Bøger i Chapman & Hall/CRC Monographs and Research Notes in Mathematics serien

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 book is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions, including generalized Lehner, simple, and Hirzebruch-Jung continued fractions.

This book provides a thorough introduction to the theory of nonlinear PDEs with a variable exponent, particularly those of elliptic type. It presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences.

This book presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley¿Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras. Along with revising all existing chapters, this edition includes four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs. It also contains two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs.

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.

Modeling and Inverse Problems in the Presence of Uncertainty collects recent researchΓÇöincluding the authorsΓÇÖ own substantial projectsΓÇöon uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation itself. After a useful review of relevant probability and statistical concepts, the book summarizes mathematical and statistical aspects of inverse problem methodology, including ordinary, weighted, and generalized least-squares formulations. It then discusses asymptotic theories, bootstrapping, and issues related to the evaluation of correctness of assumed form of statistical models. The authors go on to present methods for evaluating and comparing the validity of appropriateness of a collection of models for describing a given data set, including statistically based model selection and comparison techniques. They also explore recent results on the estimation of probability distributions when they are embedded in complex mathematical models and only aggregate (not individual) data are available. In addition, they briefly discuss the optimal design of experiments in support of inverse problems for given models. The book concludes with a focus on uncertainty in model formulation itself, covering the general relationship of differential equations driven by white noise and the ones driven by colored noise in terms of their resulting probability density functions. It also deals with questions related to the appropriateness of discrete versus continuum models in transitions from small to large numbers of individuals.With many examples throughout addressing problems in physics, biology, and other areas, this book is intended for applied mathematicians interested in deterministic and/or stochastic models and their interactions. It is also s

Although the theory behind solitary waves of strain shows that they hold promise in nondestructive testing and other applications, an enigma has long persisted - the absence of observable solitary waves in practice. This work explores how to construct a powerful deformation pulse in a waveguide without plastic flow or fracture.

One of the most important areas of study in mathematics, physics and engineering involves scattering and the propagation of scalar and vector waves. This topic is very mathematical, which often obscures the physics and engineering of scattering and propagation. It is the goal of this author to introduce this topic in a manner where the emphasis is placed on the physical interpretations of the mathematics involved without losing the mathematical rigor. Lastly, a number of important developments in this field are discussed that have never been mentioned in books before as they are hidden away in many different journal articles.

The second edition of this book has a new title that more accurately reflects the table of contents. Over the past few years, many new results have been proven in the field of partial differential equations. This edition takes those new results into account, in particular the study of nonautonomous operators with unbounded coefficients, which has received great attention. Additionally, this edition is the first to use a unified approach to contain the new results in a singular place.

Although the theory behind solitary waves of strain shows that they hold promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable solitary waves in practice. Inspired by this contradiction, Strain Solitons in Solids and How to Construct Them refines the theory, explores how to con

Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.

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.

Adding new results that have appeared in the last 15 years, this second edition provides an easy way for researchers to locate an inequality by name or subject. This edition offers an up-to-date, alphabetical listing of each inequality with a short statement of the result, some comments, references to related inequalities, and sources of information on proofs and other details. It includes more than 100 new inequalities, a new name index, and an updated bibliography that contains URLs for important references.

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.