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In this innovative book, Celia Lury argues that the time has come for us to explore the world not only with new methods, but with a new approach to methodology itself. Fundamental changes are taking place in how we produce knowledge, how we communicate it and, indeed, what we consider to be knowledge. These changes demand innovative and creative responses to research questions. Lury's rethinking of the nature of social inquiry starts by reconceptualizing the 'problem space'. Problems are not static or a 'given'; rather, they are created and continually recomposed as part of the methodological process itself. Following the line of thought that methods are practices that articulate as much as capture a social problem, Lury further develops the notion of compositional methodology to think through its implications. With remarkable fluency, the book draws into conversation a range of hot-button issues, both longstanding and novel, from observation, reflexivity, recursive measurement and feminist methodologies, to participation, context, datafication and platformization. Always with an eye to the methodological potential of new trends, the book provides a strong challenge to much received wisdom and argues that a combination of techniques can contribute to better understanding of the problem spaces we all inhabit.
In this innovative book, Celia Lury argues that the time has come for us to explore the world not only with new methods, but with a new approach to methodology itself. Fundamental changes are taking place in how we produce knowledge, how we communicate it and, indeed, what we consider to be knowledge. These changes demand innovative and creative responses to research questions. Lury's rethinking of the nature of social inquiry starts by reconceptualizing the 'problem space'. Problems are not static or a 'given'; rather, they are created and continually recomposed as part of the methodological process itself. Following the line of thought that methods are practices that articulate as much as capture a social problem, Lury further develops the notion of compositional methodology to think through its implications. With remarkable fluency, the book draws into conversation a range of hot-button issues, both longstanding and novel, from observation, reflexivity, recursive measurement and feminist methodologies, to participation, context, datafication and platformization. Always with an eye to the methodological potential of new trends, the book provides a strong challenge to much received wisdom and argues that a combination of techniques can contribute to better understanding of the problem spaces we all inhabit.
This volume endeavours to summarise all available data on the theorems on isomorphisms and their ever increasing number of possible applications. It deals with the theory of solvability in generalised functions of general boundary-value problems for elliptic equations. In the early sixties, Lions and Magenes, and Berezansky, Krein and Roitberg established the theorems on complete collection of isomorphisms. Further progress of the theory was connected with proving the theorem on complete collection of isomorphisms for new classes of problems, and hence with the development of new methods to prove these theorems. The theorems on isomorphisms were first established for elliptic equations with normal boundary conditions. However, after the Noetherian property of elliptic problems was proved without assuming the normality of the boundary expressions, this became the natural way to consider the problems of establishing the theorems on isomorphisms for general elliptic problems. The present author's method of solving this problem enabled proof of the theorem on complete collection of isomorphisms for the operators generated by elliptic boundary-value problems for general systems of equations. Audience: This monograph will be of interest to mathematicians whose work involves partial differential equations, functional analysis, operator theory and the mathematics of mechanics.
In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data. The first part of the monograph, which can be read independently, provides optimal ranges of exponents for functional calculus and adapted Hardy spaces for the associated boundary operator. Methods use and improve, with new results, all the machinery developed over the last two decades to study such problems: the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions, and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions.
Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied.
New York Times bestselling adult author of The Bear and the Nightingale makes her middle grade debut with a creepy, spellbinding ghost story destined to become a classic. After suffering a tragic loss, eleven-year-old Ollie only finds solace in books. So when she happens upon a crazed woman at the river threatening to throw a book into the water, Ollie doesn't think—she just acts, stealing the book and running away. As she begins to read the slender volume, Ollie discovers a chilling story about a girl named Beth, the two brothers who both loved her, and a peculiar deal made with "the smiling man," a sinister specter who grants your most tightly held wish, but only for the ultimate price. Ollie is captivated by the tale until her school trip the next day to Smoke Hollow, a local farm with a haunting history all its own. There she stumbles upon the graves of the very people she's been reading about. Could it be the story about the smiling man is true? Ollie doesn't have too long to think about the answer to that. On the way home, the school bus breaks down, sending their teacher back to the farm for help. But the strange bus driver has some advice for the kids left behind in his care: "Best get moving. At nightfall they'll come for the rest of you." Nightfall is, indeed, fast descending when Ollie's previously broken digital wristwatch, a keepsake reminder of better times, begins a startling countdown and delivers a terrifying message: RUN. Only Ollie and two of her classmates heed the bus driver's warning. As the trio head out into the woods—bordered by a field of scarecrows that seem to be watching them—the bus driver has just one final piece of advice for Ollie and her friends: "Avoid large places. Keep to small." And with that, a deliciously creepy and hair-raising adventure begins.
This is an introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, empahsizing spaces with constant curvature. Chapters 1-4 provide basic notations for studying two-body dynamics. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 investigates the classical counterpart of the quantum system introduced in Chapter 5. Chapter 8 discusses applications in the quantum realm.
In this publication a framework for parallel planning agents is developed and applied to planning problems ranging from domain independent planning to planning for autonomous vehicle systems. The framework contains both logic-based and cost-based planning approaches.
Recent progress in artificial intelligence (AI) has revolutionized our everyday life. Many AI algorithms have reached human-level performance and AI agents are replacing humans in most professions. It is predicted that this trend will continue and 30% of work activities in 60% of current occupations will be automated. This success, however, is conditioned on availability of huge annotated datasets to training AI models. Data annotation is a time-consuming and expensive task which still is being performed by human workers. Learning efficiently from less data is a next step for making AI more similar to natural intelligence. Transfer learning has been suggested a remedy to relax the need for data annotation. The core idea in transfer learning is to transfer knowledge across similar tasks and use similarities and previously learned knowledge to learn more efficiently. In this book, we provide a brief background on transfer learning and then focus on the idea of transferring knowledge through intermediate embedding spaces. The idea is to couple and relate different learning through embedding spaces that encode task-level relations and similarities. We cover various machine learning scenarios and demonstrate that this idea can be used to overcome challenges of zero-shot learning, few-shot learning, domain adaptation, continual learning, lifelong learning, and collaborative learning.