- Table View
- List View
Operators Between Sequence Spaces and Applications
by Eberhard Malkowsky Vladimir Rakočević Bruno de MalafosseThis book presents modern methods in functional analysis and operator theory along with their applications in recent research. The book also deals with the solvability of infinite systems of linear equations in various sequence spaces. It uses the classical sequence spaces, generalized Cesaro and difference operators to obtain calculations and simplifications of complicated spaces involving these operators. In order to make it self-contained, comprehensive and of interest to a larger mathematical community, the authors have presented necessary concepts with results for advanced research topics. This book is intended for graduate and postgraduate students, teachers and researchers as a basis for further research, advanced lectures and seminars.
Operators, Geometry and Quanta
by Dmitri Fursaev Dmitri VassilevichThis book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.
Operators, Inequalities and Approximation: Theory and Applications (Industrial and Applied Mathematics)
by Hemen Dutta Susanta Kumar Paikray Binod Chandra Tripathy Bidu Bhusan JenaThe book collects chapters on operator theory as well as related approximation results and analytic inequalities. It discusses the properties of various types of operators, methods for approximating such operators, proximity point problems, applications of approximation methods in other fields such as engineering, and some analytic inequalities. It seeks to capture both the pure and applied aspects of the topics discussed. Several of the concepts covered in the book are fundamental to many aspects of applied science and engineering. The intriguing and novel aspect of the book is that it focuses on foundational aspects of the topics as well as reasonable application ideas and inputs useful information for practical applications in a variety of other scientific and engineering fields.
Operators, Semigroups, Algebras and Function Theory: Volume from IWOTA Lancaster 2021 (Operator Theory: Advances and Applications #292)
by Gordon Blower Yemon Choi Matthew DawsThis volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.
Opinion Analysis in Interactions: From Data Mining to Human-Agent Interaction
by Chloe ClavelAs time goes on, big companies such as Amazon, Microsoft, Google and Apple become increasingly interested in virtual assistants. The interest and development of social robots has put research into affective and social computing at the forefront of the scene. The aim of Opinion Analysis in Interactions is to present methods based on artificial intelligence through a combination of machine learning models and symbolic approaches. Also discussed are natural language processing and affective computing, via the analysis and generation of socio-emotional signals. The book explores the analysis of opinions in human–human interaction and tackles the less-explored (yet crucial) challenges related to the analysis methods of user opinions within the context of human–agent interaction. It also illustrates the implementation of strategies for selecting and generating agent utterances in response to user opinions, and opens up perspectives on the agent’s multimodal generation of utterances that hold attitudes.
Opportunities and Challenges for Applied Demography in the 21st Century
by David A. Swanson Nazrul HoqueApplied demography continues its rapid pace of evolution in concert with the emerging trends of the 21st century. One significant area of change is the extension of applied demography beyond the United States; this book includes material dealing with applied demography in Australia, Canada, Estonia, and Mexico. Opportunities and Challenges for Applied Demography in the 21st Century presents a score of selected papers from the second post-2000 national conference on Applied Demography, held in San Antonio, Texas, in January, 2010, under the sponsorship of the Institute for Demographic and Socioeconomic Research at The University of Texas at San Antonio. Coverage includes the assembly of data by government agencies, with a focus on issues facing the United States; demographic issues associated with globalization; business demography and health demography, as well as a section examining methodological advances in the areas of estimation and projection.
Opportunities and Risks in AI for Business Development: Volume 1 (Studies in Systems, Decision and Control #545)
by Islam Elgedawy Bahaaeddin AlareeniThis book presents a groundbreaking exploration into the dynamic synergy between artificial intelligence and business development. Titled "AI Integration for Business Development: Navigating Opportunities, Unleashing Potential, Managing Risks," it serves as an indispensable guide for leaders and visionaries aiming to harness the transformative power of AI. The book introduces a comprehensive journey that unveils the strategic integration of AI into business development strategies. This book shows how to navigate a myriad of opportunities, strategically unleash untapped potential, and adeptly manage risks in the ever-evolving landscape of artificial intelligence. Through meticulous insights, real-world examples, and actionable strategies, readers gain the knowledge to make informed decisions and drive competitive advantage. This book presents not only a roadmap for identifying lucrative opportunities but also a blueprint for unlocking the full potential of AI technologies. Whether you are a seasoned executive, entrepreneur, or decision-maker, this book empowers you to proactively manage risks inherent in AI adoption, ensuring resilience and adaptability in your business model. Discover how to stay ahead in the rapidly changing business landscape, shaping the future of your business development initiatives. This book is your indispensable companion, offering profound insights into AI integration and empowering you to seize the transformative potential of AI. This book is your key to charting a course toward sustained success and innovation in the dynamic world of modern business.
Opportunities and Risks in AI for Business Development: Volume 2 (Studies in Systems, Decision and Control #546)
by Islam Elgedawy Bahaaeddin AlareeniThis book presents a groundbreaking exploration into the dynamic synergy between artificial intelligence and business development. Titled "AI Integration for Business Development: Navigating Opportunities, Unleashing Potential, Managing Risks," it serves as an indispensable guide for leaders and visionaries aiming to harness the transformative power of AI. The book introduces a comprehensive journey that unveils the strategic integration of AI into business development strategies. This book shows how to navigate a myriad of opportunities, strategically unleash untapped potential, and adeptly manage risks in the ever-evolving landscape of artificial intelligence. Through meticulous insights, real-world examples, and actionable strategies, readers gain the knowledge to make informed decisions and drive competitive advantage. This book presents not only a roadmap for identifying lucrative opportunities but also a blueprint for unlocking the full potential of AI technologies. Whether you are a seasoned executive, entrepreneur, or decision-maker, this book empowers you to proactively manage risks inherent in AI adoption, ensuring resilience and adaptability in your business model. Discover how to stay ahead in the rapidly changing business landscape, shaping the future of your business development initiatives. This book is your indispensable companion, offering profound insights into AI integration and empowering you to seize the transformative potential of AI. This book is your key to charting a course toward sustained success and innovation in the dynamic world of modern business.
Optical Binding Phenomena: Observations and Mechanisms
by Jonathan M. TaylorThis thesis addresses optical binding - a new area of interest within the field of optical micromanipulation. It presents, for the first time, a rigorous numerical simulation of some of the key results, along with new experimental findings and also physical interpretations of the results. In an optical trap particles are attracted close to areas of high optical intensities and intensity gradients. So, for example, if two lasers are pointed towards each other (a counter propagating trap) then a single particle is trapped in the centre of the two beams - the system is analogous to a particle being held by two springs in a potential well. If one increases the number of particles in the trap then naively one would expect all the particles to collect in the centre of the well. However, the effect of optical binding means that the presence of one particle affects the distribution of light experienced by another particle, resulting in extremely complex interactions that can lead to unusual 1D and 2D structures to form within the trap. Optical binding is not only of theoretical interest but also has applications in micromanipulation and assembly.
Optical Compressive Imaging
by Adrian SternThis dedicated overview of optical compressive imaging addresses implementation aspects of the revolutionary theory of compressive sensing (CS) in the field of optical imaging and sensing. It overviews the technological opportunities and challenges involved in optical design and implementation, from basic theory to optical architectures and systems for compressive imaging in various spectral regimes, spectral and hyperspectral imaging, polarimetric sensing, three-dimensional imaging, super-resolution imaging, lens-free, on-chip microscopy, and phase sensing and retrieval. The reader will gain a complete introduction to theory, experiment, and practical use for reducing hardware, shortening image scanning time, and improving image resolution as well as other performance parameters. Optics practitioners and optical system designers, electrical and optical engineers, mathematicians, and signal processing professionals will all find the book a unique trove of information and practical guidance.
Optical Computing (Scottish Graduate Ser. #34)
by B.S. Wherrett; F.A.P. TooleyWritten by ten leading experts in the field, Optical Computing cover topics such as optical bistability, optical interconnects and circuits, photorefractive devices, spatial light modulators, associative memory, and optical computer architectures.
Optical Fiber Sensors and AI: Exploring the Fusion (Progress in Optical Science and Photonics #34)
by Santosh Kumar Amit Rai Vanita Bhardwaj Kamal KishorThis book highlights the exciting developments in optical fiber sensors and how artificial intelligence (AI) is boosting their performance and applications. It starts with an easy-to-understand introduction to the basics of optical fiber sensors and their many uses. Then, it moves on to the latest technological advancements, showing how AI is making these sensors smarter and more efficient. The book contains chapters demonstrating how machine learning contributes to real-time data analysis and how deep learning enhances sensor systems. There is also a focus on designing better sensor networks with the help of AI. The book explains how combining AI with the Internet of Things (IoT) and optical fiber sensors can create smart infrastructure solutions. Real-world case studies illustrate how AI-enhanced fiber-optic sensors are benefiting fields like healthcare and environmental monitoring. The book wraps up with a look at future trends and challenges in the world of AI-powered optical fiber sensing. This book is perfect for researchers, engineers, and anyone interested in the powerful combination of AI and optical fiber technology. It provides valuable insights into how these technologies can work together to create innovative and practical solutions.
Optical Hall Effect in the Sharp Focus of Laser Light
by Victor V. Kotlyar Alexey A. Kovalev Anton G. NalimovThis book explores the optical Hall effect in the sharp focus of laser light. It builds upon the established theory of Richards-Wolf (1959), providing numerous real-world examples that illustrate both spin and orbital Hall effects near the focal point. Within the focal zone, distinct regions of left and right circular polarization emerge, showcasing the orbital Hall effect. This effect becomes apparent when localized areas within the focal plane experience transverse energy flow, rotating either clockwise or counterclockwise. The spin Hall effect, a fundamental occurrence, is demonstrated when a linearly polarized Gaussian beam is concentrated. Furthermore, the book reveals spin and orbital Hall effects in light fields with nonuniform linear polarization, where the polarization direction varies within the beam cross section. While the optical or photonic Hall effect has been recognized since 2004, a comprehensive monograph detailing its focal dynamics has been lacking until now. Drawing from the cohesive theoretical framework of the Richards-Wolf theory, this book offers specific examples and results from computer modeling. It equips readers with analytical relations for calculating energy and spin fluxes near a sharp focus across various initial light vector fields. Designed for a diverse audience, including scientists, engineers, and students in optics and photonics, this book serves as a valuable resource. It caters to undergraduate and graduate students in applied mathematics, physics, informatics, and optics, and can also benefit researchers and professionals in the field. Moreover, the book holds potential as a foundational text for advanced graduate courses
Optical Polymer Waveguides: From the Design to the Final 3D-Opto Mechatronic Integrated Device
by Stefan Kaierle Jörg Franke Ludger Overmeyer Klaus-Jürgen Wolter Norbert Lindlein Karlheinz Bock Oliver SuttmannLight signals in optical waveguides can be used to transmit very large amounts of data quickly and largely without interference. In the industrial and infrastructural sectors, e.g. in the automotive and aerospace industries, the demand to further exploit this potential is therefore increasing. Which technologies can be used to effectively integrate systems that transmit data by means of light into existing components? This is a central question for current research. So far, there have been some technical limitations in this regard. For example, it is difficult to couple the signal of an optical waveguide to other optical waveguides without interruption. There is also a lack of suitable fabrication technologies for three-dimensional waveguides, as well as design and simulation environments for 3D opto-MID. This book addresses these and other challenges.
Optically Trapped Microspheres as Sensors of Mass and Sound: Brownian Motion as Both Signal and Noise (Springer Theses)
by Logan Edward HillberryThis thesis makes significant advances in the use of microspheres in optical traps as highly precise sensing platforms. While optically trapped microspheres have recently proven their dominance in aqueous and vacuum environments, achieving state-of-the-art measurements of miniscule forces and torques, their sensitivity to perturbations in air has remained relatively unexplored. This thesis shows that, by uniquely operating in air and measuring its thermally-fluctuating instantaneous velocity, an optically trapped microsphere is an ultra-sensitive probe of both mass and sound. The mass of the microsphere is determined with similar accuracy to competitive methods but in a fraction of the measurement time and all while maintaining thermal equilibrium, unlike alternative methods. As an acoustic transducer, the air-based microsphere is uniquely sensitive to the velocity of sound, as opposed to the pressure measured by a traditional microphone. By comparison to state-of-the-art commercially-available velocity and pressure sensors, including the world’s smallest measurement microphone, the microsphere sensing modality is shown to be both accurate and to have superior sensitivity at high frequencies. Applications for such high-frequency acoustic sensing include dosage monitoring in proton therapy for cancer and event discrimination in bubble chamber searches for dark matter. In addition to reporting these scientific results, the thesis is pedagogically organized to present the relevant history, theory, and technology in a straightforward way.
Optics, 5th Edition
by Eugene HechtA Contemporary Approach to Optics with Practical Applications and New Focused Pedagogy Hecht Optics balances theory and instrumentation to provide you with the necessary, classical background through a lively and clear narrative. Optics, Fifth Edition is distinguished by three core imperatives for the reader: up-to-date content in line with the ever-evolving technological advances in the Optics field; a modern approach to discourse including studies on photons, phasors, and theory; and improvements and revisions to the previous edition's pedagogy including over one hundred new worked examples.
Optik und ihre Phänomene: Lichtspiele in der Natur: von Luftspiegelungen und Himmelsfarben bis in die Weiten des Alls
by Michael VollmerDieses Lehr-, Lern-, Fach- und Sachbuch präsentiert die Grundlagen der Optik in Theorie und ausführlich beschriebenem Experiment sowie vielfältige faszinierende optische Phänomene. Ob in Vorlesungen, Seminaren, für Projektarbeiten, Schulunterricht oder Selbststudium - dieses Buch ist eine wertvolle Ressource für alle, die sich für Optik interessieren. Durch die große Zahl zitierter Originalarbeiten schlägt es nicht nur die Brücke zur Lehre sondern auch zur Forschung. Besonderheiten: Das Buch besticht durch seine über 1000 Abbildungen, darunter über 200 qualitativ hochwertige Farbfotos optischer Naturphänomene sowie einer großen Zahl an wissenschaftlichen und physikdidaktischen Literaturangaben für weiterführende Studien. Die Kapitel sind jeweils auch einzeln lesbar, aber zusammen ist es eine einmalige Kombination aus einführendem Lehrbuch der klassischen Optik und detaillierter up-to-date Zusammenstellung von Anwendungen im Bereich optischer Naturphänomene. Thematisch spannt es einen sehr weiten Bogen: von geometrischer, Wellen- und Quantenoptik, Radiometrie und Photometrie über Farbtheorien und technische Anwendungen wie Spektroskopie bis hin zu Naturphänomenen oder der Frage warum der Himmel nachts dunkel ist. Die Grundlagen werden vertieft durch zahlreiche Verständnisfragen und Übungsaufgaben zusätzlich zu vielen Anwendungsbeispielen, die von Fensterreflexionen über Lichtwellenleiter und Smartphoneobjektive bis hin zu modernen Beamern reichen. Inhalt: 1. Einleitung .- 2. Geometrische Optik .- 3. Wellenoptik .- 4. Wechselwirkung von Strahlung mit Materie: Quantenoptik .- 5. Detektoren und Lichtquellen .- 6. Visuelle Wahrnehmung .- 7. Die Atmosphäre der Erde .- 8. Luftspiegelungen.- 9. Regenbögen .- 10. Koronen, Glorien und verwandte Erscheinungen .- 11. Haloerscheinungen am Himmel.- 12. Lichtstreuung und Himmelsfarben .- 13. Weitere Phänomene aufgrund von Lichtstreuung .- 14. Bis in die Stratosphäre und darüber hinaus Neuerungen (zur 2.Aufl.): Der erste Lehrbuchteil zu den Grundlagen ist komplett neu hinzugefügt. Der zweite Teil zu den Anwendungen und Naturphänomenen wurde komplett überarbeitet und aktualisiert. Zudem illustrieren nun über 200 Farbfotos die Phänomene. Die Zielgruppe: Sowohl interessierte Laien - mit und ohne Vorwissen - und Lehrkräfte an Schulen als auch Studierende diverser Fachrichtungen sowie deren Lehrende profitieren von dieser umfangreichen Zusammenstellung. Optik wird nicht nur im Bachelor bzw. Master in Physik u. Astronomie bzw. Astrophysik sowie in den Naturwissenschaften thematisiert, sondern auch in Studiengängen mit Schwerpunkten wie Licht- und Beleuchtungstechnik, Lasertechnik, optische Technologien, Optoelektronik und Photonik, Augenoptik, Meteorologie, uvm. Vorkenntnisse: Erforderlich ist kein besonderes Vorwissen, allerdings ermöglichen manche der angegebenen Querbezüge ein tieferes Verständnis, welches sich erst mit Vorkenntnissen aus einigen Grundlagenfächern der Physik, insbesondere des Elektromagnetismus, der Festkörperphysik sowie der Quantenphysik vollständig erschließt.
Optimal Analysis of Structures by Concepts of Symmetry and Regularity
by Ali KavehOptimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models. Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented. The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms. The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.
Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems
by Nicolae Herisanu Vasile Marinca Bogdan MarincaThis book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books “Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches”, Springer-2011 and “The Optimal Homotopy Asymptotic Method. Engineering Applications”, Springer-2015.
Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
by Martin GugatThis brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.
Optimal Control
by Ravi P. Agarwal Dmitriy V. Dolgy Taekyun Kim Leonid T. AshchepkovThis textbook, now in its second edition, results from lectures, practical problems, and workshops on Optimal Control, given by the authors at Irkutsk State University, Far Eastern Federal University (both in Vladivostok, Russia), and Kwangwoon University (Seoul, South Korea).In this work, the authors cover the theory of linear and nonlinear systems, touching on the basic problem of establishing the necessary and sufficient conditions of optimal processes. Readers will find two new chapters, with results of potential interest to researchers with a focus on the theory of optimal control, as well as to those interested in applications in Engineering and related sciences. In addition, several improvements have been made through the text.This book is structured in three parts. Part I starts with a gentle introduction to the basic concepts in Optimal Control. In Part II, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of reachability set in the class of piecewise continuous controls and touch on the problems of controllability, observability, identification, performance, and terminal control. Part III, in its turn, is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Problem sets at the end of chapters and a list of additional tasks, provided in the appendix, are offered for students seeking to master the subject. The exercises have been chosen not only as a way to assimilate the theory but also as to induct the application of such knowledge in more advanced problems.
Optimal Control Applied to Biological Models (Chapman & Hall/CRC Mathematical Biology Series)
by Suzanne Lenhart John T. WorkmanFrom economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t
Optimal Control Problems Arising in Forest Management (SpringerBriefs in Optimization)
by Alexander J. ZaslavskiThis book is devoted to the study of optimal control problems arising in forest management, an important and fascinating topic in mathematical economics studied by many researchers over the years. The volume studies the forest management problem by analyzing a class of optimal control problems that contains it and showing the existence of optimal solutions over infinite horizon. It also studies the structure of approximate solutions on finite intervals and their turnpike properties, as well as the stability of the turnpike phenomenon and the structure of approximate solutions on finite intervals in the regions close to the end points. The book is intended for mathematicians interested in the optimization theory, optimal control and their applications to the economic theory.
Optimal Control Problems Related to the Robinson–Solow–Srinivasan Model (Monographs in Mathematical Economics #4)
by Alexander J. ZaslavskiThis book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson–Solow–Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further studied by Robinson, Nobuo Okishio, and Joseph Stiglitz. Since then, the study of the RSS model has become an important element of economic dynamics. In this book, two large general classes of optimal control problems, both of them containing the RSS model as a particular case, are presented for study. For these two classes, a turnpike theory is developed and the existence of solutions to the corresponding infinite horizon optimal control problems is established. The book contains 9 chapters. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model. The first class of optimal control problems is studied in Chaps. 2–6. In Chap. 2, infinite horizon optimal control problems with nonautonomous optimality criteria are considered. The utility functions, which determine the optimality criterion, are nonconcave. This class of models contains the RSS model as a particular case. The stability of the turnpike phenomenon of the one-dimensional nonautonomous concave RSS model is analyzed in Chap. 3. The following chapter takes up the study of a class of autonomous nonconcave optimal control problems, a subclass of problems considered in Chap. 2. The equivalence of the turnpike property and the asymptotic turnpike property, as well as the stability of the turnpike phenomenon, is established. Turnpike conditions and the stability of the turnpike phenomenon for nonautonomous problems are examined in Chap. 5, with Chap. 6 devoted to the study of the turnpike properties for the one-dimensional nonautonomous nonconcave RSS model. The utility functions, which determine the optimality criterion, are nonconcave. The class of RSS models is identified with a complete metric space of utility functions. Using the Baire category approach, the turnpike phenomenon is shown to hold for most of the models. Chapter 7 begins the study of the second large class of autonomous optimal control problems, and turnpike conditions are established. The stability of the turnpike phenomenon for this class of problems is investigated further in Chaps. 8 and 9.
Optimal Control Theory and Static Optimization in Economics
by Daniel Leonard Ngo Van LongOptimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This book is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigor. Economic intuition is emphasized, examples and problem sets covering a wide range of applications in economics are provided, theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with the simple formulations and progressing to advanced topics. Optimal control theory is introduced directly, without recourse to the calculus of variations, and the connection with the latter and with dynamic programming is explained in a separate chapter. Also, the book draws the parallel between optimal control theory and static optimization. No previous knowledge of differential equations is required.