Bøger i Chapman & Hall/CRC Pure and Applied Mathematics serien

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for various principal types of partial differential equations. It covers methods of linear and nonlinear analysis, and the theory of differential equations in Banach spaces.

Presents a study of linear abstract degenerate differential equations, using the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. This title describes the results on PDEs and algebraic-differential equations.

Celebrating the work of Professor W Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring a collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana.

Utilizes linear algebra and operator techniques to develop classical and modern results in linear systems analysis and control design. This title presents stability and performance results for linear systems, provides a geometric perspective on controllability and observability, and develops state space realizations of transfer functions.

Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. This title covers fractality and Fredholmness. It explains the phenomena of the asymptotic splitting of the singular values, and more.

Focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry.

Discusses graph domination. This book covers various developments in domination in graphs and digraphs, dominating functions, and combinatorial problems on chessboards.

Describes the basic theory and multitude of applications in the study of differential subordinations.

This work presents the principles of space and surface potential theory involving Euclidean and spherical concepts. It offers new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The authors build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They then discuss surface potential theory on the unit sphere along with corresponding applications.

Presents the concepts of type dimension, a natural class, and a type submodule, by exploring how they enter into much of ring and module theory. This book develops the foundations of the subject and the advanced theorems. It is suitable for those with some background in basic ring and module theory.

Presents important results in classical analysis, wavelets, and interpolation theory. This book contains topics such as Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, and various measures of the smoothness of functions.

Offers a comprehensive listing of the various translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and sketches of the major relevant theorems.

Beginning with an introduction to modeling and functional and numerical analysis, this title deals with the chapters to models involving adhesion and material damage, exploring a particular model. For various models, it provides a variational formulation and establishes the existence and uniqueness of a weak solution.

Presents an introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M Sato and his colleagues. It also reviews hyperfunction-microfunction theory and the theory of D-modules.

Explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory. This work clarifies foundational concepts such as symmetric and limiting distributions of products. It describes models of interactive particles.

Presents hyperspace fundamentals, offering an overview and a foundation. This text contains topics such as the topology for hyperspaces, examples of geometric models for hyperspaces, 2x and C(X) for Peano continua X, arcs in hyperspaces, the shape and contractability of hyperspaces, hyperspaces and the fixed point property, and Whitney maps.

This classic text provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then introducing a more general treatment based on abstract notions characterized by axioms and with less geometric content. Packed with new exercises and material, the long-awaited second edition of this highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students, instructors, and mathematicians.

Covers the standard topics (groups, modules, rings, and vector spaces) associated with abstract algebra and advanced topics such as Galois fields, noncommutative rings, group extensions, and Abelian groups. This book illustrates the theory of finitely generated modules over principal ideal domains, and discusses tensor products.

Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's Lp-estimates for boundary value problems, using the theory of singular integrals and the Hilbert transform.

A comprehensive presentation of abstract algebra and a treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

Research on number theory has produced a wealth of interesting and beautiful results yet topics are strewn throughout the literature, the notation is far from being standardized, and a unifying approach to the different aspects is lacking. Covering both classical and recent results, this book unifies the theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational. It highlights the connection between Gauss¿s theory of binary forms and the arithmetic of quadratic orders.

Presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. This book compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows.

Graph algebras possess the capacity to relate fundamental concepts of computer science, combinatorics, graph theory, operations research, and universal algebra. This book defines graph algebras and reveals their applicability to automata theory. It proceeds to explore assorted monoids, semigroups, rings, codes, and other algebraic structures.

Uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of higher dimension than the initial space.

"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."

Explores the analog of the theory of functions of a complex variable.

Stressing the use of several software packages based on simplex method variations, this work teaches linear programming's four phases through actual practice. It shows how to decide whether LP models should be applied, set up appropriate models and use software to solve them.

Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force

With many examples and historical notes, this book provides a treatment of the Hahn-Banach theorem. It explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes a chapter on vector-valued Hahn-Banach theorems.