This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.
An Introduction to Redox Polymers for Energy-Storage Applications Presents a well-founded introduction to the field or Redox Polymers, with didactical features like summary boxes and a Q&A sections An Introduction to Redox Polymers for Energy-Storage Applications discusses fundamental aspects related to polymer-based batteries, such as types of batteries, their historic development, design and synthesis criteria of the active material, and summarizes the various types of redox polymers and their applications. Each chapter contains learning objectives, summary boxes, and questions to allow for efficient exam preparation. In An Introduction to Redox Polymers for Energy-Storage Applications, readers will find detailed information on: Fundamental aspects of redox-active polymers, along with their historical classification, taking the key applications of the materials into account Energy-storage devices, containing polymers as the electrode active materials, and specific material requirements for the desired applications Classification of redox-active polymers, e.g., according to the nature of the actual redox-active moieties, their backbone structure, or topology Electrical conductivity of conjugated polymers, covering their most prominent representatives (polyaniline, polypyrrole, polythiophene, and polyacetylene) An Introduction to Redox Polymers for Energy-Storage Applications also covers the synthesis and applications of these materials, making it an excellent book for graduates, PhD students, and professionals who are starting in this field.
Explore modern characterization methods and new applications in this modern overview of supramolecular polymer chemistry Supramolecular Polymers and Assemblies: From Synthesis to Properties and Applications delivers a superlative summary and description of general concepts and definitions in the field. The book offers informative and accessible treatments of crucial concepts like metal-containing compounds, hydrogen bonding, ionic interactions, pi-pi stacking, and more. Characterization remains a primary focus of the book throughout, making it extremely useful for practitioners in the field. Emphasis is also placed on metallo-supramolecular polymers and materials which have found applications in areas like smart or intelligent materials and systems with special photochemical and photophysical properties, like LEDs and solar cells. Applications, including self-healing materials, opto-electronics, sensing, and catalysis are all discussed as well. The book details many of the exciting developments in the field of supramolecular chemistry that have occurred since the 1987 Nobel Prize was awarded to pioneers in this rapidly developing field. Readers will also benefit from the inclusion of: A thorough introduction to supramolecular assemblies based on ionic interactions Explorations of supramolecular polymers based on hydrogen-bonding interactions, metal-to-ligand interactions, p-Electronic interactions, crown-ether recognition, cucurbiturils, and host-guest chemistry of calixarenes A discussion of cyclodextrins in the field of supramolecular polymers Examinations of supramolecular polymers based on the host-guest chemistry of pillarenes, and those formed by orthogonal non-covalent interactions A treatment of the characterization of supramolecular polymers Supramolecular Polymers and Assemblies: From Synthesis to Properties and Applications will earn a place in the libraries of researchers and practitioners of the material science, as well as polymer chemists seeding a one-stop reference for supramolecular polymers.
This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.
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