Books in the Chapman & Hall/CRC Monographs and Research Notes in Mathematics series

This introductory book presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent and advanced research literature on numerical geometric integration. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.

In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). This book presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems. He gives a detailed structure theorem for canonical Seifert surfaces of a given genus and covers applications, such as the braid index of alternating knots and hyperbolic volume.

This book presents both long-standing and recent mathematical results from this field in a uniform way. It focuses on exact analytic formulas for reconstructing a function or a vector field from data of integrals over lines, rays, circles, arcs, parabolas, hyperbolas, planes, hyperplanes, spheres, and paraboloids. The book also addresses range characterizations and collects necessary definitions and elementary facts from geometry and analysis. Coverage is motivated by both applications and pure mathematics.

This book treats the extending structures problem in the context of groups, Lie/Leibniz algebras, associative algebras and Poisson/Jacobi algebra. This monograph offers the reader an incursion into the extending structures problem which provides a common ground for studying both the extension problem and the factorization problem.

This work focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The authors present interesting results that highlight the beauty of icosahedral symmetries of the variety V5. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and gives a proof of its A5-birational rigidity.

This book shows how four types of higher-order nonlinear evolution PDEs have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs, describe many properties of the equations, and examine traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities. The book illustrates how complex PDEs are used in a variety of applications and describes new nonlinear phenomena for the equations.

This book brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author¿s considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing.

Bringing together research that was otherwise scattered throughout the literature, this book collects the main results on the conditions for the existence of large algebraic substructures. Many examples illustrate lineability, dense-lineability, spaceability, algebrability, and strong algebrability in different areas of mathematics, including real and complex analysis. The book presents general techniques for discovering lineability in its diverse degrees, incorporates assertions with their corresponding proofs, and provides exercises in every chapter.

This second edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. It contains five new chapters on the normal holonomy of complex submanifolds, the Berger¿Simons holonomy theorem, the skew-torsion holonomy theorem, and polar actions on symmetric spaces of compact type and noncompact type. It also includes several new sections on orbits for isometric actions, geodesic submanifolds, and symmetric spaces.

This book explains how mathematical tools can be used to solve problems in signal processing. Assuming an advanced undergraduate- or graduate-level understanding of mathematics, this second edition contains new chapters on convolution and the vector DFT, plane-wave propagation, and the BLUE and Kalman filters. It expands the material on Fourier analysis to three new chapters to provide additional background information, presents real-world examples of applications that demonstrate how mathematics is used in remote sensing, and includes robust appendices and problems for classroom use.

Across two volumes, the authors of this book discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces.

This book provides a broad introduction to the mathematics of difference equations and their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with more problems and an expanded bibliography, this edition includes two new chapters on special topics (such as discrete Cauchy¿Euler equations) and the application of difference equations to complex problems arising in the mathematical modeling of phenomena in engineering and the natural and social sciences.

The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques.

Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups.