Copyright 2027
Hardback
ISBN 9781032807027
200 Pages 86 Color Illustrations
September 2, 2026 by Chapman & Hall
Weakened Ramsey Theory provides readers with an overview of weakened generalizations of various parameters studied in Ramsey theory. Rather that determining how large a structure must be to guarantee the existence of monochromatic substructures in a t-coloring, weakened Ramsey theory considers how large a structure must be to guarantee the existence of a substructure that uses at most a given number of colors. Weakened generalizations of Ramsey numbers, Gallai-Ramsey numbers, Schur numbers, Rado numbers, rainbow Schur numbers, and others have all been studied in the literature, and this book offers a thorough overview of the known results, with complete proofs.
This book should prove a valuable resource to advanced undergraduates, graduate students, and researchers working in Ramsey theory. Only a basic background in graph theory, algebra, and number theory are assumed, although a concise review of important definitions and background results is included.
Self-contained treatment of the subject, requiring only a minimal background in graph theory, algebra, and number theory
Complete proofs of major results in weakened Ramsey theory
Numerous color figures to assist the reader
Comprehensive list of references
Tables of known weakened parameters in Ramsey theory, providing a useful reference for researchers.
Table of Contents
1. Foundations in Ramsey Theory
2. Chromatic Ramsey Numbers
3. Weakened Ramsey Numbers
4. Weakened Ramsey Theory on the Integers
5. Going Forward
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with n faces and boundary component lengths of order
n
or of lower order. Endow this quadrangulation with the usual graph metric renormalized by n
−1/4
, mark it on each boundary component, and endow it with the counting measure on its vertex set renormalized by n
−1
, as well as the counting measure on each boundary component renormalized by n
−1/2
. We show that, as n goes to infinity, this random marked measured metric space converges in distribution for the Gromov–Hausdorff–Prokhorov topology, toward a random limiting marked measured metric space called a Brownian surface.
This extends known convergence results of uniform random planar quadrangulations with at most one boundary component toward the Brownian sphere and toward the Brownian disk, by considering the case of quadrangulations on general compact orientable surfaces. Our approach consists in cutting a Brownian surface into elementary pieces that are naturally related to the Brownian sphere and the Brownian disk and their noncompact analogs, the Brownian plane and the Brownian half-plane, and to prove convergence results for these elementary pieces, which are of independent interest.
Format: Hardback, 573 pages, height x width: 279x210 mm, XV, 573 p.
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Pub. Date: 25-May-2026
ISBN-13: 9783032191878
This book presents new editions and investigations of 114 Babylonian planetary tables: cuneiform tablets inscribed with computed dates, positions, and other data for the planets Mercury, Venus, Mars, Jupiter, and Saturn. The tablets originate from Babylon and Uruk, two main centers of Babylonian astronomy. They were written in the period 400-50 BCE. Along with lunar tables and procedure texts they belong to a corpus of texts known as Babylonian mathematical astronomy. They contain the earliest known form of mathematical astronomy in the ancient world. All computations are based on the uniform zodiac with twelve signs of thirty degrees and the 60-based number system known as sexagesimal place value notation.
The book begins with a general overview of the planetary tables, covering the history of research, a comparative analysis of various archaeological, archival, material, and notational aspects, a discussion of regional variations, scribal errors, the production process of the tables, mathematical and astronomical aspects, an overview of the tables arranged by planet and algorithm, and a study of dependencies and offsets between the tables. This is followed by editions of the tablets, including previously unpublished ones. Each commentary includes a full account of the material, archival, paleographic, orthographic, and other features of the tablet, a summary of previous research, and reconstructions of the underlying algorithms, in some cases with significant new insights about the Babylonian methods.
1 Planetary tables.- 2 Editions.- A Extended table for Jupiter system
B.- B Photographs of the cuneiform tablets. Bibliography.- Index of tablets
and fragments.- Concordance with ACT and other editions.
Format: Paperback / softback, 79 pages, height x width: 235x155 mm, 1 Illustrations, black and white
Series: SpringerBriefs in Mathematics
Pub. Date: 29-May-2026
ISBN-13: 9789819587421
Graph packing problem is one of the central problems in graph theory and combinatorial optimization. The famous Steiner tree packing problem in undirected graphs has become an well-established area. It is natural to extend this problem to digraphs. The corresponding problems in digraphs are called directed Steiner type packing problems which are highly related to some important problems in graph theory.
In this book, the author tried to collect known results on several Steiner type packing problems in digraphs, including directed Steiner tree packing problem, directed Steiner path packing problem, strong subgraph packing problem, strong arc decomposition problem, directed Steiner cycle packing problem. This book also contains some conjectures and open problems for further study.
The author hopes this book can motivate more young researchers and graduate students to do further study in this subject, and promote the interdisciplinary research of graph theory, combinatorial optimization, theoretical computer science and communication networks.
1 Introduction.- 2 Directed Steiner tree packing problem.- 3 Directed
Steiner path packing problem.- 4 Strong subgraph packing problem.- 5 Strong
arc decomposition problem.- 6 Directed Steiner cycle packing problem.
Format: Hardback, 343 pages, height x width: 235x155 mm, 11 Illustrations, color; 13 Illustrations, black and white
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 22-Apr-2026
ISBN-13: 9783032178299
Lie group representation theory and harmonic analysis on Lie groups and their homogeneous spaces form a significant area of mathematical research. Interest in these areas began soon after World War II and has gained much strength since then. These areas are interrelated with various other mathematical fields such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations, and mathematical physics. Keeping up with the fast development of this exciting area of research, Ali Baklouti (University of Sfax) and Takaaki Nomura (Kyushu University) launched a series of seminars on the topic. The main focus of these seminars was in the area of harmonic analysis, Lie theory, geometry and representation theory. Many experts from both countries have been involved in running this seminar and have contributed greatly to making seminars successful. This has been a major incentive for both Ali Baklouti and Hideyuki Ishi (Osaka University) to continue the organization of these meetings which aim at exploring topics such as commutative harmonic analysis (Fourier analysis on Euclidean spaces), analysis of homogeneous spaces, uncertainty principles, and geometric analysis and some of their interactions with operator algebras.
Format: Hardback, 270 pages, height x width: 235x155 mm, 20 Illustrations, color; 20 Illustrations, black and white
Series: University Texts in the Mathematical Sciences
Pub. Date: 10-Jun-2026
ISBN-13: 9789819588152
This book introduces the theory of univalent functions, focusing on the key subclasses of starlike, convex and close-to-convex functions. These subclasses play a central role in the study of geometric function theory. The book begins with the general class of univalent functions and studies their basic properties. It then explores essential mathematical tools, including results on growth, distortion and coefficients for bounded analytic functions, as well as the theory of functions with positive real parts and differential subordination. The last three chapters delve into starlike, convex and close-to-convex functions, presenting key results on coefficient bounds, growth, distortion estimates and subordination theorems. Designed for graduate students and early-stage researchers, the book requires minimal prerequisites of a basic course in complex analysis. Detailed proofs have been provided for all results, ensuring that readers can follow the logical development of the material. Exercises given at the end of each chapter offer opportunities for further study and deeper understanding of the concepts. This book serves as both a textbook and a resource for those beginning research in geometric function theory. Its accessible style, coupled with its clear explanations and motivating examples, makes it an ideal choice for anyone looking to explore the fascinating world of univalent functions.
Chapter 1. Analytic Functions.
Chapter 2. Univalent Functions.-
Chapter 3. Bounded Functions.
Chapter 4. Functions with Positive Real Part.-
Chapter 5. Differential Subordinations.
Chapter 6. Starlike Functions.-
Chapter 7. Convex Functions.
Chapter 8. Close-to-convex Functions.
Format: Hardback, 192 pages, height x width: 240x168 mm, 7 Illustrations, black and white
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 21-May-2026
ISBN-13: 9783032220035
This Second Edition presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. The author presents thoroughly class-tested classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. This new edition features coverage on equations with multiple symmetries (inherited symmetries), contact symmetries, and second order equations vs. equivalent systems.
An Introduction.- Ordinary Differential Equations.- Partial Differential
Equations.- Nonclassical Symmetries and Compatibility.
Format: Paperback / softback, 122 pages, height x width: 235x155 mm, 1 Illustrations, black and white
Series: SpringerBriefs in Mathematics
Pub. Date: 23-May-2026
ISBN-13: 9783032200648
This book introduces a new multifractal vectorial formalism based on Hewitt-Stromberg measures, with particular emphasis on its application to branching random walks on the Galton-Watson tree. This formalism relies on the use of vector-valued functions defined on balls in a metric space and taking values in a Banach space, thus offering a generalization of classical multifractal analysis. These measures lie between Hausdorff and packing measures and then, the authors study is specially imported especially when the classical multifractal formalism does not hold. The authors investigate the fractal dimension of the sets of infinite branches of the boundary of a super-critical Galton-Watson tree (endowed with a random metric) along which the averages of a valued branching random walk, have a given set of limit points.
Furthermore, the authors examine additional general sets of levels in multifractal analysis, leading to the development of a relative multifractal vectorial formalism. They explore this relative formalism within the framework of the branching random walk.
Introduction.- Vectorial multifractal measures and dimensions.- A
relative vectorial multifractal formalism of the level sets X ().- A
relative vectorial multifractal formalism of the level sets X (, ).-
Relative multifractal formalism of branching random walk with random metric.-
Appendix.