalent function theory, control theory, fractional calculus, special functions, operation research, theory of inequalities, equilibrium problem, Fourier and wavelet analysis, mathematical physics, graph theory, stochastic orders and numerical analysis. Some chapters of the book discuss the applications to real-life situations. This book will be of value to researchers and students associated with the field of pure and applied mathematics.Table of ContentsG. K. Srinivasan, A note on isolated removable singularities of harmonic functions.- O. Chadli, Ram N. Mohapatra, B. K. Sahu, Equilibrium Problems and Variational Inequalities: a Survey of Existence Results.- O. Chadli, Ram N. Mohapatra, G. Pany, Nonlinear evolution equations by a Ky Fan minimax inequality approach.- L. A. Wani and A. Swaminathan, Sufficient Conditions Concerning the Unified Class of Starlike and Convex Functions.- S. Menchavez and I. Mae Antabo, One Dimensional Parametrized Test Functions Space of Entire Functions.- D. Raghavan and S. Nagarajan, Extremal mild solutions of Hilfer fractional Impulsive systems.- B. Roy and S. N. Bora, On existence of integral solutions for a class of mixed Volterra-Fredholm integro fractional differential equations.- P. Kumar, A. Kumar, R. Kumar Vats and A. Kumar, Trajectory Controllability of Integro-differential Systems of Fractional Order γ ∈ (1, 2] in a Banach Space with Deviated Argument.- A. S. Kelil and A. Rao Appadu, Shehu-Adomian Decomposition Method for dispersive KdV-type Equations.- A. S. Kelil, A. R. Appadu and S. Arjika, On certain properties of perturbed Freud-type weight: a revisit.- A. K. Singh, Complex chaotic systems and its complexity.- M. Incesu, S. Y. Evren and O. Gursoy, On the bertrand pairs of open non uniform B-spline curves.- M. Verma, P. Sharma and N. Gupta, Convergence analysis of a sixth-order method under weak continuity condition with First-order Frechet derivative.- B. Kour and S. Ram, (m, n)-paranormal composition operators.- T. Yaying, On the domain of q-Euler matrix in c0 and c.- N. Sarkar and M. Sen, Study on some particular class of non linear integral equation with a hybridized approach.- D. Saha, M. Sen and S. Roy, Investigation of the existence criteria for the solution of the functional integral equation in the Lp space.- S. Das and K. Mehrez, Functional Inequalities for the Generalized Wright Functions.- S. Dutta and P. Guha, An Information Theoretic Entropy Related to Ihara $\zeta$ Function and Billiard Dynamics.- S. Baskaran, G. Saravanan and K. Muthunagai, On a new subclass of Sakaguchi type functions using (p;q)- derivative operator.- N. K. Jangid, S. Joshi and S. D. Purohit, Some Double integral Formulae Associated with Q Function and Galue Type Struve Function.- M. Jain, M. Singh and R. K. Meena, Time-dependent analytical and computational study of an M/M/1 queue with disaster failure and multiple working vacations.- M. Datta and N. Gupta, Usual stochastic ordering results for series and parallel systems with components having Exponentiated Chen distribution.
£999.99
Springer Verlag, Singapore Analytic Continuation and q-Convexity
Book SynopsisThe focus of this book is on the further development of the classical achievements in analysis of several complex variables, the analytic continuation and the analytic structure of sets, to settings in which the q-pseudoconvexity in the sense of Rothstein and the q-convexity in the sense of Grauert play a crucial role. After giving a brief survey of notions of generalized convexity and their most important results, the authors present recent statements on analytic continuation related to them. Rothstein (1955) first introduced q-pseudoconvexity using generalized Hartogs figures. Słodkowski (1986) defined q-pseudoconvex sets by means of the existence of exhaustion functions which are q-plurisubharmonic in the sense of Hunt and Murray (1978). Examples of q-pseudoconvex sets appear as complements of analytic sets. Here, the relation of the analytic structure of graphs of continuous surfaces whose complements are q-pseudoconvex is investigated. As an outcome, the authors generalize results by Hartogs (1909), Shcherbina (1993), and Chirka (2001) on the existence of foliations of pseudoconcave continuous real hypersurfaces by smooth complex ones. A similar generalization is obtained by a completely different approach using L²-methods in the setting of q-convex spaces. The notion of q-convexity was developed by Rothstein (1955) and Grauert (1959) and extended to q-convex spaces by Andreotti and Grauert (1962). Andreotti–Grauert's finiteness theorem was applied by Andreotti and Norguet (1966–1971) to extend Grauert's solution of the Levi problem to q-convex spaces. A consequence is that the sets of (q-1)-cycles of q-convex domains with smooth boundaries in projective algebraic manifolds, which are equipped with complex structures as open subsets of Chow varieties, are in fact holomorphically convex. Complements of analytic curves are studied, and the relation of q-convexity and cycle spaces is explained. Finally, results for q-convex domains in projective spaces are shown and the q-convexity in analytic families is investigated.Table of Contents1. Analytic Continuation and Pseudoconvexity.- 2. q-Plurisubharmonicity.- 3. q-Pseudoconvexity.- 4. q-Convexity and q-Completeness.- References.- Index.
£999.99
McGraw-Hill Education - Europe Students Solutions Manual to accompany Complex
Book Synopsis
£999.99
Oxford University Press Real Analysis and Infinity
Book SynopsisReal Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts.Trade ReviewReal Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. * MathSciNet *This is a thorough introduction to the subject for undergraduates. There are very few prerequisites (less than in most similar textbooks) because topics such as infinity, countable and uncountable sets, and even the principle of mathematical induction are discussed in an early chapter. [...] The main advantage this book offers is its reader-friendly style. * Miklós Bóna, University of Florida, Department of Mathematics *Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. * zb Math Open *Table of ContentsPreface 1: Manifestations of Infinity: An Overview 2: Sets, Functions, Logic and Countability 3: Sequences and Limits 4: The Real Numbers 5: Infinite Series of Constants 6: Differentiation and Continuity 7: Integration 8: Infinite Sequences and Series of Functions Appendix: Cantor's Construction: Additional Detail Appendix: Discontinuity in a Space of Functions References and Further Reading
£92.99
Birkhauser Verlag AG Lecture Notes on Wavelet Transforms
Book SynopsisThis book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors’ teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India. Trade Review“This textbook is mainly written for advanced undergraduates and master students in mathematics, physics, computer sciences, and electrical engineering. It presents a short, well-written introduction to wavelet transforms and the underlying Fourier theory. … This textbook is very convenient for all students interested in an introduction to wavelet transforms.” (Manfred Tasche, zbMATH 1379.42001, 2018)Table of ContentsThe Fourier Transform.- The Time-Frequency Analysis.- The Wavelet Transforms.- Construction of Wavelets via MRA.- Elongations of MRA Based Wavelets.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Funktionentheorie 1
Book SynopsisDie ersten vier Kapitel dieser Darstellung der klassischen Funktionentheorie vermitteln mit minimalem Begriffsaufwand und auf geringen Vorkenntnissen aufbauend zentrale Ergebnisse und Methoden der komplexen Analysis einer Veränderlichen. Sie gipfeln in einem Beweis des kleinen Riemannschen Abbildungssatzes und einer Charakterisierung einfach zusammenhängender Gebiete. Weitere Themen sind: elliptische Funktionen (Weierstraßscher, Jacobischer Ansatz), die elementare Theorie der Modulformen einer Variablen, Anwendungen der Funktionen- auf die Zahlentheorie (einschl. eines Beweises des Primzahlsatzes). Plus: über 400 Übungsaufgaben mit Lösungen. Trade Review"... Jeder einzelne Abschnitt enthält sorgfältig ausgewählte Übungsaufgaben." Monatshefte für Mathematik "... Positiv hervorzuheben sind die optisch sehr übersichtliche Aufbereitung und der Versuch der Autoren, alle Begriffsbildungen dem Leser gegenüber soweit wie möglich zu motivieren ..." Internationale Mathematische Nachrichten ÖsterreichTable of ContentsDifferentialrechnung im Komplexen.- Integralrechnung im Komplexen.- Folgen und Reihen analytischer Funktionen, Residuensatz.- Konstruktion analytischer Funktionen.- Elliptische Funktionen.- Elliptische Modulformen.- Analytische Zahlentheorie.
£999.99
Springer New York Hidden HarmonyGeometric Fantasies The Rise of
Book SynopsisThis book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place.Trade Review“There is much in this book that will educate, be appreciated by, and no doubt provoke mathematicians as well as historians of mathematics and of science. … It stands its ground as a scholarly treatise that fills many lacunae in the extant historical literature. It will surely provoke further debate and research. As a bonus, it comes filled with treasures for both the specialist and the novice.” (Tushar Das, MAA Reviews, July, 2015)“The book is devoted to the history of complex (analytic) function theory from its origins to 1914. … The book is highly recommended for historians of mathematics, mathematicians with historical interests, and everyone who is interested in complex function theory and its history. It offers a wealth of information that is well documented.” (Karl-Heinz Schlote, Mathematical Reviews, October, 2014)“This comprehensive, massively researched volume … is a detailed historical account of the development of analytic function theory in the 19th century, tracing its rise and ramification through that period up until about 1910. … It is a very dense and scholarly work, suitable for specialists. Summing Up: Recommended. Graduate students, researchers/faculty, and professionals/practitioners.” (D. Robbins, Choice, Vol. 51 (9), May, 2014)“This book is the first one devoted to the history of complex function theory. The authors present the rise of analytic function theory from its origins to 1914. … This book is of great interest and help, not only for mathematicians interested in complex function theory, but also for everyone who likes the history of mathematics.” (Agnieszka Wisniowska-Wajnryb, zbMATH, Vol. 1276, 2014)Table of ContentsList of Figures.- Introduction.- 1. Elliptic Functions.- 2. From real to complex.- 3. Cauch.- 4. Elliptic integrals.- 5. Riemann.- 6. Weierstrass.- 7. Differential equations.- 8. Advanced topics.- 9. Several variables.- 10. Textbooks.
£179.99
Springer International Publishing AG Analysis and Quantum Groups
Book SynopsisThis volume presents a completely self-contained introduction to the elaborate theory of locally compact quantum groups, bringing the reader to the frontiers of present-day research. The exposition includes a substantial amount of material on functional analysis and operator algebras, subjects which in themselves have become increasingly important with the advent of quantum information theory. In particular, the rather unfamiliar modular theory of weights plays a crucial role in the theory, due to the presence of ‘Haar integrals’ on locally compact quantum groups, and is thus treated quite extensively The topics covered are developed independently, and each can serve either as a separate course in its own right or as part of a broader course on locally compact quantum groups. The second part of the book covers crossed products of coactions, their relation to subfactors and other types of natural products such as cocycle bicrossed products, quantum doubles and doublecrossed products. Induced corepresentations, Galois objects and deformations of coactions by cocycles are also treated. Each section is followed by a generous supply of exercises. To complete the book, an appendix is provided on topology, measure theory and complex function theory.Table of ContentsPreface.- Set theoretic preliminaries.- Banach spaces.- Bases in Banach spaces.- Operators on Hilbert spaces.- Spectral theory.- States and representations.- Types of von Neumann algebras.- Tensor products.- Unbounded operators.- Tomita-Takesaki theory.- Spectra and type III factors.- Quantum groups and duality.- Special cases.- Classical crossed products.- Crossed products for quantum groups.- Generalized and continuous crossed products.- Basic construction and quantum groups.- Galois objects and cocycle deformations.- Doublecrossed products of quantum groups.- Induction.-Appendix.- Bibliography.- Index.- Exercises.
£80.99
Birkhauser Verlag AG Introduction to Complex Theory of Differential
Book SynopsisThis book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.Table of ContentsLeray residues.- Ramied integrals.- Asymptotics of ramied integrals.- Ramied Fourier transform.- Properties of ramied Fourier transform.- The Cauchy problem for equations with constant coefficients.- Singularities of the solution of Cauchy problem.- The Cauchy problem for equations with variable coefficients. Leray's uniformization.- Balayage inwards problem.- Mother body problem.- Hints for exercises.
£44.99
