Format: Hardback, 540 pages, height x width: 235x155 mm, 51 Illustrations, black and white; XI, 540 p. 51 illus., 1 Hardback
Pub. Date: 24-Mar-2025
ISBN-13: 9783031772030
This book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints.
Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmuller theory, complex manifolds, extremal problems, and many others.
This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field.
Introduction.- The Riemann Mapping Theorem.- The Ahlfors Map.- A
Riemann Mapping Theorem for Two-Connected Domains in the Plane.- Riemann
Multiply Connected Domains.- Quasiconformal Mappings.- Manifolds.- Riemann
Surfaces.- The Uniformization Theorem.- Automorphism Groups.- Ridigity of
Holomorphic Mappings and a New Schwarz Lemma at the Boundary.- The Schwarz
Lemma and Its Generalizations.- Invariant Distances on Complex Manifolds.-
Hyperbolic Manifolds.- The Fatou Theory and Related Matters.- The Theorem of
Bun Wong and Rosay.- Smoothness to the Boundary of Biholomorphic Mappings.-
Solution problem.- Harmonic measure.- Quadrature.- Teichmuller Theory.-
Bibliography.- Index.
Format: Paperback / softback, 371 pages, height x width: 235x155 mm, 8 Illustrations, color; 7 Illustrations,
black and white; XI, 371 p. 15 illus., 8 illus. in color., 1 Paperback
Series: Research Perspectives
Pub. Date: 03-Mar-2025
ISBN-13: 9783031770494
This volume contains the contributions of the participants of the 14th ISAAC congress, held at the University of S?o Paulo, Campus Ribeir?o Preto, Brazil, on July 17-21, 2023. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume constitutes a valuable resource on current research in mathematical analysis and its various interdisciplinary applications, both for specialists and non-specialists alike.
- Part I: Complex Geometry.- On the Jacobian Variety of the
Accola-Maclachlan Curve of Genus Four.- T-Invariant Points on T-varieties.-
Computations on the Hilbert-Mumford Criterion for Grassmanians.- Rational
Homotopy and Hodge Theory of Moduli Stacks of Principal G-Bundles.- On Slice
Regular Bergman Spaces and Fiber Bundles.- Part II: Complex Variables and
Potential Theory.- Inequalities for the Inner Radii of Domains Containing an
Arbitrary Ellipse Points and Infinity.- On the Carleman-Bers-Vekua Equation.-
On Asymptotics of Ring Q-Homeomorphisms with Respect to p-Modulus near the
Origin.- Approximate Solutions of some Problems in Thermoelasticity.- On
Local Holder and Lipschitz Continuities of Solutions to Nonlinear Beltrami
Equation.- A Piecewise Continuous Schwarz-Type Boundary-Value Problem in an
Angle for Monogenic Functions in a Commutative Biharmonic Algebra.- On
Distortion Estimates of Mappings with the Poletsky Condition in Domains with
Poincare Inequality.- Part III: Function Spaces and their Applications.-
Well-Posedness for a System of Nonlinear Schrodinger Equations with
Derivative Nonlinearity via the Energy Method.- Part IV: Harmonic Analysis
and Related Topics.- Geometric Herz Spaces and Poisson Kernels in the Upper
Half-Space.- Part V: Partial Differential Equations Oncurved Spacetime.-
Optimal L-Decay Rate of Solutions to a Dissipative Nonlinear Schrodinger
Equation System.- Global Solutions of the Klein-Gordon Equation under the
Quartic Potential in the de Sitter Spacetime.- About Critical Exponents in
Semi-Linear de Sitter Models.- Part VI: PDEs in Fluid Mechanics.- A Family of
Systems Including the Herschel-Bulkley Fluid Equations.- On the
Well-Posedness for the Inviscid Boussinesq Equations in Besov-Herz Spaces.-
Blowing up and Dissipation for a Couple of One-Dimensional Non-Local
Conservation Laws.- Part VII: Recent Progress in Evolution Equations.- Lp
Lq Estimates for Very Strongly Damped Wave Equations.- Decay Estimates for
Space-Time Fractional Equations with Structural Damping and Nonlinear
Memory.- Revisit on Global Existence of Solutions for Semilinear Damped Wave
Equations in RN with Noncompactly Supported Initial Data.- Part VIII:
Stochastic Processes.- Hedging in a Market with Jumps A FBSDE Approach.-
Global Smooth Solutions for the Stochastic Navier-Stokes Equations with
Super-Linear Stratonovich Noise in the 3D Torus.- Part IX: Wavelet theory and
its Related Topics.- On Characterization of the Gabor Wavelet Transform of
Analytic Functionals.- The p-Adic Fourier Transform of the Locally Constant
Functions.- Fractional Neural Network Interpolation Operator for Irregular
Grid Points.
Format: Hardback, 400 pages, height x width: 240x168 mm, 3 Illustrations, black and white; XXVI, 400 p. 3 illus., 1 Hardback
Pub. Date: 16-Mar-2025
ISBN-13: 9789819611683
This is an invaluable book that presents the original work published in French, in 1904, by Henry Leon Lebesgue, the creator of the theory of integration. Translated into English for the first time, the book offers readers a unique opportunity to explore Lebesgues groundbreaking ideas and delves into the mind of one of the greatest mathematicians in history. The book provides historical context and explanations that enhance readers comprehension and appreciation of the material. Covering a wide range of topics, from the integration before Riemann to the search for primitive functions, it offers a comprehensive understanding of Lebesgues theories and their significance in the field of mathematics. It inspires readers to explore further in the field, stimulates new ideas, and opens avenues for future research. The book bridges the gap between theory and practice by providing examples and applications that contributed to the development of Lebesgue integration theory.
The book serves as a valuable resource for courses in analysis, measure theory, and Lebesgue integration theory, providing students with the opportunity to study the original work of Lebesgue and deepen their understanding of integration theory. It is meant for a broad audience, including advanced undergraduate and graduate students, mathematics scholars, researchers, educators, and enthusiasts, seeking a comprehensive understanding of Lebesgues theories and the historical development of integration theory. Mathematicians and researchers will find this book essential for its historical significance and the preservation of important mathematical literature.
The Integration before Riemann.- The Definition of Integral Given by Riemann.- Geometric Definition of the Integral.- The Functions of the Bounded Variation.- The Search for Primitive Functions.- The Integration Defined with the Help of Primitive Functions.- The Definite Integral of Summable Functions.- The Indefinite Integral of Summable Functions.- The Seach of Primitive Functions. The Existence of Derivatives.- The Totalisation.- The Integral of Steiltjes.
Format: Paperback / softback, 203 pages, height x width: 240x168 mm, 40 Illustrations, black and white; XIV, 203 p. 40 illus., 1 Paperback
Series: Frontiers in Mathematics
Pub. Date: 27-Feb-2025
ISBN-13: 9783031776120
This book provides readers with an engaging explanation of the Aleksandrov problem, giving readers an overview of the process of solving Aleksandrov-Rassias problems, which are still actively studied by many mathematicians, and familiarizing readers with the details of the proof process. In addition, effort has been put into writing this book so that readers can easily understand the content, saving readers the trouble of having to search the literature on their own. In fact, this book logically and kindly introduces the basic theories of related fields.
Preface.- Preliminaries.- Aleksandrov Problem.- Aleksandrov-Benz
Problem.- Aleksandrov-Rassias Problems.- Rassias and Xiangs Partial
Solutions.- Inequalities for Distances between Points.- Jung, Lee, and Nams
Partial Solutions.- Miscellaneous.- Bibliography.- Index.
Format: Paperback / softback, 297 pages, height x width: 240x168 mm, 139 Illustrations, black and white; X, 297 p. 139 illus., 1 Paperback
Series: Advanced Courses in Mathematics - CRM Barcelona
Pub. Date: 16-Mar-2025
ISBN-13: 9783031777783
This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the Higher homotopical structures programme.
Since their introduction 60 years ago, the notions of infinity algebras (Stasheff, Sugawara), higher categories (Boardman-Vogt), operads (May), and model categories (Quillen) have given rise to powerful new tools which made possible the resolution of open problems and prompted revolutions in many domains like algebraic topology (rational homotopy theory, faithful algebraic invariants of the homotopy type of spaces), deformation theory (formality theorems, formal moduli problems), and mathematical physics (quantization of Poisson manifolds, quantum field theories), to name but a few.
This theory of higher structures using operadic calculus is currently under rapid development. The aim of this book is to provide the community with an accessible state-of-the-art, while at the same time giving interested researchers and advanced students a brief overview on the subject.
Foreword.- Alexander Berglund and Robin Stoll: Higher structures in
rational homotopy theory.- Ricardo Campos and Albin Grataloup: Operadic
deformation theory.- Coline Emprin and Geoffroy Horel: Weight structures and
formality.- Damien Calaque and Victor Roca I Lucio: Associators from an
operadic point of view.- Olivia Borghi and Marcy Robertson: Lecture notes on
modular infinity operads and grothendieck-teichmuller theory.
Format: Hardback, 199 pages, height x width: 235x155 mm, 49 Illustrations, color; 12 Illustrations, black and white; X, 199 p. 61 illus., 49 illus. in color., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 479
Pub. Date: 13-Mar-2025
ISBN-13: 9783031784002
This volume features a collection of peer-reviewed contributions from the biannual conference organized by the Mexican Statistical Society, held in Cuernavaca, Mexico, from September 27-29, 2023. Statistical research in Latin America is vibrant and far-reaching, with extensive networks both within the region and beyond. However, much of this work is published in Spanish, limiting access for a broader audience. This volume aims to bridge that gap by presenting selected research from Latin American scholars and their collaborators to a wider readership. Academics will find value in the latest methodological advancements, while practitioners from various fields may discover innovative tools for data analysis. The volume places special emphasis on environmental statistics and applications that address societal issues or directly model social phenomena.
Preface.- Towards Inference for Finite Populations.- A Splitting
Criterion for CARTs Based on Bayesian Optimisation.- A little bird told me:
Roadmap towards frequent and representative official statistical information,
through joint use of social network posts and survey data.- Dynamic
Evaluation of Electoral Preferences in Mexico: A Bayesian Power
Ranking Model.- Modeling Oral Glucose Tolerance Test (OGTT) data and its
Bayesian Inverse Problem.- A conditional approach to Bayesian inference in
copula models.- A new bivariate model based on Gamma
distributions.- Mortality estimation with controlled smoothing by segments
applied to potentially insured missing persons in Mexico.- Development of
Cyclical Indicators Based on Multivariate Spectral Analysis.- A Copula-based
Fully Bayesian Nonparametric Evaluation of Cardiovascular Risk Markers for
Normoglycemic Patients in the Mexico City Diabetes Study.- University
infrastructure as a factor influencing entrepreneurial intention:
a structural equation model.- An approach of latent class mixed models for
analyzing new genotypes of Saccharum spp.- Kernel Feature Ordering by
Conditional Independence in Species Diversity.- Antisocial behaviour in young
Mexicans. Lifestyle assessment and risk factors detection.- Author Index.