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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.
Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.
A revised and reorganized practical reference for the working field forester, incorporating the latest information and new, improved methods in such critical areas as U.S. forest law and policy, forest taxation, cost accounting and accomplishment reporting, pesticide and environmental aspects, safety, and public involvement procedures.
Develop the skills and knowledge to make informed decisions regarding technical factors and diagnostic imaging quality with the vibrantly illustrated Radiologic Science for Technologists, 10th Edition. Updated with the latest advances in the field, this full-color and highly detailed edition addresses a broad range of radiologic disciplines and provides a strong foundation in the study and practice of radiologic physics, imaging, radiobiology, radiation protection, and more. Unique learning tools strengthen your understanding of key concepts and prepare you for success on the ARRT certification exam and in clinical practice. Broad coverage of radiologic science topics — including radiologic physics, imaging, radiobiology, radiation protection, and more — allows you to use the text over several semesters. Highlighted math formulas call attention to mathematical information for special focus. Important Concept boxes recap the most important chapter information. Colored page tabs for formulas, conversion tables, abbreviations, and other data provide easy access to frequently used information. End-of-chapter questions include definition exercises, short answer, and calculations to help you review material. Key terms and expanded glossary enable you to easily reference and study content. Chapter introductions, summaries, objectives, and outlines help you organize and pinpoint the most important information. NEW! Chapters on digital radiographic technique and digital image display prepare you to use today’s technology. NEW! Streamlined physics and math sections ensure you are prepared to take the ARRT exam and succeed in the clinical setting.
An introduction to Einstein's general theory of relativity, this work is structured so that interesting applications, such as gravitational lensing, black holes and cosmology, can be presented without the readers having to first learn the difficult mathematics of tensor calculus.
In its 114th year, Billboard remains the world's premier weekly music publication and a diverse digital, events, brand, content and data licensing platform. Billboard publishes the most trusted charts and offers unrivaled reporting about the latest music, video, gaming, media, digital and mobile entertainment issues and trends.