Format: Hardback, 169 pages, height x width: 235x155 mm, XII, 169 p.
Series: Progress in Mathematical Physics
Pub. Date: 09-Sep-2026
ISBN-13: 9783032272553
This monograph develops a semiglobal scattering theory for a broad class of quasilinear wave equations in a neighbourhood of spacelike infinity, including both past and future null infinity. Scattering data are prescribed on an ingoing null cone and at past null infinity.
The authors establish weighted, optimalindecay energy estimates and prove the propagation of polyhomogeneous asymptotics from past to future null infinity. They further introduce an explicit algorithm for computing the coefficients in the resulting expansions and apply it to several linear and nonlinear models. A key consequence is the summability in the sphericalharmonic index of fixedmode estimates previously obtained in the series The Case Against Smooth Null Infinity.
The framework extends beyond finiteenergy solutions and applies directly to systems such as the Einstein vacuum equations in harmonic gauge. A novel ansatz accommodating the strongerthanSchwarzschildean divergence of light cones enables the treatment of slowly decaying data, thereby enlarging the regime of known stability results for Minkowski space in harmonic gauge.
This book is intended for researchers and graduate students in partial differential equations, mathematical relativity, and geometric analysis who seek a precise and versatile framework for understanding asymptotics near null and spacelike infinity.
Introduction and setup.- Discussion of a toy model problem.-
Definitions, Preliminaries and Notation.- ODE Lemmata.- Energy estimates for
the finite problem.- Scattering theory for perturbations of = 0.-
Propagation of polyhomogeneity for = f.- Propagation of polyhomogeneity
for perturbations of = 0 and applications.- Wave equations on
Schwarzschild and the summing of the -modes.- The specificity of peeling to
even spacetime dimensions and asymptotics for the scale-invariant wave
equation.- The no incoming radiation condition on Cauchy data.- Scattering
theory for general quasilinear perturbations.- Analysis of the Einstein
vacuum equations in harmonic gauge.
Format: Hardback, 303 pages, height x width: 235x155 mm, 1 Illustrations, color; 1 Illustrations, black and white
Series: Probability Theory and Stochastic Modelling
Pub. Date: 08-Sep-2026
ISBN-13: 9783032291431
This book presents the modern theory of the geometrical characteristics of random fields and explores their interdisciplinary applications. The first five chapters concentrate on the theoretical and mathematical foundations of the expected measure of level sets, including critical points and Morse theory. They provide a streamlined proof of the Kac-Rice formula, adapted to non-Gaussian cases, and address the problem of the finiteness of moments. The text balances pedagogical explanations with recent, powerful mathematical results. Chapter 4 notably offers an accessible presentation of Hermite representation, the diagram formula, and the fourth moment theorem to establish central limit theorems for the measure of the level set, intentionally avoiding overly complex tools like Malliavin calculus. The latter chapters demonstrate the practical application of these tools across domains such as high-dimensional statistics, theoretical physics, optics and the study of critical points, concluding with a comprehensive bibliographic review. This monograph will be useful for students and researchers in probability theory, geometry, and applied sciences. It will equip them with powerful geometric tools and explicit examples to solve modern problems involving random fields.
Chapter 1. The KacRice Formula, Dimension 1.
Chapter 2. Multidimensional Methods.
Chapter 3. Distributions, Expectations and Moments for Gaussian Processes and Fields.
Chapter 4. Hermite Expansions of Level Functionals.
Chapter 5. Critical Points of Isotropic Gaussian Fields.-
Chapter 6. Second Maximum and Sparse Models.
Chapter 7. Shot Noise Processes.
Chapter 8. Related Works.
Format: Hardback, 360 pages, height x width: 235x155 mm, X, 360 p.
Series: Operator Theory: Advances and Applications
Pub. Date: 27-Sep-2026
ISBN-13: 9783032284105
This book is devoted to the study of evolution equations via form methods. The theory is presented both in the language of Kato, with densely defined forms, and that of Lions, in the spirit of Gelfand triples. The main object is the semigroup associated with a form, for which topics such as positivity, invariance of closed convex sets and the Trotter product formula are discussed.
A wide range of applications is treated, for example, parabolic equations with various boundary conditions, the Stokes operator, the Dirichlet-to-Neumann operator, and non-autonomous semilinear parabolic equations.
The book grew out of the Internet Seminar Form Methods for Evolution Equations, and Applications organized by the authors. Each of the 19 chapters is devoted to one particular subject and includes exercises. As a special feature, carefully placed interludes provide background results, all with complete proofs, to make the book fully self-contained.
Chapter 1. C0-semigroups.
Chapter 2. Characterisation of generators of C0-semigroups.
Chapter 3. Holomorphic semigroups.
Chapter 4. The Sobolev space H1 and applications.
Chapter 5. Forms and operators.
Chapter 6. Adjoint operators and compactness.
Chapter 7. Neumann and Robin boundary conditions.
Chapter 8. The Dirichlet-to-Neumann operator.
Chapter 9. Invariance of closed convex sets.
Chapter 10. Interpolation of holomorphic semigroups.
Chapter 11. Elliptic operators.
Chapter 12. Sectorial forms.-
Chapter 13. Approximation of strongly continuous semigroups.
Chapter 14. Form convergence theorems.
Chapter 15. The Trotter product formula for forms.
Chapter 16. The Stokes operator.
Chapter 17. Non-autonomous equations.
Chapter 18. Maximal regularity for non-autonomous equations.-
Chapter 19. Nonlinear non-autonomous equation
Format: Hardback, 320 pages, height x width: 235x155 mm, II, 320 p.
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 16-Sep-2026
ISBN-13: 9789819205523
This book presents a comprehensive collection of research contributions from the National Conference on Modeling, Analysis, and Simulation (MAS 2024), held at the Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India, from 2830 June 2024. It discusses the foundational and emerging topics vital to solving scientific and engineering challengesranging from mathematical modeling, dynamical systems, and mechanics of solids and fluids to advanced statistical approaches and the application of artificial intelligence, machine learning, and the Internet of Things. Emphasizing mathematical modeling as a powerful lens to represent and analyze complex phenomena, this book bridges disciplines through quantitative abstraction and predictive insight.
This book highlights the role of computational models in capturing the behavior of physical systems, particularly within solid mechanics and fluid dynamics, where accurate simulations support efficient design and analysis. Contributions on dynamical systems theory explore intricate aspects of system stability, nonlinear dynamics, and bifurcation analysis, deepening our understanding of evolving systems. By showcasing the integration of AI and ML with traditional modeling frameworks, this book illustrates how intelligent tools enhance predictive capabilities, facilitate data-driven decision making, and offer scalable solutions to real-world complexity.
Modelling Spatiotemporal Dynamics and Delayed Predation in
PreyPredator Systems with Holling Type IV Functional Response.- Image
quality assessment using CLIP Embeddings.- Intuitionistic Fuzzy
Characteristic Module of Gamma Ring.- Modeling of single-cell electroporation
to evaluate transmembrane potential and pore density: Analytical solution.-
Prediction of turbulence anisotropy with Artificial Neural Network in a
wall-wake flow downstream of two horizontal cylinders.- A New Approach:
Decision-Making from Similarity Measures of Fuzzy and Vague Sets.-
Propagation of Love waves in a functionally graded porous piezoelectric
structure with quadratic variation.- Computational Modeling of Coronary
Artery Stenosis: Symmetric vs. Asymmetric Hemodynamic Effects.- Random Forest
Regression for Vanadium Leaching Prediction: RMSE and MSE Analysis.- Theory
of Light Wave Propagation in Graded-Index Claded Optical Fibers.- Anti-Plane
Wave Dynamics in a Layered Model Featuring Interfacial Strain Gradient
Effects.- Stability Theory of System of Generalized Fractional Order
Wiener-Hopf Resolvent Dynamical System and System of Generalized Nonlinear
Variational Inequality Problem.- Mathematical modelling of hollow fibre
membrane bioreactor containing deformable porous scaffold: application to
tissue engineering.- Dynamics of Rayleigh waves at the junction of
orthotropic and piezo-thermoelastic media under rotation.
Format: Paperback / softback, 201 pages, height x width: 235x155 mm, XI, 201 p.
Series: Universitext
Pub. Date: 04-Aug-2026
ISBN-13: 9783032315496
This book provides a rigorous introduction to Fourier analysis and the theory of distributions without presupposing an advanced background in functional analysis or measure-theoretic integration.
The guiding principle throughout is to present the material in an elementary and direct manner without sacrificing mathematical precision or depth. After introducing Fourier series and their fundamental properties in the first chapter, the main ideas of Fourier analysis are developed first for non-periodic functions on Euclidean space, where many concepts can be presented more transparently, and are subsequently transferred to the periodic setting. Likewise, distribution theory is initially developed in the framework of tempered distributions, which allows for a simpler exposition and is particularly well suited to applications in partial differential equations, including those discussed in Chapter 7. Distributions on open subsets of Euclidean space are then introduced via localization, emphasizing their inherently local character. The final chapter presents an elementary proof of the Schwartz kernel theorem based on expansions in Hermite functions, from which the tensor product of distributions is obtained as an immediate consequence. Each chapter concludes with a collection of exercises ranging from routine applications to more challenging problems.
1 The Basic Idea of Fourier Analysis: Expansion of Periodic Functions
into Trigonometric Series.- 2 Fourier Transform and Convolution on
R𝒏.- 3 Fourier Series and the Poisson Summation Formula.- 4 Tempered
Distributions.- 5 Distributions in Open Subsets of R𝒏.- 6
Distributions with Compact Support.- 7 Fundamental Solutions.- 8 On the
Regularity Theory of Linear Partial Differential Equations: The Singular
Support and Hypoellipticity.- 9 The Schwartz Kernel Theorem, and the Tensor
Product of Distributions.- Appendix A: The Baire Category Theorem and the
BanachSteinhaus Theorem*.
Format: Paperback / softback, 245 pages, height x width: 235x155 mm, 7 Illustrations, black and white
Series: UNITEXT
Pub. Date: 26-Sep-2026
ISBN-13: 9783032315113
Geometric Methods in Mathematical Physics I: Tensors, Special Relativity, Spinors provides a rigorous and pedagogically coherent introduction to the algebraic and geometric language used in modern mathematical physics.The book develops the foundations of multilinear algebra and tensor calculus from first principles, covering dual and conjugate spaces, multilinear maps, tensor products, the universal property of tensor products, tensor algebra, abstract index notation, exterior algebra, scalar products, metric tensors, pseudo-tensors, and tensor densities. Particular attention is given to the relationship between the abstract mathematical definition of tensors and the practical index notation commonly used in physics.The text then applies these tools to group theory, representation theory, and relativistic physics. It discusses tensor products of group representations, symmetry of tensors, Grassmann algebra, pseudo-orthogonal groups, and polar decomposition. These topics prepare the reader for a geometric presentation of Special Relativity, including Minkowski spacetime, Lorentz and Poincaré transformations, relativistic kinematics and dynamics, four-momentum, conservation laws, four-force, and the stress-energy tensor for macroscopic systems.The final chapters introduce the structure of the Lorentz group, its Lie algebra, boosts and rotations, the relation between SL(2,C) and SO(1,3), and the basic theory of Weyl and Dirac spinors, including the Dirac equation.
Designed for graduate students and advanced readers in mathematics, physics, and mathematical physics, the book offers a compact but rigorous bridge between multilinear algebra, tensor methods, Special Relativity, and spinorial techniques. It is suitable both as a course text and as a reference for readers seeking a solid mathematical foundation for the geometric methods of theoretical physics.
Geometric Methods in Mathematical Physics I: Multilinear Algebra,
Tensors, Spinors, and Special Relativity.- Introduction.-Multilinear Maps and
Tensors.- Tensor algebra, abstract index notation and some applications.-
Some applications to general group theory.- Scalar Products and Metric
Tools.- Polar Decomposition Theorem in the finite-dimensional case.- Special
Relativity: a Geometric Presentation.- Lorentz group structure.- SL(2,C) and
SO(1,3).- Introduction to Spinors.- Elements of matrix Lie group theory.-
Index.- Index of Symbols.
Format: Hardback, 299 pages, height x width: 235x155 mm, VIII, 299 p.
Series: Operator Theory: Advances and Applications
Pub. Date: 01-Oct-2026
ISBN-13: 9783032266118
This book originates from the International Workshop on Operator Theory and its Applications (IWOTA) held in Canterbury, University of Kent, UK, in August 2024. It includes both original research articles and broad survey articles on current developments in the field. IWOTA is a major series of annual workshops in mathematical analysis which covers operator-theoretic aspects of topics such as complex analysis, harmonic analysis, linear algebra, random matrix theory, mathematical physics, and their applications, such as control theory, signal processing and AI.
Long- and Short-Time Behavior of Hypocoercive Evolution Equations
via Modal Decompositions.- A quick guide to ordinary state-dependent delay
differential equations.- Turing meets Moore-Penrose: Computing the
Pseudoinverse on Turing Machines.- Bicomplex Cauchys Theorem: several
versions.- Some Open Problems from IWOTA 2024 Presented at the Special
Session on Orthogonal Polynomials and Special Functions.- Automatic time
continuity of positive matrix and operator semigroups.- Spectra and
semigroups of linear differential operators with periodic coefficients.-
Composition of outer functions.- Critical points of the 4×4 unistochastic
map.- Tauberian Theorems for Sequences and the KatznelsonTzafriri Theorem.-
Lie theory of the slice Riemannian geometry on the quaternionic unit ball.-
Toeplitz operators with invariant symbols under the action of some subgroups
of 𝑆𝑛 T𝑛 on the Fock Space on C𝑛.- An
estimate for 𝛽-Hermite ensembles via the zeros of Hermite
polynomials.- A Note on Maximal Operators for Moment Curves.
Format: Hardback, 243 pages, height x width: 235x155 mm, II, 243 p.
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 22-Sep-2026
ISBN-13: 9789819207503
This proceedings volume contains chapters presented at the International Conference on Lie Algebras and Number Theory (ICLANT-2024), held at the Department of Mathematics, National Institute of Technology Calicut, Kerala, India, from 1014 June 2024. It discusses recent research on Lie algebras and number theory and studies their applications in several areas in mathematics and physics. Chapters in the book address the representation theory of Lie algebras, superalgebras and number theory. The book aims to emphasize the diversity of Lie theory and its applications to other branches of mathematics, in particular number theory and other areas of physics.
Highest Weight Modules and Quasi-Integrality over Twisted Affine Lie
Superalegbras.- Schur Multiple Zeta-Functions of Hurwitz Type.- A Survey on
Power Maps in Groups.- On Central Derivation of n-Lie Algebras.- Lifting of
Maass Forms to O(1, 8n + 1) and Applications to the Sup-Norm Problem.- On
Classical and Quaternionic SaitoKurokawa Lifting.- What is an L-function
from Euler to Langlands and Beyond.- Zeta Functions on Infinite Extensions.-
Atkin's Up Operator on Modular Forms Mod p.- Variants of ErdosKac via
Tauberian Theorems.- Stability of 2-class Group in Z2-extensions.-
Surjectivity of Trace for Relative Extensions.- Squarefree Part of a
Discriminant and abc-conjecture.- Lower Bound on Height Functions.- (an, bn)-
f-statistical Convergence and Korovkin Type Approximation Theorems.-
Arithmetic Density and Infinite Families of Congruences Modulo 2 for (u,
v)-Regular Bipartitions.- Report on Modular forms and L-functions.
Format: Paperback / softback, 362 pages, height x width: 235x155 mm, 33 Illustrations, color; 33 Illustrations, black and white
Series: Lecture Notes in Mathematics
Pub. Date: 09-Oct-2026
ISBN-13: 9783032294265
This volume presents seven invited lecture series from the DFG Priority Programme Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness, surveying recent developments in mathematical fluid dynamics across a broad range of scales, from kinetic theory to turbulence, mixing, and relativistic flows. The contributions reflect current research directions in the field. Hana Mizerovį and Simon Markfelder discuss aspects of the emerging theory of non-standard weak and generalized solutions to the compressible Euler equations. Theodore Drivas addresses turbulence, Gianluca Crippa studies mixing phenomena, TaiPing Liu and ShihHsien Yu develop the theory of nonlinear waves for the Boltzmann equation, and Marcelo Disconzi focuses on dissipative relativistic fluid dynamics.
The volume is intended for researchers and advanced graduate students in partial differential equations and applied mathematics.
Chapter 1. A general framework for convex integration and its application to the compressible Euler equations.
Chapter 2. Convergence of entropy-stable finite volume approximations of compressible Euler equations.-
Chapter 3. Mathematical theorems on turbulence.
Chapter 4. Introduction to the theory of mixing for incompressible flows.
Chapter 5. Micro-micro decomposition: Positivity of Boltzmann shock profile and Greens function.-
Chapter 6. Coupling of boundary layer and fluid waves for the Boltzmann equation.
Chapter 7. Recent progress in relativistic viscous fluid dynamics.