Format: Hardback, 306 pages, height x width: 235x155 mm, 15 Tables, color; 15 Illustrations,
color; 6 Illustrations, black and white; IV, 306 p. 21 illus., 15 illus. in color
Pub. Date: 02-Sep-2022
ISBN-13: 9783031053306
Analysis at Large is dedicated to Jean Bourgain whose research has deeply influenced the mathematics discipline, particularly in analysis and its interconnections with other fields. In this volume, the contributions made by renowned experts present both research and surveys on a wide spectrum of subjects, each of which pay tribute to a true mathematical pioneer. Examples of topics discussed in this book include Bourgain's discretized sum-product theorem, his work in nonlinear dispersive equations, the slicing problem by Bourgain, harmonious sets, the joint spectral radius, equidistribution of affine random walks, Cartan covers and doubling Bernstein type inequalities, a weighted Prekopa-Leindler inequality and sumsets with quasicubes, the fractal uncertainty principle for the Walsh-Fourier transform, the continuous formulation of shallow neural networks as Wasserstein-type gradient flows, logarithmic quantum dynamical bounds for arithmetically defined ergodic Schroedinger operators, polynomial equations in subgroups, trace sets of restricted continued fraction semigroups, exponential sums, twisted multiplicativity and moments, the ternary Goldbach problem, as well as the multiplicative group generated by two primes in Z/QZ. It is hoped that this volume will inspire further research in the areas of analysis treated in this book and also provide direction and guidance for upcoming developments in this essential subject of mathematics.
On the joint spectral radius (E. Breuillard).- The failure of the fractal uncertainty principle for the Walsh-Fourier transform (C. Demeter).- The continuous formulation of shallow neural networks as Wasserstein-type gradient flows (X. Fernandez-Real).- On the Origins, Nature and Impact of Bourgain's Discretized Sum-Product Theorem (A. Gamburd).- Cartan Covers and Doubling Bernstein Type Inequalities on Analytic Subsets of C2 (M. Goldstein).- A Weighted Prekopa-Leindler inequality and sumsets with quasicubes (B. Green).- Equidistribution of affine random walks on some nilmanifolds (E. Lindenstrauss).- Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrodinger operators with smooth potentials (S. Jitomirskaya).- The slicing problem by Bourgain (B. Klartag).- On the work of Jean Bourgain in nonlinear dispersive equations (E. Kenig).- On Trace sets of restricted continued fraction semigroups (A. Kontorovich).- Polynomial Equations in Subgroups and Applications (V. Konyagin).- Exponential sums, twisted multiplicativity and moments (E. Kowalski).- The ternary Goldbach problem with a missing digit and other primes of special types (Th. Rassias).- A note on harmonious sets (Y. Franc cois Meyer).- On the multiplicative group generated by two primes in Z/QZ (P. Varju).
Format: Hardback, 498 pages, height x width: 235x155 mm, 50 Tables, color; 75 Illustrations, color; 29 Illustrations,
black and white; VIII, 498 p. 104 illus., 75 illus. in color
Pub. Date: 22-Sep-2022
ISBN-13: 9783031071706
This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Symposium on the Theory and Applications of Integral Methods in Science and Engineering, held virtually in July 2021, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.
Approximate Solution for One-Dimensional Compressible Two-Phase Immiscible Flow in Porous Media for Variable Boundary Conditions (P. Pires).- On Pseudo-Cross Sections for Neutron Escape from a Domain by a Physical Monte Carlo Simulation (D.G. Benvenutti).- From a Unitary Symmetry Hypothesis to Dynamical Structures in Quantum Mechanics Models (B.E.J. Bodmann).- The Traction Boundary Value Problem for Thin Elastic Structures (C. Constanda).- Mapping Properties of Potential Operators Related to the 2D Compressible Stokes System in Weighted Sobolev Spaces (C. Fresneda-Portillo).- Stochastic effects of the meander on the dispersion of pollutants in the planetary boundary layer under low wind conditions (D. Buske).- Asymptotics for the spectrum of a Floquet-parametric family of homogenization problems associated with a Dirichlet waveguide (Perez-Martinez).- The Wavelet-Based Integral Formula for the Solutions of the Wave Equation in an inhomogeneous Medium: Convergence of Integrals (Perel).- Modelling The Spread of a Disease in an Epidemic Through a Country Divided into Geographcal Regions (P.J. Harris).- Computing Elastic Interior Transmission Eigenvalues (A. Kleefeld).- A Novel Solution of the Multi-Group Neutron Diffusion Equation by the Hankel Transform Formalism (J.C.L. Fernandes).- A Simple Numerical Scheme to Obtain Reflectivity and Transmissivity of an Isotropically Scattering Slab (C.A. Ladeia).- A Unified Integral Equation Formulation for Linear and Geometrically Nonlinear Analysis of Thick Plates: Derivation of Equations (R.J. Marczak).- On viscous fluid flow in curvilinear coordinate systems (Meneghetti).- Impact Loading of Interface Cracks: Effects of Cracks Closure and Friction (Menshykova).- Periodic Solutions in Rn for Stationary Anisotropic Stokes and Navier-Stokes Systems (S.E. Mikhailov).- Null-solutions of elliptic partial differential equations with power growth (D. Mitrea).- On the Use of the Adjoint Technique to the Estimation of Neutron Source Distributions in the Context of Subcritical Nuclear Reactors (R.C. Barros).- The Nodal LTSN Solution and a New Approach to Determine the Outgoing Angular Flux at the Boundary in a Retangular Domain (A.R. Parigi).- A numerical study of the convergence of two hybrid convolution quadrature schemes for broadband wave problems (D.J. Chappell).- Analytical Reconstruction of the Nonlinear Transfer Function for a Wiener-HammersteinModel (J. Schmith).- Variation of Zero-Net Liquid Holdup in Gas-Liquid Cylindrical Cyclone (GLCC c) (O. Shoham).- On the Mono-Energetic Neutron Space Kinetics Equation in Cartesian Geometry: An Analytic Solution by a Spectral Method (F. Tumelero).
Format: Hardback, 196 pages, height x width: 235x155 mm, 19 Illustrations, color; 10 Illustrations,
black and white; XII, 196 p. 29 illus., 19 illus. in color.
Series: Studies in Computational Intelligence 1040
Pub. Date: 11-Sep-2022
ISBN-13: 9783031077067
The recent book of the series continues the collection of articles dealing with the important and efficient combination of traditional and novel mathematical approaches with various computational intelligence techniques, with a stress of fuzzy systems, and fuzzy logic.
Complex systems are theoretically intractable, as the need of time and space resources (e.g., computer capacity) exceed any implementable extent. How is it possible that in the practice, such problems are usually manageable with an acceptable quality by human experts? They apply expert domain knowledge and various methods of approximate modeling and corresponding algorithms. Computational intelligence is the mathematical tool box that collects techniques which are able to model such human interaction, while (new) mathematical approaches are developed and used everywhere where the complexity of the sub-task allows it. The innovative approaches in this book give answer to many questions on how to solve “unsolvable” problems.
Decidability of real-valued S4 Godel logic.- Basic logic versus multi-adjoint logic.- Fuzzy logic programming with generalized quantifiers.- Fuzzy relations: the fundament for fuzzy rough approximation, fuzzy concept analysis and fuzzy mathematical morphology.- Information bireducts and its relationship with reducts.- On the applicability of fuzzy lines in circular Hough transform in lesion segmentation on liver CT images.- Directional properties of semi-aggregation functions.- Generalized Phi-Transform of Aggregation Functions on Bounded Lattices.- Sugeno Integral for Atanassov Intuitionistic Fuzzy Sets.- Facilitating the simulation of domestic energy systems through linguistic representations.- Experiments with the Discrete Bacterial Memetic Evolutionary Algorithm for solving the Cumulative Capacitated Vehicle Routing Problem.- Fuzzy Inference System-like Aggregation Operator (FISAO) for Fuzzy Signatures.- Context of a local congruence concept reduction.- One-sided concept lattices by blocks.- From Fuzzy Partitions to Riemannian Manifolds.- Discrete universal fuzzy integrals.- Energy determined membership function of viscoelastic models.- Advances in forgery detection of driving licences using truthfulness degrees.- A formal method for driver identification.- Analysis and identification of forensic events using non-parametric density estimation.- Fuzzy signature based model in material handling management.- On Choquet integral in ranking crimes.- The Effects of Knowledge Extraction Approaches on Cryptanalysis Studies and Analysis of the Success of Chaos-Based Countermeasures.
Format: Paperback / softback, 249 pages, height x width: 240x168 mm, 8 Tables, color; 6 Illustrations,
color; 35 Illustrations, black and white; IX, 249 p. 41 illus., 6 illus. in color.
Series: Frontiers in the History of Science
Pub. Date: 01-Sep-2022
ISBN-13: 9783031057199
The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon’s program of braid monodromy factorization.
By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods.
Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.
Chapter 1: Introduction.
Chapter 2: Prolog: Separate beginnings during the 19th century.
Chapter 3: 1900s-1930s: Branch curves and the Italian school of algebraic geometry.
Chapter 4: Chisini's branch curves: the decline of the classical approach.
Chapter
5. From the 1970s onwards: the rise of braid monodromy factorization.-Chapter 6: Epilogue: On ramified and ignored spaces.
Format: Hardback, 610 pages, height x width: 254x178 mm, 100 Illustrations,
black and white; XX, 610 p. 100 illus.
Series: Encyclopedia of Complexity and Systems Science Series
Pub. Date: 24-Sep-2022
ISBN-13: 9781071626207
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [ write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.
Diagrammatic Methods in Classical Perturbation TheoryHamiltonian Perturbation Theory (and Transition to Chaos)Kolmogorov-Arnold-Moser (KAM) Theory for Finite and Infinite Dimensional Systemsn-Body Problem and ChoreographiesNekhoroshev TheorySymmetry and Perturbation Theory in Non-linear DynamicsNormal Forms in Perturbation TheoryPerturbation Analysis of Parametric ResonancePerturbation of Equilibria in the Mathematical Theory of EvolutionPerturbation of Systems with Nilpotent Real PartPerturbation TheoryPerturbation Theory in Celestial MechanicsIntroduction to Perturbation TheoryPerturbation Theory and Molecular DynamicsPerturbation Theory for Non-smooth SystemsPerturbation Theory for PDEsPerturbation Theory in Quantum MechanicsSemiclassical Perturbation TheoryConvergence of Perturbative ExpansionsQuantum BifurcationsPerturbation of superintegrable systemsComputational methods in perturbation theoryPerturbation Theory for Water Waves Perturbation Theory and the Method of DetuningPeriodic Rogue Waves and Perturbation TheoryConvergent perturbative expansion in Condensed Matter and Quantum Field TheoryQuantum Adiabatic TheoremExact and perturbation methods in the dynamics of legged locomotionCorrelation corrections as a perturbation to the quasi-free approximation in many-body quantum systems
Format: Hardback, 298 pages, height x width: 235x155 mm, 7 Illustrations, color; 2 Illustrations,
black and white; X, 298 p. 9 illus., 7 illus. in color., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 15-Oct-2022
ISBN-13: 9783031075308
This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications.
As in the case of other interesting quaternionic function theories, the original motivations were the richness of the theory of holomorphic functions of one complex variable and the fact that quaternions form the only associative real division algebra with a finite dimension n>2. (Slice) regular functions quickly showed particularly appealing features and developed into a full-fledged theory, while finding applications to outstanding problems from other areas of mathematics. For instance, this class of functions includes polynomials and power series. The nature of the zero sets of regular functions is particularly interesting and strictly linked to an articulate algebraic structure, which allows several types of series expansion and the study of singularities. Integral representation formulas enrich the theory and are fundamental to the construction of a noncommutative functional calculus. Regular functions have a particularly nice differential topology and are useful tools for the construction and classification of quaternionic orthogonal complex structures, where they compensate for the scarcity of conformal maps in dimension four.
This second, expanded edition additionally covers a new branch of the theory: the study of regular functions whose domains are not axially symmetric. The volume is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.
Introduction.- 1.Definitions and Basic Results.- 2.Regular Power Series.- 3.Zeros.- 4.Infinite Products.- 5.Singularities.- 6.Integral Representations.- 7.Maximum Modulus Theorem and Applications.- 8.Spherical Series and Differential.- 9.Fractional Transformations and the Unit Ball.- 10.Generalizations.-
11. Function Theory over Non-symmetric Slice Domains.-12. Applications.- Bibliography.- Index.
Format: Paperback / softback, 96 pages, height x width: 235x155 mm, 4 Tables,
color; 5 Illustrations, black and white; XI, 96 p. 5 illus., 1 Paperback / softback
Pub. Date: 22-Aug-2022
ISBN-13: 9789811936883
This book discusses the invertibility of fuzzy topological spaces and related topics. Certain types of fuzzy topological spaces are introduced, and interrelations between them are brought forth. Various properties of invertible fuzzy topological spaces are presented, and characterizations for completely invertible fuzzy topological spaces are discussed. The relationship between homogeneity and invertibility is examined, and, subsequently, the orbits in an invertible fuzzy topological space are studied. The structure of invertible fuzzy topological spaces is investigated, and a clear picture of the inverting pairs in an invertible fuzzy topological space is introduced. Further, the related spaces such as sums, subspaces, simple extensions, quotient spaces, and product spaces of invertible fuzzy topological spaces are examined. In addition, the effect of invertibility on fuzzy topological properties like separation axioms, axioms of countability, compactness, and fuzzy connectedness in invertible fuzzy topological spaces is established. The book sketches ideas extended to the bigger canvas of L-topology in a very interesting manner.
Motivation and Preliminaries.- H-fuzzy topological spaces.- Invertible fuzzy topological spaces.- Types of invertible fuzzy topological spaces.- Properties of invertible fuzzy topological spaces.- Invertibility of the related spaces.- Invertible R-topological spaces.