Format: Paperback / softback, 149 pages, height x width: 235x155 mm, 44 Illustrations, color
Series: Springer Undergraduate Mathematics Series
Pub. Date: 30-Apr-2026
ISBN-13: 9783032164902
This book introduces the core ideas of L.E.J. Brouwers approach to constructivity in mathematics, focusing on analysis, set theory, and topology, while considering his philosophical motivations. Brouwers intuitionism offers a coherent alternative to classical (nonconstructive) mathematics.
Starting with the rejection of the Principle of the Excluded Middle, the book reconstructs number systems and analysis using Cauchy sequences. It compares constructive and classical methods, highlights where classical theorems fail through weak counterexamples, and examines Brouwers classical and constructive versions of the Fixed-Point Theorem. Intuitionistic concepts like choice sequences and the Creating Subject lead to surprising results, such as the continuity of all total real functions and the existence of effective but non-recursive functions. Brief but fundamental comparisons are made with the later alternatives of Markov and Bishop.
Intended as an introduction for undergraduates, this book is suitable for mathematics students interested in philosophy as well as philosophers with some mathematical background.
1 Introduction.- 2 Logic.- 3 Natural numbers, integers, and rationals.-
4 Real numbers.- 5 Functions and continuity.- 6 Going forth.
Format: Hardback, 210 pages, height x width: 235x155 mm, XXI, 210 p.
Series: Algebra and Applications
Pub. Date: 30-Mar-2026
ISBN-13: 9783032145741
Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provides the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects.
The development of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example and extends it to modular representation theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups.
At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. With the provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well as researchers and lecturers with an interest in Deligne-Lusztig theory.
Part I: Preliminaries.-
1 Structure of SL2(Fq).-
2 The Geometry of the Drinfeld Curve.-
Part II: Ordinary Characters.-
3 Harish-Chandra Induction.-
4 Deligne-Lusztig Induction.-
5 The Character Table.-
6 McKay Conjecture.-
Part III: Modular Representations: Unequal Characteristic.-
7 Generalities.-
8 Equivalences of Categories.-
9 Simple Modules, Decomposition Matrices.-
Part IV: Modular representations: equal characteristic.-
10 Simple Modules, Decomposition Matrix, Blocks.-
11 Canonical Representation Associated with Y.-
Part V: Complements.-
12 Special Cases.-
13 Deligne-Lusztig Theory: an Overview*.-
Part VI: Appendices.-
A -Adic Cohomology.-
B Block Theory.-
C Review of Reflection Groups.
Format: Paperback / softback, 104 pages, height x width: 235x155 mm, VI, 104 p.
Series: SpringerBriefs in Mathematical Physics
Pub. Date: 28-Apr-2026
ISBN-13: 9789819570294
This book introduces Nambus generalized Hamiltonian dynamics. In 1973, Nambu proposed extending classical Hamiltonian mechanics by replacing the canonical doublet (p,q) with a three-dimensional phase space defined by a canonical triplet (x,y,z). The equations of motion are formulated using a triple bracketa generalization of the Poisson bracketwith two 'Hamiltonians' treated on an equal footing. This framework can further be extended to an n-tuple of phase-space coordinates, an n-bracket, and equations of motion involving n1 Hamiltonians in an n-dimensional phase space. Nambus original motivation was to generalize the Liouville theorem, which states that the volume of an ensemble in phase space is preserved under dynamical flowsa principle fundamental to statistical mechanics. He sought to construct systems with analogous properties for arbitrary-dimensional phase spaces, including odd dimensions. Although his proposal attracted little attention for more than a decade, subsequent developments revealed its relevance in diverse areas of theoretical and mathematical physics, notably in string/M-theory and fluid mechanics. This book introduces the reader to classical Nambu dynamics by explaining its principal aspects from an elementary viewpoint and developing it further from a coherent and unified standpoint. It is intended for readers with a reasonable understanding of classical analytical mechanics and working knowledge of basic physics and standard mathematical methods in theoretical physics.
Introduction: Historical Overview and Basic Concepts.
- The Construction of Generalized Canonical Structure for Nambu Dynamics.
- The Extension of Variational Principle and HamiltonJacobi Theory to Nambu Dynamics.
- Bibliographical Remarks.
Format: Hardback, 128 pages, height x width: 235x155 mm, 20 Illustrations, color; 4 Illustrations, black and white
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 16-May-2026
ISBN-13: 9783032175250
This open access volume discusses advanced tools and techniques for the analysis and prediction of environmental variables with a spatial or spatio-temporal structure. In various environmental science applications, developing models that accurately describe the spatio-temporal evolution of key variables is essential for monitoring eco-sustainability. This book presents theoretical reviews on spatio-temporal covariance modeling, as well as innovative approaches for assessing environmental quality and its effects on climate change. These approaches integrate georeferenced data from multiple sources and apply novel methodologies for analyzing multivariate spatio-temporal data. This volume presents the scientific contributions presented at the Workshop Exploration of Spatio-Temporal Environmental Conditions: Harmonized Databases and Analytical Techniques (ECoST-DATA), held at the University of Bari on July 3-4, 2025.
. Random fields and Covariance modelling.- Covariance functions.-
Spatio-temporal Complex Covariance Functions for Vectorial Data.-
Non-Separable Covariance Kernels for Spatiotemporal Gaussian Processes Based
on the Hybrid Spectral Method.- Stationary subspace analysis for
spatio-temporal data.- II. Environmental control and integration.- Space
turns to Time: the Advent of Time series of Remote Sensing Images.- Ensemble
Smoother with Multiple Data Assimilation for Atmospheric Dust Source
Identification: A Generic Framework Approach.- Optimizing Pollution Control
for an Economic Growth System.- Exploring Functional Structure and Variation
of Italian Carbon Emissions.- III. Environmental analysis.- Ozone Predictions
through a Generalized Additive Model.- Geostatistical Characterization of
Climate Extremes Dynamics: The Drought Phenomenon.- Using Machine Learning
Methods to explore the Effects of Environmental Variables on Biodiversity.-
Modeling and Prediction of Ground-level Ozone Concentrations in a
Spatio-temporal Multivariate Context.
Format: Hardback, 339 pages, height x width: 235x155 mm, 114 Illustrations, color; 10 Illustrations, black and white
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 24-Apr-2026
ISBN-13: 9783032170781
This volume presents a peer-reviewed selection of papers from the MISI25 conference, held on July 910, 2025, in Safi, Morocco. It showcases recent advances at the intersection of mathematics and intelligent systems, offering solutions to real-world industrial, economic, and environmental challenges.
The volume highlights novel methodologies in optimization, data science, machine learning, numerical simulation, and control systems, applied across domains like healthcare, finance, energy, and education. It features case studies, algorithmic frameworks, comparative analyses, and data-driven modeling, supported by figures and tables for clarity and practical relevance. This book provides a comprehensive reference for researchers, practitioners, and graduate students seeking innovative approaches and applied strategies in mathematical and intelligent system applications.
H. El Boudali, S. Lahlou, Z. Farahat, N. Zrira, Bahia El Abdi, A.
Benomar, Y. Bouhafra, I. Benmiloud and N. Ngote, 3D Modeling and Printing of
a Middle Ear Surgery Simulator: A Case Study on Cholesteatoma.- A. Jraifi, I.
Medarhri, and I. El Bouhali, Machine Learning Enhanced Calibration of
Stochastic Volatility Jump-Diffusion Models via Tikhonov Regularization.- K.
El Haddad, A. Bekkari, W. Bouari and J. Abdelilah, Brain Tumors Prediction
and Classication Using Automated Models.- W. El Kadmiri, A. Benghabrit, M.
Moufaddal, and A. Nait Sidi Moh, Identifying Key Drivers of Supply Chain
Resilience for Modeling Using AI and Hybrid Predictive Models.- I. El
Bokamiri, A. Benghabrit, Predictive Modeling of Customer Churn in the
Moroccan Telecommunications Sector Using Advanced Machine Learning
Algorithms.- I. Elkinani, M. Hosni, T. Masrour, I. Medarhri, Meta-Ensemble
Learning for Predicting NASDAQ Stock Movements: An Empirical Study.- P.
Manfoumbievouandi; Zineb Farahat; Nabila Zrira; Ibtissam Benmiloud; Bahia El
Abdi; Adam Benomar; Hibat Allah Eddaoui; And Nabil Ngote, Reconstruction and
Printing Techniques for the Development of an Anatomical Simulator of
Lumbar Disc Herniation: A Case Study.- H. Mouncif, A. Kassimi, C.
Benhammacht, T. B. Gardelle, H. Tairi, J. Riffi, Industrial Defect
Classification Through 2D and 3D Data Integration.- S. Sahbani Abdennebi
Hasnaoui; Mustapha Kchikach, Efficiency Analysis and Optimization of a Buck
Converter for Electric Vehicle Charging.- M. Ouakarrouch, M. Garoum; N.
Laaroussi, M. Lifi, H. Salmi, H. Lifi, and A. Jraifi, Mathematical modeling
of the Flash method for determing the thermal diffusivity of materials.- J.
Zerhouni; I. El Ouadi, M. Hosni, M. Bakkas, Artificial Intelligence and
Internet of Things in Solar Energy: A Systematic literature Review.
Format: Hardback, 512 pages, height x width: 235x155 mm, 31 Illustrations, color; 24 Illustrations, black and white
Pub. Date: 13-May-2026
ISBN-13: 9783032139917
In 2024, Andrew Barron turned 65 and retired. This is a Festschrift volume honoring his career and contributions. Andrew R. Barron, a professor of Statistics and Data Science at Yale University, has been one of the most influential figures in information theory research over the past 40 years. He has made profound, broad and consistent contributions to information theory, as well as its interactions with probability theory, statistical learning, and neural networks. From his Ph.D. thesis work in 1985 until today, Barron has been recognized as a leader in both information theory and statistics, especially in the area where the two fields intersect and fertilize each other. There has been a powerful tradition of important work on this interface and it has had a strong impact on both fields. Through the introduction of novel ideas and techniques, and through his outstanding scholarship, Barron has clarified some of the foundations of the mathematical and statistical side of Shannon theory, and he has helped solidify our understanding of the connection between information theory and statistics. This volume consists of invited papers, by prominent researchers that either personally or through the topics of the work have some connection with Barron. The papers in this volume are written by people working in all three areas where Barron has made major contributions: Information theory, probability, and statistical learning. These topics are very timely as there is major current activity in all three areas, especially in connection with the explosive current advances in machine learning theory and its applications.
Information Theory.- Probability Theory.- Statistical Learning.
Format: Hardback, 460 pages, height x width: 235x155 mm, 20 Illustrations, black and white
Series: Series in Contemporary Mathematics
Pub. Date: 10-May-2026
ISBN-13: 9789819559640
This book presents the advanced theory of Hamiltonian dynamics, with an emphasis on the recent development of variational methods and its application to the problem of Arnold diffusion. The main theme of the book is to study the dynamics of finite dimensional nearly integrable Hamiltonian systems, which are small perturbations of integrable systems.
The book consists of two parts. Part I includes the main techniques in Hamiltonian dynamics such as the integrability and nonintegrability theory, the normal form theory (KAM theory, Nekhoroshev theorem), the hyperbolicity theory (the theorem of normally hyperbolic invariant manifold), the variational theory, systems of two degrees of freedom and the connecting orbit theory. In the more advanced Part II, authors specialize to the proof of Arnold diffusion. The techniques in Part I are fully exploited in Part II for people to understand theorems better via applications.The proof the classical Tonelli theorem, some preliminaries of ergodic theory and some basics of genercitity and transversality are given in the Appendix.
This book can be used as the textbook for graduate students in the field of Hamiltonian dynamics. It can also be used as reference for working mathematicians. Before reading this book, obtaining some understanding on Arnold's book Mathematical Methods in Classical Mechanics, algebraic topology, differential topology and convex analysis will be helpful.
Part I Advanced Hamiltonian Dynamics.
Chapter 1. Integrability and Nonintegrability.-
1.1 The Lagrangian, Hamiltonian and Hamilton-Jacobi PDE formalisms.-
1.2 The algebraic, symplectic and geometric structures.-
1.3 Dynamical properties: Liouville Theorem and Poincare recurrence.-
1.4 Integrable systems, the Liouville-Arnold theorem.-
1.5 Newtonian two-body problem*.-
1.6 Poincares theorem: onset of chaos.-
1.7 Further examples of integrable systems*.
Chapter 2. The Normal Form Theory.-
2.1 The 𝑵-body problem*.-
2.2 The Kolmogorov-Arnold-Moser (KAM) theory.-
2.3 The Nekhoroshev theorem.-
2.4 Resonance produces pendulum: the normal form package.-
2.5 Complete resonance, synchronization and closing lemma*.-
2.6 Circle maps.-
2.7 The problem of stability of the solar system*.-
2.8 KAM tori in perturbed Kerr blackhole*.
Chapter 3. The Hyperbolicity Theory.-
3.1 Arnold diffusion in Arnolds example.-
3.2 Normally hyperbolic invariant manifolds(NHIM).-
3.3 The symplectic NHIM theorem.- 3.4 NHIM near resonance.-
3.5 The scattering map*.
Chapter 4. The Variational Theory.-
4.1 Tonelli Lagrangian and minimal measures.-
4.2 (Co)homology aspects of the variational principle.-
4.3 The Aubry set and the Mane set.-
4.4 The pendulum as a prototypical example.-
4.5 The Aubry sets and the 𝜶-function.-
4.6 The variational theory meets the normal form theory.-
4.7 Generic properties of minimal measures.-
4.8 The weak KAM theory.-
4.9 The hyperbolic dynamics picture of the weak KAM theory.-
4.10 Preliminary viscosity solutiontheory*.-
4.11 Literature review.
Chapter 5. Systems of Two Degrees of Freedom.-
5.1 Twist maps I: the structure theory.-
5.2Twist maps II: advanced topics.-
5.3 Zero energy level I: flat of 𝜶-function.-
5.4 Zero energy level II: destroy Mane sets.-
5.5. Intermediate energy levels: hyperbolic periodic orbits.-
5.6 High and low energy levels: uniform normal hyperbolicity.-
5.7 Lorentzian systems*.
Chapter 6. The Connecting Orbit Theory.-
6.1 Cohomological equivalence.-
6.2 Local connecting orbits.-
6.3 Global connecting orbits.- Part II Arnold Diffusion.
Chapter 7. Arnold Diffusion Emerging from Chaos: an Overview.-
7.1 Statements of the main theorems and their implications.-
7.2 Outline of the proofs.-
7.3 Outreaches*.
Chapter 8. Arnold Diffusion in a priori Unstable Systems.-
8.1 The big gap problem and the globalization problem.-
8.2 The globalization theory.
Chapter 9. Arnold Diffusion in Systems of Three Degrees of Freedom.-
9.1 Frequency path and three regimes.-
9.2 Normal forms, normal hyperbolicity and strong double resonances.-
9.3 Dynamics around strong double resonances.-
9.4 Proof of the main theorem in the case of 𝒏 = 3.-
9.5 NHICs get arbitrarily close to the strong double resonances.-
9.6 Literature review.-
Chapter 10. Arnold Diffusion in Systems of 𝒏(> 3) Degrees of Freedom.-
10.1 Superstructure of the proof.-
10.2 The first approximation of frequency segment.-
10.3 Double resonances.-
10.4 The frequency refinement.-
10.5 Triple resonances.-
10.6 Crossing triple resonances.-
10.7 Construction of the global frequency path.-
10.8 Crossing complete resonances.-
A Elliptic and Hyperelliptic Curves, Abel-Jacobi Theorem*.- B Preliminary Ergodic
Theory.- C Tonellis Theorem.- D Transversality and Genericity.- References.
Format: Hardback, 600 pages, height x width: 235x155 mm, XXII, 600 p.
Series: Applied Mathematical Sciences
Pub. Date: 29-Apr-2026
ISBN-13: 9783032177780
This book introduces integrable peaked soliton (peakon) systems, which has been used by mathematical analysists and theoretical physicists to study the Camassa-Holm (CH) equation from various points and extended to create peakon models in nonlinear science. Recently integrable peakon models have been designed that are scalar and vector forms of the peakon systems. Quadratic and cubic peakon models as well as multi-component peakon dynamical systems, new multi-peakon/kink interactions, Hamiltonian systems, Lax pairs, and applications in nonlinear sciences are detailed and explained with examples to aid scientific scholars to conduct theoretical and applied research projects.
Advanced undergraduate and graduate students in applied mathematics, physics and engineering can use this book for a course in integrable peakon systems. The technical aspect of peakon solution will be useful for graduate students and researchers in mathematics, theoretical physics, engineering, nonlinear science and other related fields. Researchers will find the techniques and complicated simulation procedure explored in this book vital for advancing their individual research.
Introduction.- Camassa-Holm (CH) peakon model.- Degasperis-Procesi (DP)
peakon model.- Cubic Camassa-Holm (also called FORQ) peakon model.- Two
component Camassa-Holm systems with cubic nonlinearity.- N-component
Camassa-Holm systems with cubic nonlinearity.- Integrable peakon models and
negative order hierarchies.
Format: Hardback, 483 pages, height x width: 235x155 mm, 78 Illustrations, color; 20 Illustrations, black and white
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 19-Apr-2026
ISBN-13: 9783032170705
This book gathers selected works covering research in mathematics on new methods and techniques for the applications of differential equations, presented at the 12th International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES), held in Saints Constantine and Helena, Bulgaria, from September 14, 2025.
The book is organized around eight key themes, with applications in mathematical physics, mathematical biology, financial mathematics, mechanics, fractional analysis, numerical methods, big data and computer science, and artificial intelligence and neural networks.
By showcasing fundamental research in both theoretical and applied mathematics, this book aims to promote new tools and approaches that can effectively address real-life challenges through the application of differential equations.
Weighted resolvent estimates for Laplace Operator with point
interactions.- Cauchy Problem for Non-local Parabolic PDEs.- From Lipschitz
to One Sided Lipschitz.- Short Overview of the Advances in the SEsM
Methodology for Obtaining Exact Solutions of Nonlinear Differential
Equations.- Simulations of Local Characteristics on Flow, Heat Transfer, and
Electrostatics, Using Potentials by Analytical Functions.- Exact Solutions of
a Model Equation for Shallow-Water Waves.- Localized Traveling Waves in a
Spatio-Temporal Population Interaction Model.- Investigation of Fire Wave
Dynamics in Forest Ecosystems via a Hyperbolic Advection - Reaction-Diffusion
Equation: Part I. Analytical Solutions.- Travelling Wave Solutions for a
Two-Species Competitive Model in Ecology.- Explicit Formulae to the Solutions
of the Cauchy Problem for Schrödinger Type Linear PDEs Depending on Small
Parameter.- Application of Ordinary Differential Equations for Modeling the
Cutting Process in Robotic Harvesting of Fruits and Vegetables.- Exact
solutions of another model equation for shallow-water waves.