Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's element
The concepts represented in this textbook are explored for the first time in assistive and rehabilitation robotics, which is the combination of physical, cognitive, and social human-robot interaction to empower gait rehabilitation and assist human mobility. The aim is to consolidate the methodologies, modules, and technologies implemented in lower-limb exoskeletons, smart walkers, and social robots when human gait assistance and rehabilitation are the primary targets. This book presents the combination of emergent technologies in healthcare applications and robotics science, such as soft robotics, force control, novel sensing methods, brain-computer interfaces, serious games, automatic learning, and motion planning. From the clinical perspective, case studies are presented for testing and evaluating how those robots interact with humans, analyzing acceptance, perception, biomechanics factors, and physiological mechanisms of recovery during the robotic assistance or therapy. Interfacing Humans and Robots for Gait Assistance and Rehabilitation will enable undergraduate and graduate students of biomedical engineering, rehabilitation engineering, robotics, and health sciences to understand the clinical needs, technology, and science of human-robot interaction behind robotic devices for rehabilitation, and the evidence and implications related to the implementation of those devices in actual therapy and daily life applications.
Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.
Lactose-Derived Prebiotics: A Process Perspective is the first scientific reference to provide a comprehensive technological overview of the processes to derive oligosaccharides from dairy for use in functional foods. With their combined 90+ years in industry and research, the authors present the functional properties of prebiotics derived from lactose and the production technology required to make them. The book focuses on process engineering and includes an overview of green chemistry processes involving enzyme biocatalysis, providing detailed coverage of the use of whey lactose as raw material for producing oligosaccharides. The book’s focus on processes and products allows the reader to understand the constraints and impacts of technology on lactose-derived prebiotics. Presents the challenges of and opportunities for deriving oligosaccharides from lactose Details the technologies and methods required to produce lactose-derived prebiotics, including a comparison between chemical and enzymatic synthesis Discusses the potential use of whey as a raw material for the synthesis of non-digestible lactose-derived oligosaccharides Provides a process engineer perspective and includes valuable information about kinetics and reactor design for the enzymatic synthesis of lactose-derived oligosaccharides
This volume is the first to present a unified perspective on the control of underactuated mechanical systems. Based on real-time implementation of parameter identification, this book provides a variety of algorithms for the Furuta pendulum and the inertia wheel pendulum, which are two-degrees-of-freedom mechanical systems. Specifically, this work addresses and solves the problem of motion control via trajectory tracking in one joint coordinate while another joint is regulated. Besides, discussions on extensions to higher degrees-of-freedom systems are given. The book, aimed at control engineers as well as graduate students, ranges from the problem of parameter identification of the studied systems to the practical implementation of sophisticated motion control algorithms. Offering real-world solutions to manage the control of underactuated systems, this book provides a concise tutorial on recent breakthroughs in the field, original procedures to achieve bounding of the error trajectories, convergence and gain tuning guidelines.
This second edition reveals Cuba's true island spirit: from colonial Havana and the world-heritage site of Trinidad, to the Afro-Cuban culture of Santiago. This guide also covers famous beaches and provides travelers with countless shortcuts and tips for independent travel in Cuba.
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