Part of Cambridge Studies in Advanced Mathematics
FORMAT: Hardback
ISBN: 9781108429061
LENGTH: 450 pages DIMENSIONS: 229 x 152 mm
AVAILABILITY: Not yet published - available from May 2022
This is the first full-length book on the major theme of symmetry in graphs.
Forming part of algebraic graph theory, this fast-growing field is concerned with the study of highly
symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures,
primarily by group-theoretic techniques. In practice the street goes both ways and these
investigations shed new light on permutation groups and related algebraic structures.
The book assumes a first course in graph theory and group theory but no specialized knowledge
of the theory of permutation groups or vertex-transitive graphs. It begins with the basic material
before introducing the field's major problems and most active research themes in order to motivate
the detailed discussion of individual topics that follows. Featuring many examples and over 450 exercises,
it is an essential introduction to the field for graduate students and a valuable addition to any algebraic
graph theorist's bookshelf.
The first book on 'symmetry in graphs:' the interplay of the theory of vertex transitive graphs and permutation groups
Suitable for graduate students with a first course in group theory and graph theory
Includes many examples and over 450 exercises
Introduces the reader to the major open research problems in the area
1. Introduction and constructions
2. The Petersen graph, blocks, and actions of A5
3. Some motivating problems
4. Graphs with imprimitive automorphism group
5. The end of the beginning
6. Other classes of graphs
7. The Cayley isomorphism problem
8. Automorphism groups of vertex-transitive graphs
9. Classifying vertex-transitive graphs
10. Symmetric graphs
11. Hamiltonicity
12. Semiregularity
13. Graphs with other types of symmetry: Half-arc-transitive graphs and semisymmetric graphs
14. Fare you well
References
Author index
Index of graphs
Index of symbols
Index of terms.
Part of London Mathematical Society Student Texts
FORMAT: PaperbackI
SBN: 9781009151139
FORMAT: Hardback
ISBN: 9781009151146
LENGTH: 460 pages DIMENSIONS: 229 x 152 mm
AVAILABILITY: Not yet published - available from May 2022
Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows
the historical development of the theory culminating in recent results: the Kolmogorov?Arnold?Moser
theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students
to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's
theorem, the proof of Poincare?'s non-integrability theorem and the nonlinear dynamics in the neighbourhood
of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability
of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is
devoted to the discovery of chaos by Poincare? and its relations with integrability, also including recent
results on superexponential stability. Written in an accessible, self-contained way with few prerequisites,
this book can serve as an introductory text for senior undergraduate and graduate students.
Helps the reader understand the relations between the two recent theorems of Kolmogorov and Nekhoroshev
and the classical theorems of Liouville, Arnold, Jost and Poincare by including detailed proofs
Employs constructive algorithms based on Lie transform methods, which researchers may later apply to concrete
systems using algebraic manipulation, as is common in Celestial Mechanics, for example
Allows students to learn the material in an easy-to-follow analytical style, which adapts to the development
of perturbation methods
Explains how small divisors cause divergence of perturbation series, and why they allow convergence in the case
of Kolmogorov's theorem
Presents the phenomenon of homoclinic intersections discovered by Poincare, helping the reader to understand
the root of chaos in elementary terms
1. Hamiltonian formalism
2. Canonical transformations
3. Integrable systems
4. First integrals
5. Nonlinear oscillations
6. The method of Lie series and of Lie transform
7. The normal form of Poincare and Birkhoff
8. Persistence of invariant tori
9. Long time stability
10. Stability and chaos
A. The geometry of resonances
B. A quick introduction to symplectic geometry
References
Index.
Part of Cambridge Tracts in Mathematics
FORMAT: Hardback
ISBN: 9781316519936
LENGTH: 263 pages DIMENSIONS: 229 x 152 mm
AVAILABILITY: Not yet published - available from May 2022
This exploration of the relation between periods and transcendental numbers brings
Baker's theory of linear forms in logarithms into its most general framework,
the theory of 1-motives. Written by leading experts in the field, it contains original results
and finalises the theory of linear relations of 1-periods, answering long-standing questions
in transcendence theory. It provides a complete exposition of the new theory for researchers,
but also serves as an introduction to transcendence for graduate students and newcomers.
It begins with foundational material, including a review of the theory of commutative algebraic
groups and the analytic subgroup theorem as well as the basics of singular homology and de
Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples
like the transcendence of ƒÎ, before the authors turn to periods of algebraic varieties in Part III.
Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.
Builds a bridge between transcendence, algebraic geometry and cohomology theory, appealing to a wide readership
Presents the basic concepts and background material on which the theory relies
Written by leading experts in the area
Part of Encyclopedia of Mathematics and its Applications
FORMAT: Hardback
ISBN: 9781009098441
LENGTH: 379 pages DIMENSIONS: 234 x 156 mm
AVAILABILITY: Not yet published - available from June 2022
Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications
of probability. At the same time, they are a natural generalization of random walks, the most
well-studied classical objects in probability theory. This monograph, written for researchers and
graduate students, presents the general asymptotic theory and generalizes many well-known results
concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems,
integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space
and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs,
with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs
to the domain of moderately large and small deviations. Applications establish the key limit laws for
Markov additive processes, including limit theorems in the domains of normal and large deviations.
Provides a single source for both classical and functional key limit theorems for compound renewal processes,
useful for further research or real-world applications
Presents new deep results on the large deviation theory for compound renewal processes
Generalizes well-known results for random walks to a larger class of processes
Introduction
1. Main limit laws in the normal deviation zone
2. Integro-local limit theorems in the normal deviation zone
3. Large deviation principles for compound renewal processes
4. Large deviation principles for trajectories of compound renewal processes
5. Integro-local limit theorems under the Cramer moment condition
6. Exact asymptotics in boundary crossing problems for compound renewal processes
7. Extension of the invariance principle to the zones of moderately large and small deviations
A. On boundary crossing problems for compound renewal processes when the Cramer condition is not fulfilled
Basic notation
References
Index.
Part of London Mathematical Society Lecture Note Series
FORMAT: Paperback
ISBN: 9781108792042
LENGTH: 300 pages DIMENSIONS: 228 x 152 mm
AVAILABILITY: Not yet published - available from June 2022
Matrices and kernels with positivity structures, and the question of entrywise functions preserving them,
have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional
covariance estimation. This is the first book to systematically develop the theoretical foundations of
the entrywise calculus, focusing on entrywise operations - or transforms - of matrices and kernels
with additional structure, which preserve positive semidefiniteness. Designed as an introduction for students,
it presents an in-depth and comprehensive view of the subject, from early results to recent progress.
Topics include: structural results about, and classifying the preservers of positive semidefiniteness
and other Loewner properties (monotonicity, convexity, super-additivity); historical connections to metric geometry;
classical connections to moment problems; and recent connections to combinatorics and Schur polynomials.
Based on the author's course, the book is structured for use as lecture notes, including exercises for students,
yet can also function as a comprehensive reference text for experts.
Ideal for beginners with some background in linear algebra and analysis
Provides a comprehensive survey with detailed proofs, and will be a useful reference book for experts and students alike
Designed for use as lecture notes, the book is split into small sections that introduce topics in a linear fashion making
it suitable for a one- or two- semester course