Format: Hardback, 201 pages, height x width: 235x155 mm, 7 Illustrations,
color; 8 Illustrations, black and white; XII, 201 p. 15 illus., 7 illus. in color., 1 Hardback
Series: Trends in Mathematics 13
Pub. Date: 12-Jul-2025
ISBN-13: 9783031894626
The present volume collects extended abstracts of lectures and talks presented at the Summer School and Conference "Analysis, PDEs and Applications" held 24 June - 6 July 2024 at Yerevan State University, Armenia. The thematic scope of contributions includes linear and non-linear partial differential equations, spectral theory and microlocal analysis, harmonic and functional analysis, theory of functions and approximation theory, and applications in mathematical physics. Each talk or lecture begins with a survey of a body of mathematical work, either classic or modern, leading up to recent advances. This is followed by an exposition of either a specific research problem or a broader area of modern mathematical research, presented by an expert in the field.
The volume will be of interest to not only students and young researchers, but also experts looking for a crash course in the main concepts and ideas in one of the many advanced mathematical topics discusse
Mapping Properties of Maximal Functions on Graded Lie Groups.- An
Invitation to Quantum Field Theory and to its Interplay with Microlocal
Analysis and PDEs.- Fourier Analysis via Mild Distributions: Group
Theoretical Aspects.- On the Theory of Functions of Omega-Bounded Type.-
Subsequences of Sequences of Multiple Partial Trigonometric Fourier Sums.- A
Vectorial Free Boundary Transmission Problem (A Short Exposition).- On the
??2-Analogue of the Inverse Source Heat Equation.- On Typical and
Atypical Asymptotic Behavior of Singular Solutions to EmdenFowler Type
Equations.- Some Harmonic Bergman-Type Projections on Besov and Bloch
Spaces.- On a Dirichlet Problem for a Properly Elliptic Equation in the Space
of Continuous Functions, in the Case of Multiple Roots.- On the Behavior of
Fourier Coefficients in the Trigonometric System.- Discrete-Time Replicator
Equations, Gradient Vector Fields of Nonlinear Mappings, and Optimal
Transport Networks.- Deviation Identity for Linear Differential Operators and
Its Application to Obstacle Problems.- Nonlinear Approximation with Respect
to the Walsh Generalized System.- On the Convergence of Negative-Order Cesaro
Means of Fourier and Fourier-Walsh Series.- Irreversibility of a Classical
Three-Body Problem: Complexity of a Low-Dimensional System.- On Polynomial
Solutions of a PDE with Constant Coefficients.- On Weighted Integral
Operators for Solution of ?? Equation in the Siegel Domain of
??n.- On Directionally-Differentiable Selections of Set-Valued
Mappings.- On the Convergence of Hard Sampling Operators.-
Orientation-Dependent Section Distributions for Convex Bodies.- On the Issues
of Modeling the Elimination of Deadlock Situations and Synchronization
Problems Using Petri Nets.- Generalized Abel-Plana Formula as a
Renormalization Tool in Quantum Field Theory.- On the Universal Functions for
Weighted Spaces.- On the Convergence Fourier-Vilenkin Series.- On the
Universal Functions for Weighted Spaces.- Construction of a Mathematical
Model and Optimization of the Bending of a Beam.- Delaunay Triangulation in
Numerical Solution of Two-Dimensional Boundary Value Problems.- Normal
Solvability and Fredholm Properties for Regular Hypoelliptic Operators.
Format: Hardback, 210 pages, height x width: 235x155 mm, 105 Illustrations,
color; 21 Illustrations, black and white; X, 210 p. 126 illus., 105 illus. in color., 1 Hardback
Series: Springer INdAM Series 65
Pub. Date: 22-Jul-2025
ISBN-13: 9789819645497
This book collects contributions presented at the INdAM Workshop "Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage?MACH2023” held in Rome, Italy in September 2023. The book is focused on mathematical modeling and simulation techniques with the aim of improving the current strategies of conservation and restoration in cultural heritage, sharing different experiences and approaches. The main topics are corrosion and sulphation of materials, damage and fractures, stress in thermomechanical systems, contact and adhesion problems, phase transitions and reaction-diffusion models, restoration techniques, additive manufacturing, with a particular focus on the effective improvements of the fruition of cultural heritage. The final goal is to strengthen the bridge between the experts in different fields of cultural heritage and the mathematical community.
A reaction diffusion model with a stochastic boundary condition.- A
stochastic interacting particle model for the marble sulphation process.-
Mathematical Modelling of Calcium Carbonate Sulphation - A Computational
Study.- Space feature curves recognition and approximation for artifacts
characterization.- Homogenization of a Kresling-tube origami.- Modelling
paintings on canvas and simulation of local crack patterns.- Griffith
criterion for steady and unsteady-state crack propagation.- Artificial
Intelligence algorithms for the characterisation of visitors trajectories in
a cultural context.- Museum for social inclusion: the challenge of
mathematical exhibitions and educational experiences.- Applications and Open
Issues in the Structural Health Monitoring of Historic Buildings.- An
archaeological view on the sidelines of the structural analysis of Porta
Maggiore, Rome.- Assessing structural resilience: some thoughts on Porta
Maggiore, Rome.- A multidisciplinary Mission for Aga Khan Necropolis, the
Egyptian Italian Mission at West Aswan (EIMAWA).
Format: Hardback, 252 pages, height x width: 235x155 mm, 7 Illustrations, black and white; XIV, 252 p. 7 illus., 1 Hardback
Series: Texts in Applied Mathematics 81
Pub. Date: 12-Jul-2025
ISBN-13: 9783031889028
Martingale theory is a cornerstone of modern probability, offering a natural extension of the study of sums of independent random variables. Although its roots can be traced back to the work of Paul Levy in 1937, it was Joseph L. Doob in the 1940s who formally developed the theory, culminating in his landmark book Stochastic Processes in 1953. Since then, martingale theory has evolved significantly, with deep contributions from mathematicians such as Donald L. Burkholder, Richard Gundy, and Burgess Davis, among others. This is what is now known as advanced martingale theory, which began with the publication of Burkholders seminal paper Martingale Transforms in 1966.
This book provides a comprehensive treatment of both classical and advanced martingale theory. It opens with a historical introduction, exploring foundational functions such as Rademacher, Haar, and Walsh functions, before delving into the core concepts of conditional probability. The classical theory, as developed by Doob, is meticulously presented, followed by an in-depth examination of modern advancements, including Burkholders inequalities, Burkholder-Davis-Gundy inequality, and their generalizations, as well as good-lambda inequalities. The final chapter showcases a wide range of applications, highlighting the theorys profound impact on Banach space theory, harmonic analysis, and beyond.
Intended for graduate students and researchers in probability and analysis, this book serves as both an introduction and a reference, offering a clear and structured approach to a subject that continues to shape mathematical research and its applications.
Chapter 1: Introduction.
Chapter 2: Probability and Conditional Expectation.
Chapter 3: Advanced Topics in Martingale Theory.
Chapter 4: Burkholders inequalities and Davissinequality.
Chapter 5: Applications of Martingales.
Format: Hardback, 475 pages, height x width: 235x155 mm, X, 475 p., 1 Hardback
Series: Texts in Applied Mathematics 82
Pub. Date: 14-Jul-2025
ISBN-13: 9783031914164
This book provides an in-depth exploration of nonsmooth optimization, covering foundational algorithms, theoretical insights, and a wide range of applications. Nonsmooth optimization, characterized by nondifferentiable objective functions or constraints, plays a crucial role across various fields, including machine learning, imaging, inverse problems, statistics, optimal control, and engineering. Its scope and relevance continue to expand, as many real-world problems are inherently nonsmooth or benefit significantly from nonsmooth regularization techniques. This book covers a variety of algorithms for solving nonsmooth optimization problems, which are foundational and recent. It first introduces basic facts on convex analysis and subdifferetial calculus, various algorithms are then discussed, including subgradient methods, mirror descent methods, proximal algorithms, alternating direction method of multipliers, primal dual splitting methods and semismooth Newton methods. Moreover, error bound conditions are discussed and the derivation of linear convergence is illustrated. A particular chapter is delved into first order methods for nonconvex optimization problems satisfying the Kurdyka-Lojasiewicz condition. The book also addresses the rapid evolution of stochastic algorithms for large-scale optimization. This book is written for a wide-ranging audience, including senior undergraduates, graduate students, researchers, and practitioners who are interested in gaining a comprehensive understanding of nonsmooth optimization.
Preface.- Introduction.- Convex sets and convex functions.- Subgradient
and mirror descent methods.- Proximal algorithms.- Karush-Kuhn-Tucker theory
and Lagrangian duality.- ADMM: alternating direction method of multipliers.-
Primal dual splitting algorithms.- Error bound conditions and linear
convergence.- Optimization with Kurdyka- Lojasiewicz property.- Semismooth
Newton methods.- Stochastic algorithms.- References.- Index.
Format: Paperback / softback, 293 pages, height x width: 235x155 mm,
7 Illustrations, color; 54 Illustrations, black and white; XI, 293 p. 61 illus., 7 illus. in color.,
Series: La Matematica per il 3+2 173
Pub. Date: 24-Jun-2025
ISBN-13: 9783031866692
This book was created with the goal of helping students transition from the theoretical and methodological concepts of statistical inference to their implementation on a computer. The first part of the book is primarily focused on exercises to be solved with pen and paper, so that students can apply knowledge derived from lemmas and theorems; while the second part consists of labs, which involve both the manual implementation of algorithms and the learning of built-in tools for efficient analysis of datasets derived from real-world problems. To optimize the understanding of the topics developed and to guide the reader through their studies, the book is organized into chapters, each of which includes an introductory section that reviews the theoretical foundations of statistical inference, followed by a second part with exercises, each accompanied by a comprehensive solution on paper and, when appropriate, using software. This book is aimed at undergraduate students in Statistics, Mathematics, Engineering, and for graduate-level courses in Data Science.
Part I: Statistical Inference.- 1 Fundamentals of Probability and
Statistics.- 2 Sufficient, Minimal, and Complete Statistics.- 3 Point
Estimators.- 4 Uniform Minimum Variance Unbiased Estimators (UMVUEs).- 5
Likelihood Ratio Test.- 6 Uniformly Most Powerful Test.- 7 Confidence
Intervals.- 8 Asymptotic Statistics.- Part II: Regression Models and Analysis
of Variance.- 9 Linear Regression.- 10 Generalized Linear Models.- 11 ANOVA:
Analysis of Variance.- 12 Summary Exercises.- Appendix A: Probability
Distributions.
Format: Hardback, 356 pages, height x width: 235x155 mm, 17 Illustrations, color;
9 Illustrations, black and white; X, 356 p. 26 illus., 17 illus. in color., 1 Hardback
Series: Springer Optimization and Its Applications 225
Pub. Date: 21-Jul-2025
ISBN-13: 9783031911743
This book offers as exploration into the emerging field of Inverse Combinatorial Optimization Problems (ICOPs), a transformative area within operations research. As traditional optimization focuses on maximizing or minimizing objectives under constraints, ICOPs reverse this process, allowing for the inference of hidden parameters from observed outcomes. This monograph provides a comprehensive framework for understanding and applying ICOPs across various domains.
Key concepts such as inverse shortest path, spanning tree, and center location problems are meticulously examined, offering theoretical insights and algorithmic solutions. The authors present a structured approach to these complex problems, making this work an essential resource for both academic and practical applications. By addressing critical questions and providing algorithmic tools, this book is a must-read for those seeking to enhance network design, logistics, and strategic planning.
Researchers, academics, and practitioners in operations research and management science will find this monograph invaluable. It not only contributes to academic discourse but also equips professionals with the knowledge to tackle real-world challenges. This book is a vital addition to any library supporting advanced studies in optimization and decision-making processes.
Preface.- Part I. An Introduction to Inverse Combinatorial Optimization
Problems.- An Outline of Inverse Combinatorial Optimization Problems.-
Generalized Inverse Bottleneck Optimization Problems.- Generalized Inverse
Maximum Capacity Path Problems.- Some General Methods to Solve Inverse Linear
Programming Problem under Weighted ??1 Norm.- Part II. Generalized
Inverse Shortest Path Problems.- Shortest Path Improvement Problems.-
Shortest Path Interdiction Problems on Trees.- Sum of Root-leaf Distance
Interdiction Problems on Trees.- Restricted Inverse Optimal Value Problem on
Shortest Path under Weighted ??1 Norm on Trees.- Part III. Generalized
Inverse Spanning Tree Problems.- Inverse Minimum Spanning Tree Problems.-
Inverse Max+Sum Spanning Tree Problems.- Restricted Inverse Optimal Value
Problem on Minimum Spanning Tree.- Partial Inverse Minimum Spanning Tree
Problems.- Part IV. Generalized Inverse Center Location Problems.- Inverse
vertex obnoxious 1-center location problems.- Inverse Quickest 1-Center
Location Problem on Trees.- References.
Format: Hardback, 285 pages, height x width: 235x155 mm, 22 Illustrations,
color; 13 Illustrations, black and white; X, 285 p. 35 illus., 22 illus. in color.,
Series: Graduate Texts in Mathematics 304
Pub. Date: 14-Jul-2025
ISBN-13: 9783031907050
Microlocal analysis provides a powerful, versatile, and modular perspective on the analysis of linear partial differential equations. This text, developed from a first-year graduate course, provides an accessible introduction and develops, from first principles, the core notions and results including pseudodifferential operators, wave front sets, and propagation phenomena. The reader is assumed to have some exposure to functional analysis and the theory of smooth manifolds. With detailed proofs, a wealth of exercises of varying levels of difficulty, and connections to contemporary research in general relativity, the book serves as both a comprehensive textbook for graduate students and a useful reference for researchers.
Preface.-
1. Introduction.-
2. Schwartz functions and tempered distributions.-
3. Symbols.-
4. Pseudodifferential operators.-
5. Pseudodifferential operators on manifolds.-
6. Microlocalization.-
7. Hyperbolic evolution equations and Egorov's theorem.-
8. Real principal type propagation of singularities.-
9. Solving wave-type equations.-
10. Propagation of singularities at radial sets.-
11. Late time asymptotics of linear waves on de Sitter space.-
Bibliography.- I
ndex.