Discrete-Time Control Systems

Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.

Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This 2003 book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appeared here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.

This book provides a detailed introduction to the ergodic theory of equilibrium states giving equal weight to two of its most important applications, namely to equilibrium statistical mechanics on lattices and to (time discrete) dynamical systems. It starts with a chapter on equilibrium states on finite probability spaces which introduces the main examples for the theory on an elementary level. After two chapters on abstract ergodic theory and entropy, equilibrium states and variational principles on compact metric spaces are introduced emphasizing their convex geometric interpretation. Stationary Gibbs measures, large deviations, the Ising model with external field, Markov measures, Sinai-Bowen-Ruelle measures for interval maps and dimension maximal measures for iterated function systems are the topics to which the general theory is applied in the last part of the book. The text is self contained except for some measure theoretic prerequisites which are listed (with references to the

Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and quickly develops a coherent and rigorous theory whilst showing also how actually to apply it. Both discrete-time and continuous-time chains are studied. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice. It will therefore be an ideal text either for elementary courses on random processes or those that are more oriented towards applications.

This 2002 monograph offers a broad investigative tool in ergodic theory and measurable dynamics. The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the allowed distortion will lead to different restricted orbit equivalence theories. These include Ornstein's Isomorphism theory, Kakutani Equivalence theory and a list of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all these examples simultaneously and gives insight into how to seek further applications. The work is placed in the context of discrete amenable group actions where time is not required to be one-dimensional, making the results applicable to a much wider range of problems and examples.

This 2002 monograph offers a broad investigative tool in ergodic theory and measurable dynamics. The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the allowed distortion will lead to different restricted orbit equivalence theories. These include Ornstein's Isomorphism theory, Kakutani Equivalence theory and a list of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all these examples simultaneously and gives insight into how to seek further applications. The work is placed in the context of discrete amenable group actions where time is not required to be one-dimensional, making the results applicable to a much wider range of problems and examples.

Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engin

Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engin

How much influence do citizens have to control the government? What guides voters at election time? Why do governments survive? How do institutions modify the power of the people over politicians? The book combines academic analytical rigor with comparative analysis to identify how much information voters must have to select a politician for office, or for holding a government accountable; whether parties in power can help voters to control their governments; how different institutional arrangements influence voters' control; why politicians choose particular electoral systems; and what economic and social conditions may undermine not only governments, but democracy. Arguments are backed by vast macro and micro empirical evidence. There are cross-country comparisons and survey analyses of many countries. In every case there has been an attempt to integrate analytical arguments and empirical research. The goal is to shed new light on perplexing questions of positive democratic theory.

How much influence do citizens have to control the government? What guides voters at election time? Why do governments survive? How do institutions modify the power of the people over politicians? The book combines academic analytical rigor with comparative analysis to identify how much information voters must have to select a politician for office, or for holding a government accountable; whether parties in power can help voters to control their governments; how different institutional arrangements influence voters' control; why politicians choose particular electoral systems; and what economic and social conditions may undermine not only governments, but democracy. Arguments are backed by vast macro and micro empirical evidence. There are cross-country comparisons and survey analyses of many countries. In every case there has been an attempt to integrate analytical arguments and empirical research. The goal is to shed new light on perplexing questions of positive democratic theory.

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Prevailing classification systems backed by the American Psychiatric Association (DSM) and World Health Organization (ICD) generally assume that mental health conditions are best represented by discrete entities that are qualitatively distinct from one another and from mental health. These diagnostic categories, such as major depression, antisocial personality disorder, and obsessive-compulsive disorder, are ubiquitous in research, clinical, training, legal, and public health contexts. Yet they are out of sync with a vast quantity of scientific data on the presentation, causes, and treatments of psychopathology. Empirically speaking, categorical diagnoses tend to be unreliable (over time and across reporters), have fuzzy boundaries with one another and mental health, do not capture many clinical presentations encountered in routine practice, and lack distinctive causes and recommended treatments. Dimensional perspectives recognize the same signs and symptoms as categorical rubrics, but

This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.

This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.

Wireless sensor networks promise an unprecedented fine-grained interface between the virtual and physical worlds. They are one of the most rapidly developing information technologies, with applications in a wide range of fields including industrial process control, security and surveillance, environmental sensing, and structural health monitoring. Originally published in 2005, this book provides a detailed and organized survey of the field. It shows how the core challenges of energy efficiency, robustness, and autonomy are addressed in these systems by networking techniques across multiple layers. The topics covered include network deployment, localization, time synchronization, wireless radio characteristics, medium-access, topology control, routing, data-centric techniques, and transport protocols. Ideal for researchers and designers seeking to create algorithms and protocols and engineers implementing integrated solutions, it also contains many exercises and can be used by graduate

Wireless sensor networks promise an unprecedented fine-grained interface between the virtual and physical worlds. They are one of the most rapidly developing information technologies, with applications in a wide range of fields including industrial process control, security and surveillance, environmental sensing, and structural health monitoring. Originally published in 2005, this book provides a detailed and organized survey of the field. It shows how the core challenges of energy efficiency, robustness, and autonomy are addressed in these systems by networking techniques across multiple layers. The topics covered include network deployment, localization, time synchronization, wireless radio characteristics, medium-access, topology control, routing, data-centric techniques, and transport protocols. Ideal for researchers and designers seeking to create algorithms and protocols and engineers implementing integrated solutions, it also contains many exercises and can be used by graduate

Design and deploy advanced vibration protection systems based on elastic composites under post-buckling, with this essential reference. Methods for designing vibration protection systems with negative and quasi-zero stiffness are formulated, explained, and demonstrated in practice. All key steps of the system design are covered, including the type and number synthesis, modelling and studying of stress-strain state under post-buckling of elastic composite designs, chaotic dynamics and stability conditions, real-time dimensioning, and active motion control. In addition to coverage of underlying theory, the use in helicopters, buses, railroad vehicles, construction equipment and agricultural machinery are included. An excellent reference for researchers and practicing engineers, as well as a tutorial for university students and professors with an interest in study, development and application of alternative methods of vibration protection anywhere.

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

Dependability metrics are omnipresent in every engineering field, from simple ones through to more complex measures combining performance and dependability aspects of systems. This book presents the mathematical basis of the analysis of these metrics in the most used framework, Markov models, describing both basic results and specialised techniques. The authors first present both discrete and continuous time Markov chains before focusing on dependability measures, which necessitate the study of Markov chains on a subset of states representing different user satisfaction levels for the modelled system. Topics covered include Markovian state lumping, analysis of sojourns on subset of states of Markov chains, analysis of most dependability metrics, fundamentals of performability analysis, and bounding and simulation techniques designed to evaluate dependability measures. The book is of interest to graduate students and researchers in all areas of engineering where the concepts of lifetime

Since the early days of integrated pest management a sound ecological foundation has been considered essential for the development of effective systems. From time to time, there have been attempts to evaluate the ways in which ecological theory is exploited in pest control, and to review the lessons that ecologists learn from pest management. In the last 20 years there have been many developments within the contribution of ecological theory to integrated pest management. This book captures some of the themes in both pest management and ecology that have emerged and provides an updated assessment of the role that basic ecology plays in the development of rational and sustainable pest management practices. Major themes are examined, assessing the significance and potential impact of recent technological and conceptual developments for the future of integrated pest management.

How do Family and Medical Leave Act rights operate in practice in the courts and in the workplace? This empirical study examines how institutions and social practices transform the meaning of these rights to recreate inequality. Workplace rules and norms built around the family wage ideal, the assumption that disability and work are mutually exclusive, and management's historical control over time all constrain opportunities for social change. Yet workers can also mobilize rights as a cultural discourse to change the social meaning of family and medical leave. Drawing on theoretical frameworks from social constructivism and new institutionalism, this study explains how institutions transform rights to recreate systems of power and inequality but at the same time also provide opportunities for law to change social structure. It provides a fresh look at the perennial debate about law and social change by examining how institutions shape the process of rights mobilization.

Many natural phenomena ranging from climate through to biology are described by complex dynamical systems. Getting information about these phenomena involves filtering noisy data and prediction based on incomplete information (complicated by the sheer number of parameters involved), and often we need to do this in real time, for example for weather forecasting or pollution control. All this is further complicated by the sheer number of parameters involved leading to further problems associated with the 'curse of dimensionality' and the 'curse of small ensemble size'. The authors develop, for the first time in book form, a systematic perspective on all these issues from the standpoint of applied mathematics. The book contains enough background material from filtering, turbulence theory and numerical analysis to make the presentation self-contained and suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required to enlighten obs

How do Family and Medical Leave Act rights operate in practice in the courts and in the workplace? This empirical study examines how institutions and social practices transform the meaning of these rights to recreate inequality. Workplace rules and norms built around the family wage ideal, the assumption that disability and work are mutually exclusive, and management's historical control over time all constrain opportunities for social change. Yet workers can also mobilize rights as a cultural discourse to change the social meaning of family and medical leave. Drawing on theoretical frameworks from social constructivism and new institutionalism, this study explains how institutions transform rights to recreate systems of power and inequality but at the same time also provide opportunities for law to change social structure. It provides a fresh look at the perennial debate about law and social change by examining how institutions shape the process of rights mobilization.

This simple, compact toolkit for designing and analyzing stochastic approximation algorithms requires only basic literacy in probability and differential equations. Yet these algorithms have powerful applications in control and communications engineering, artificial intelligence and economic modelling. The dynamical systems viewpoint treats an algorithm as a noisy discretization of a limiting differential equation and argues that, under reasonable hypotheses, it tracks the asymptotic behaviour of the differential equation with probability one. The differential equation, which can usually be obtained by inspection, is easier to analyze. Novel topics include finite-time behaviour, multiple timescales and asynchronous implementation. There is a useful taxonomy of applications, with concrete examples from engineering and economics. Notably it covers variants of stochastic gradient-based optimization schemes, fixed-point solvers, which are commonplace in learning algorithms for approximate

Nerve and muscle systems in helminth parasites interact in a highly co-ordinated manner to control movements associated with alimentation, reproduction, locomotion and attachment. All metazoan parasites rely on some or all of these activities for their survival. For a long time it has been known that neuromuscular function in parasites is susceptible to chemotherapeutic attack, and that compromising this aspect of parasite biology is sufficient to cure many parasite infections. This volume outlines the latest research in this area, showing why this system is so amenable to drug intervention and outlining potential targets for new treatments. Written by experts in the field, this volume will be invaluable to anyone interested in the molecular biology, physiology and biochemistry of parasites as well as those looking to exploit these for the creation of new treatments.

Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.

Application of Artificial Intelligence in Hybrid Electric Vehicle Energy Management presents the state-of-the-art in hybrid electric vehicle system modelling and management. With a focus on learning-based energy management strategies, the book provides detailed methods, mathematical models, and strategies designed to optimize the energy management of the energy supply module of a hybrid vehicle.The book first addresses the underlying problems in Hybrid Electric Vehicle (HEV) modeling, and then introduces several artificial intelligence-based energy management strategies of HEV systems, including those based on fuzzy control with driving pattern recognition, multi objective optimization, fuzzy Q-learning and Deep Deterministic Policy Gradient (DDPG) algorithms. To help readers apply these management strategies, the book also introduces State of Charge and State of Health prediction methods and real time driving pattern recognition. For each application, the detailed experimental process

Rivers are important agents of change that shape the Earth's surface and evolve through time in response to fluctuations in climate and other environmental conditions. They are fundamental in landscape development, and essential for water supply, irrigation, and transportation. This book provides a comprehensive overview of the geomorphological processes that shape rivers and that produce change in the form of rivers. It explores how the dynamics of rivers are being affected by anthropogenic change, including climate change, dam construction, and modification of rivers for flood control and land drainage. It discusses how concern about environmental degradation of rivers has led to the emergence of management strategies to restore and naturalize these systems, and how river management techniques work best when coordinated with the natural dynamics of rivers. This textbook provides an excellent resource for students, researchers, and professionals in fluvial geomorphology, hydrology, ri

This concise overview of digital signal generation will introduce you to powerful, flexible and practical digital waveform generation techniques. These techniques, based on phase-accumulation and phase-amplitude mapping, will enable you to generate sinusoidal and arbitrary real-time digital waveforms to fit your desired waveshape, frequency, phase offset and amplitude, and to design bespoke digital waveform generation systems from scratch. Including a review of key definitions, a brief explanatory introduction to classical analogue waveform generation and its basic conceptual and mathematical foundations, coverage of recursion, DDS, IDFT and dynamic waveshape and spectrum control, a chapter dedicated to detailed examples of hardware design, and accompanied by downloadable Mathcad models created to help you explore 'what if?' design scenarios, this is essential reading for practitioners in the digital signal processing community, and for students who want to understand and apply digital

This collection of essays was the first relatively comprehensive survey of the environmental history of China. Written by some of the world's leading Western and Chinese experts, Sediments of Time crystallises a new and distinct field of scholarship that studies what happens when human social systems interact with the rest of the natural world. This book shows how deforestation, land-reclamation, settlement, and water-control, when mixed with an ever-changing climate, shape a distinct and often precarious environment. Pioneering essays explore new methodologies of historical environmental research, comparative perspectives setting China in the context of the West and Japan, and the impact of the early modern ecological transformation on the spread of diseases such as cholera and tuberculosis. This is an indispensable book for anyone who wants to understand either the foundations of modern China, or the deeper origins of many of China's most daunting contemporary challenges.

The boreal forests of the world, geographically situated to the south of the Arctic and generally north of latitude 50 degrees, are considered to be one of the earth's most significant terrestrial ecosystems in terms of their potential for interaction with other global scale systems, such as climate and anthropologenic activity. This book, developed by an international panel of ecologists, provides a synthesis of the important patterns and processes which occur in boreal forests and reviews the principal mechanisms which control the forests' pattern in space and time. The effects of cold temperatures, soil ice, insects, plant competition, wildfires and climatic change on the boreal forests are discussed as a basis for the development of the first global scale computer model of the dynamical change of a biome, able to project the change of the boreal forest over timescales of decades to millennia, and over the global extent of this forest.

The last twenty-five years have seen dramatic rises in the prison populations of most industrialised nations. Unable to keep up with increased numbers of convicted offenders, governments and criminal justice systems have been seeking new ways to control and punish offenders. One sanction adopted in Canada and some parts of Europe and the US is community custody which attempts to recreate the punitive nature of prison but without incarceration. This book analyses the effectiveness of this approach and explores its implications for offenders and society as a whole. It demonstrates that if properly conceived and administered, community custody can reduce the number of prison admissions and at the same time promote multiple goals of sentencing. So that offenders given community custody orders are punished yet also given the opportunity to change their lives in ways that would be impossible if they were in prison.

The last twenty-five years have seen dramatic rises in the prison populations of most industrialised nations. Unable to keep up with increased numbers of convicted offenders, governments and criminal justice systems have been seeking new ways to control and punish offenders. One sanction adopted in Canada and some parts of Europe and the US is community custody which attempts to recreate the punitive nature of prison but without incarceration. This book analyses the effectiveness of this approach and explores its implications for offenders and society as a whole. It demonstrates that if properly conceived and administered, community custody can reduce the number of prison admissions and at the same time promote multiple goals of sentencing. So that offenders given community custody orders are punished yet also given the opportunity to change their lives in ways that would be impossible if they were in prison.

This collection of essays was the first relatively comprehensive survey of the environmental history of China. Written by some of the world's leading Western and Chinese experts, Sediments of Time crystallises a new and distinct field of scholarship that studies what happens when human social systems interact with the rest of the natural world. This book shows how deforestation, land-reclamation, settlement, and water-control, when mixed with an ever-changing climate, shape a distinct and often precarious environment. Pioneering essays explore new methodologies of historical environmental research, comparative perspectives setting China in the context of the West and Japan, and the impact of the early modern ecological transformation on the spread of diseases such as cholera and tuberculosis. This is an indispensable book for anyone who wants to understand either the foundations of modern China, or the deeper origins of many of China's most daunting contemporary challenges.

The collection consists of four parts: Part I presents three non-technical essays on economic development and economic systems. Four out of five essays in Part II deal with the theory and measurement of the so-called Index of Total Factor Productivity for several countries. The fifth essay is on the theory of index numbers. The first essay of Part III compares the American and Soviet patterns of economic development and finds that the path followed by each country might have been optimal for it at the time. The second essay develops a general theory of a producer cooperative. The third essay discusses a method for avoiding monopolistic exploitation, under either system, without price control. Part IV presents three applications of economic theory to historical problems - in particular, to serfdom and slavery. The first, on 'The Causes of Slavery or Serfdom', has become a classic. The second challenges the widely accepted view that Russian serfdom had become unprofitable for the serf-ow

The collection consists of four parts: Part I presents three non-technical essays on economic development and economic systems. Four out of five essays in Part II deal with the theory and measurement of the so-called Index of Total Factor Productivity for several countries. The fifth essay is on the theory of index numbers. The first essay of Part III compares the American and Soviet patterns of economic development and finds that the path followed by each country might have been optimal for it at the time. The second essay develops a general theory of a producer cooperative. The third essay discusses a method for avoiding monopolistic exploitation, under either system, without price control. Part IV presents three applications of economic theory to historical problems - in particular, to serfdom and slavery. The first, on 'The Causes of Slavery or Serfdom', has become a classic. The second challenges the widely accepted view that Russian serfdom had become unprofitable for the serf-ow

This book presents the twin topics of singular perturbation methods and time scale analysis to problems in systems and control. The heart of the book is the singularly perturbed optimal control syste

If you want top grades and thorough understanding of feedback and control systems--both analog and digital--in less study time, this powerful study tool is the best tutor you can have It takes you ste