Mathematics

This book explores generalized Lorenz-Mie theories when the illuminating beam is an electromagnetic arbitrary shaped beam relying on the method of separation of variables.

The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.

A comprehensive and detailed presentation of finite and infinite ergodic theory, fractal measures, and thermodynamic formalism.

A systematic modern treatise on large deviation theory for random walks with light tails, from one of its key creators.

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes.

This introduction to the theory of variational Bayesian learning summarizes recent developments and suggests practical applications.

The final volume in a series of four books presenting the seminal papers from the Caltech-UCLA ''Cabal Seminar''.

Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

Analyses bond market models with Lévy stochastic factors, suitable for graduates and researchers in probability and mathematical finance.

This book proves important new theorems in the theory of canonical inner models for large cardinal hypotheses in set theory.

Comprehensive presentation of the technical aspects and applications of the theory of structured dependence between random processes.

An explanation of the foundations of Kant''s philosophy of mathematics and its connection to his account of human experience.

Presents the current state of knowledge in all aspects of two-dimensional homotopy theory.

A systematic and comprehensive introduction of seismic risk analysis of critical engineering structures, focusing on nuclear power plants.

An introduction to integrable and non-integrable scalar field models, with topological and non-topological soliton solutions.

Develops a fresh mathematical approach to coronal seismology, explaining oscillatory phenomena by drawing upon original research and complex modelling techniques.

The first systematic account of the basic theory of normed algebras, without assuming associativity.

Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.

Exploring a novel breakthrough in the identification and investigation of solvable and integrable nonlinearly coupled evolution ordinary differential equations (ODEs) or partial differential equations (PDEs).

Develops the modern theory of symmetrization including applications to geometry, PDEs, and real and complex analysis.

Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.

Seminal papers by A.

Develops and defends a new metaphysical and logical theory of arbitrary objects that will reinvigorate the philosophy of mathematics.

Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.

Represents the state of the art in the new field of synthetic differential topology.

Surveys the state of the art in geometric and cohomological group theory.

Details some of the most recent developments at the interface of topology and geometric group theory.

Presents main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years.

This book provides a panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity.

The second volume in a series exploring the mathematics of aperiodic order.

The first of two volumes covering the Steenrod algebra and its various applications.

The second of two volumes covering the Steenrod algebra and its various applications.

A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.

The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.

Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.

This first volume of two presents classical and modern arithmetic equivalents to the Riemann hypothesis.

This second volume of two presents analytic equivalents to the Riemann hypothesis.

Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

An overview of bounded cohomology and simplicial volume covering the basics of the subject and recent research directions.

Written to honour Miles Reid''s 70th birthday, this volume covers a broad range of contemporary research, both concrete and theoretical.

Introduces an original approach to foundations of mathematics, departing from Gödel and Tarski and spanning many different areas of logic.

From measles to COVID, discover how data allied with statistical and probabilistic reasoning are essential to making rational decisions.

This book constitutes the proceedings of the 4th International Workshop on Computational Topology in Image Context, CTIC 2012, held in Bertinoro, Italy, in May 2012.

This work addresses this problem in the short-time Fourier transform (STFT) domain.

This book constitutes the thoroughly refereed papers of the 16th International Conference on Implementation and Application of Automata, CIAA 2011, held in Blois, France, in July 2011.