Bücher der Reihe Springer Monographs in Mathematics

This introduction to modern set theory opens the way to advanced current research. Coverage includes the axiom of choice and Ramsey theory, and a detailed explanation of the sophisticated technique of forcing. Offers notes, related results and references.

As well as explaining the use of ultrasound in the process, this volume proposes a new, 'solitary wave' method of evaluating complex, microstructured materials such as alloys and composites. It includes numerical examples and analysis of the solutions.

This book surveys 20th century progress in classical number theory, from the proof of the Prime Number Theorem in 1896 through the proof of Fermat's Last Theorem, focusing on the part of number theory that addresses properties of integers and rational numbers.

This book shows how to calculate arbitrarily high orders of derivatives of the Douglas Energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations.

Presenting current results on analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes, this book covers distribution of points on the sphere, the reconstruction algorithm in computerized tomography and more.

With a pedagogic format ideal for graduate students, this text includes a wealth of examples focusing on solutions in dynamical systems theory that mirror those used in Lyapunov's first method, tackling ordinary differential equations expressed as series form.

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems.

This book covers dimension theory, ANR theory (theory of retracts) and related topics, connecting with various fields in geometric and general topology. Many proofs are illustrated by figures or diagrams, making it easier to understand the underlying concepts.

This book offers a comprehensive overview of dimension theory of hyperbolic flows. It includes a detailed discussion of major open problems in the area.

This monograph provides a self-contained introduction to non-commutative multiple-valued logic algebras. It includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, and pseudo-MV algebras.

Based on the author's lectures at Cornell Probability Summer School in 2012, this book links the concept of superconcentration with probability theory. Includes a number of open problems for professional mathematicians and exercises for graduate students.

Mathematical Methods for Elastic Plates

The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties.

This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals.

This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years.

This book describes classic and new results on solvability and unsolvability of equations in explicit form, presenting the author's complete exposition of topological Galois theory, plus basics of the Picard-Vessiot theory and a great deal more.

The featured review of the AMS describes the author's earlier work in the field of approach spaces as, 'A landmark in the history of general topology'. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory.

This book presents a new approach to the analysis of networks, which emphasizes how one can compress a network while preserving all information relative to the network's spectrum.

Combinatorial Algebra: Syntax and Semantics

The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis.

This book presents fundamental concepts and seminal results to the study of vortex filaments in equilibrium. It fills a gap in the vortex statistics literature by simplifying the mathematical introduction to this complex topic, covering numerical methods, and exploring a wide range of applications with numerous examples.

This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups.

This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations.

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory.

For metric spaces the quest for universal spaces in dimension theory spanned a century of research, which breaks into two periods: the classical (separable metric) and the modern (not necessarily separable metric). This book details the modern theory.

This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly.

Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist.

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms.