Format: Hardback, 719 pages, height x width: 235x155 mm, 140 Illustrations, color; 16 Illustrations, black and white
Series: Static & Dynamic Game Theory: Foundations & Applications
Pub. Date: 11-Dec-2025
ISBN-13: 9783032070302
Mean-Field-Type Game Theory II is the second of two volumes that together form a comprehensive treatment of mean-field-type game theory and applications, focused on finding state-of-the-art solutions to issues surrounding the next generation of cloud social networking, smart energy systems, transportation and wireless networks. The text shows how mean-field-type game theory provides the ideal framework for designing robust, accurate and efficient algorithms for the autonomous and distributed architectures on which future cities and networks will rely to improve the efficiency and flexibility, security and quality of life.
This second volume fleshes out and expands upon the theoretical treatment of Volume I with a presentation of real-world applications including smart cities, energy systems and their economics, high-efficiency Wi-Fi networks, social networks, next-generation networks, sensor networks and cognitive networks.
Mean-Field-Type Game Theory II: Applications is an ideal resource for engineers,
academic researchers, and advanced undergraduate and graduate students,
surveying the varied ways in which mean-field games can be employed to
enhance real systems of one sort or another
Part 1. Engineering.
Chapter 1. Evacuation of Multi-Level Buildings.-
Chapter 2. Signal Quality-based CSMA Networks.
Chapter 3. Power savings, Mobility, and Data Queues.
Chapter 4. User and Base Station Association in Next Generation Networks.-
Part 2. Computer Science.
Chapter 5. Malware Propagation.
Chapter 6. Rent-Seeking Games in Cloud Networking.
Chapter 7. Auctions.
Chapter 8. Network of Neural Networks.-
Part 3. Evolutionary Biology and Biochemistry.
Chapter 9. BioChemical Reaction Networks.
Chapter
10. COVID-19: Data-Driven Modeling.-
Part 4. Sociology, Psychology, Ecology and Environment.
Chapter 11. Pollution Control and Fishing Strategies in Smarter Cities.
Chapter 12. Mean-Field Games for Marriage.-
Part 5. Network Economics, Finance and Insurance.
Chapter 13. Economics of Networks.-
Chapter 14. Electricity Price Dynamics in the Smart Grid.
Chapter 15. Blockchain-based Distributed Power Networks.
Chapter 16. Blockchain Token Economics.
Chapter 17. Hub-based Airline Networks.-
Part 6. Wrap-up.-
Chapter 18. Conclusions and New Directions In this chapter, we present some summary and new directions.
Format: Hardback, 113 pages, height x width: 235x155 mm, 4 Illustrations, black and white
Series: Mathematical Physics Studies
Pub. Date: 12-Dec-2025
ISBN-13: 9789819520459
This book presents a wide-ranging geometric approach to the stability of solitary wave solutions of Hamiltonian partial differential equations (PDEs). It blends original research with background material and a review of the literature. The overarching aim is to integrate geometry, algebra, and analysis into a theoretical framework for the spectral problem associated with the transverse instability of line solitary wave solutions—waves that travel uniformly in a horizontal plane and are embedded in two spatial dimensions. Rather than focusing on individual PDEs, the book develops an abstract class of Hamiltonian PDEs in two spatial dimensions and time, based on multisymplectic Dirac operators and their generalizations. This class models a broad range of nonlinear wave equations and benefits from a distinct symplectic structure associated with each spatial dimension and time. These structures inform both the existence theory (via variational principles, the Maslov index, and transversality conditions) and the linear stability analysis (through a multisymplectic partition of the Evans function). The spectral problem arising from linearization about a solitary wave is formulated as a dynamical system, with three symplectic structures contributing to the analysis. A two-parameter Evans function—depending on the spectral parameter and transverse wavenumber—is constructed from this system. This structure enables new results concerning the Evans function and the linear transverse instability of solitary waves. A key result is an abstract derivative formula for the Evans function in the regime of small stability exponents and transverse wavenumbers. To illustrate the theory, the book introduces a class of vector-valued nonlinear wave equations in 2+1 dimensions that are multisymplectic and admit explicit solitary wave solutions. In this example, the stable and unstable subspaces involved in the Evans function construction are each four-dimensional and can be explicitly computed. The example is used to demonstrate the geometric instability condition and to explore the inner workings of the theory in detail.
Chapter 1 Introduction.
Chapter 2 Literature Review.
Chapter 3 Multisymplectic Wave Equations and Dirac Operators.
Chapter 4 Solitary Wave Solutions and Their Properties.
Chapter 5 Linearisation about Solitary Waves.
Chapter 6 Spectral Stability and the Evans Function.
Chapter 7 Derivatives of the Evans Function.-
Chapter 8 Summary of Hypotheses Used.-
Chapter 9 Example: Nonlinear Wave Equation in 2 + 1.
Chapter 10 Concluding Remarks.
Format: Hardback, 318 pages, height x width: 235x155 mm, 1 Illustrations, black and white
Pub. Date: 11-Dec-2025
ISBN-13: 9789819510870
The book focuses on the mathematical foundations of boundary integro-differential equation method, with a primary focus on reducing the hypersingular integrals in traditional boundary integral equations into boundary integro-differential equations with weak singularities. It briefly introduces the theory of distributions, while the boundary integral equations method is grounded in the fundamental solutions of linear partial differential equations, hence a relatively detailed exposition of the fundamental solutions of differential equations is also provided. In the subsequent chapters, the authors sequentially discuss the boundary integro-differential equation methods and theories for Laplace equation, Helmholtz equation, Navier equations, Stokes equations, among others. Furthermore, the book addresses the boundary integro-differential equation method for certain nonlinear problems, such as thermal radiation, variational inequalities, and Steklov eigenvalue problems. Lastly, it explores the symmetric coupling issues between finite element and boundary element methods
Chapter 1 Distributions.
Chapter 2 Fundamental Solutions of Linear
Differential Operators.
Chapter 3 Boundary Value Problems of the Laplace Equations.
Chapter 4 Boundary Value Problem of Modified Helmholtz Equation.
Chapter 5 Boundary Value Problems of Helmholtz Equation
Chapter 6 Boundary Value Problems of the Navier Equations.
Chapter 7 Boundary Value Problems of the Stokes Equations.
Chapter 8 Some Nonlinear Problems.-
Chapter 9 Coercive and Symmetrical Coupling Methods of Finite Element Method and Boundary Element Method.
Format: Hardback, 200 pages, height x width: 235x155 mm, X, 200 p.
Series: Monographs in Mathematical Economics
Pub. Date: 24-Nov-2025
ISBN-13: 9789819521999
The book covers basic and advanced modules in axiomatic decision theory, intended for graduate students and working researchers. It includes cover all the proofs of all axiomatic results being presented.
The book is intended to succeed classic references such as Fishburn (1970)
and Kreps (1988), which are acclaimed for their mathematical completeness
but getting older and need to be supplemented with more recent advancements.
Although there are books on decision theory covering recent advancements,
there is a need for a book that covers all the proofs in axiomatic analysis
so that graduate school students can fully catch up with the field
Chapter 1 Preference and its representation.
Chapter 2 Revealed Preference.
Chapter 3 Choice with multiple components and separability.-
Chapter 4 Decision under risk.
Chapter 5 Decision under uncertainty and subjective belief.-
Chapter 6 Ambiguity of Belief.-
Chapter 7 Updating belief and dynamic consistency.
Chapter 8 Intertemporal choice.
Chapter 9 Choice of opportunity.
Chapter 10 Information and Knowledge.-
Chapter 11 Social decision making under uncertainty.
Chapter 12 Social decision making over time.
Format: Hardback, 562 pages, height x width: 235x155 mm, XXI, 562 p.
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Pub. Date: 25-Nov-2025
ISBN-13: 9783032026811
This book provides a history and analysis of the ideas, problems, concepts, and theories of dimension from ancient to modern times. It focuses primarily on topological and, to a lesser extent, measure-theoretic approaches.
It offers a detailed account of the contributions of key mathematicians who shaped dimension theory, including Bernard Bolzano, Bernhard Riemann, Georg Cantor, Richard Dedekind, Henri Poincaré, L.E.J. Brouwer, Paul Urysohn, Karl Menger, Witold Hurewicz, Paul Alexandroff, and Felix Hausdorff. The book examines the twists and turns in the development of the subject, including its controversies, and explores the philosophical aspects of its history.
As the first in-depth historical study of dimension theory, it serves as
a reference for historians and philosophers of mathematics. It also provides
general historical background for students and researchers with broader
mathematical interests
1 Introduction to Theories of Dimension.-
2 Ideas Touching on Dimension in Ancient Greek Philosophy and Mathematics.-
3 Dimension from the Middle Ages to the End of the Eighteenth Century.-
4 Bolzanos Investigations into Geometry and Dimension.-
5 Nineteenth-Century Theories of Higher-Dimensional Spaces.-
6 Cantor and Dedekind: Discovery of a Counterintuitive Example concerning Dimension.-
7 Early Efforts to Prove Invariance of Dimension, 18781879.-
8 Early Development of Point-Set Theory and Point-Set Topology.-
9 Poincarés Theories of Dimension.-
10 Riesz, Baire, Fréchet: New Approaches to Dimension.-
11 Brouwer: Development of Topology, Invariance of Dimension.-
12 New Ways of Proving Invariance of Dimension; BrouwerLebesgue Dispute.-
13 Problems of Curves and Dimension in the Early Twentieth Century.-
14 Urysohns Theory of Curves and Dimension.-
15 Mengers Theory of Curves and Dimension.-
16 Development of Theories of Dimension and Curves.-
17 Historical, Mathematical, and Philosophical Perspectives.-
Appendix A:
Format: Hardback, 544 pages, height x width: 235x155 mm, 46 Illustrations, color; 9 Illustrations, black and white
Series: Simons Symposia
Pub. Date: 26-Dec-2025
ISBN-13: 9783032040473
This book grew out of a series of three Simons Symposia in 2019, 2022, and 2024, that focused on the interactions between three types of dynamics—algebraic, complex, and arithmetic—and their connections to the closely related areas of algebraic, complex, and arithmetic geometry. Dynamical systems play a key role both in pure mathematics and its applications. These meetings brought experts together from across these fields for discussions on the most significant recent developments and directions for further research.
Preface.- Dynamical Degrees, Arithmetic Degrees, and Canonical Heights:
History, Conjectures, and Future Direction.- Recent Advances on
Kawaguchi-Silverman Conjecture.- Around the Dynamical Mordell-Lang
Conjecture.- Advances in the Equivariant Minimal Model Program and their
Applications in Complex and Arithmetic Dynamics.- Dynamics of Automorphism
Groups of Projective Surfaces: Classification, Examples and Outlook.-
Questions About the Dynamics on a Natural Family of Affine Cubic Surfaces.-
Holomorphic Motions of Weighted Periodic Points.- On Slice Measures of Green
Currents on CP2.- Hölder Estimates and Uniformity in Arithmetic Dynamics.-
Entire or Rational Maps with Integer Multipliers.- Tischler Graphs of
Critically Fixed Rational Maps and their Applications.- Mirrors of Conformal
Dynamics: Interplay Between Anti-Rational Maps, Reflection Groups, Schwarz
Reflections, and Correspondences.- On Boundedness of Zeroes of the
Independence Polynomial of Tori.
Format: Paperback / softback, 236 pages, height x width: 235x155 mm, 22 Illustrations, color; 4 Illustrations, black and white
Series: Compact Textbooks in Mathematics
Pub. Date: 08-Dec-2025
ISBN-13: 9783032054456
This textbook offers a comprehensive introduction to quasi-Monte Carlo methods and several of their applications. Throughout, the authors use modern concepts and notations to provide an overview of how the theory behind quasi-Monte Carlo methods developed. While the main focus of this text is on the theory, it also explores several applications with a particular emphasis on financial problems.
This second edition contains substantial revisions and additions, including several new sections that more thoroughly cover weighted problems. New sections include coverage of the weighted Koksma-Hlawka inequality, weighted discrepancy of lattice point sets and tractability properties, polynomial lattice point sets, and more. In addition, the authors have corrected minor errors from the first edition and updated the bibliography and "Further reading" sections.
Introduction to Quasi-Monte Carlo Integration and Applications is suitable for advanced undergraduate students in mathematics and computer science. Readers should possess a basic knowledge of algebra, calculus, linear algebra, and probability theory. It may also be used for self-study or as a reference for researchers interested in the area.
Preface.- Notation.- I Introduction.- II Uniform distribution modulo one.- III QMC integration in reproducing kernel Hilbert spaces.- IV Lattice point sets.- V (t, m, s)-nets and (t, s)-sequences.- VI A short discussion of the discrepancy bounds.- VII Foundations of financial mathematics.- VIII MC and QMC simulation.