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Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem computers. To mention just one field, one can name the computer tomography which could not possibly have been developed without modem tools for solving ill-posed problems. When writing this book, the authors tried to define the place and role of ill- posed problems in modem mathematics. In a few words, we define the theory of ill-posed problems as the theory of approximating functions with approximately given arguments in functional spaces. The difference between well-posed and ill- posed problems is concerned with the fact that the latter are associated with discontinuous functions. This approach is followed by the authors throughout the whole book. We hope that the theoretical results will be of interest to researchers working in approximation theory and functional analysis. As for particular algorithms for solving ill-posed problems, the authors paid general attention to the principles ofconstructing such algorithms as the methods for approximating discontinuous functions with approximately specified arguments. In this way it proved possible to define the limits of applicability of regularization techniques.
Quotient Space Based Problem Solving provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search. Drawing upon years of academic research and using numerous examples and illustrative applications, the authors, Ling Zhang and Bo Zhang provide a unique guide to computerized problem solving and granular computing. This book is a valuable guide to graduate students, research fellows, and academics specializing in artificial intelligence or concerned with computerized problem solving and granular computing. It explains the theory of hierarchical problem solving, its computational complexity, and discusses the principle and applications of multi-granular computing. It describes a human-like, theoretical framework using quotient space theory, that will be of interest to researchers in artificial intelligence. It provides many applications and examples in the engineering and computer science area. It includes complete coverage of planning, heuristic search and coverage of strictly mathematical models.
Contemporary societal problems are complex, intractable, and costly. Aiming to ameliorate them, social scientists formulate policies and programs, and conduct research testing the efficacy of the interventions. All too often the results are disappointing; partly because the theories guiding these studies are inappropriate, the study designs are flawed, and the empirical databases covering their research questions are sparse. This book confronts these problems of research by following this process: analyze the roots of the social problem both theoretically and empirically; formulate a study design that captures the nuances of the problem; gather appropriate empirical data operationalizing the study design; model these data using multilevel statistical methods to uncover potential causes and any biases to their implied effects; use the results by refining theory and by formulating evidence-based policy recommendations for implementation and testing.
Applying this process, the chapters focus on these social problems: political extremism; global human development; violence against religious minorities; computerization of work; reform of urban schools; and the utilization and costs of health care. Because these chapters exemplify the usefulness of multilevel modeling for the quantification of effects and causal inference, they can serve as vivid exemplars for the teaching of students. This use of examples reverses the usual procedure for introducing statistical methods. Rather than beginning with a new statistical model bearing on statistical theory and searching for illustrative data, each core chapter begins with a pressing social problem. The specific problem motivates theoretical analysis, gathering of relevant data, and application of appropriate statistical procedures. Readers can use the provided data sets and syntaxes to replicate, critique, and advance the analyses, thereby developing their ability to produce future applications of multilevel modeling.
The chapters address the multilevel data structures of these social problems by grouping observations on the micro units (level-1) by more macro-units (level-2) (e.g., school children are grouped by their classroom), and by conducting multilevel statistical modeling in contextual, longitudinal, and meta-analyses. Each core chapter applies a qualitative typology to nest the variance between the macro units, thereby crafting a "mixed-methods" approach that combines qualitative attributes with quantitative measures
This book is a comprehensive guide for life coaches on how to react and adapt when emotional problems get in the way of coaching. Windy Dryden uses rational-emotive cognitive behaviour therapy techniques to offer advice on:
Dealing with Clients' Emotional Problems in Life Coaching will be a valuable resource for all those involved in life coaching.
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