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"General-equilibrium" refers to an analytical approach which looks at the economy as a complete system of inter-dependent components (industries, households, investors, governments, importers and exporters). "Applied" means that the primary interest is in systems that can be used to provide quantitative analysis of economic policy problems in particular countries. Reflecting the authors' belief in the models as vehicles for practical policy analysis, a considerable amount of material on data and solution techniques as well as on theoretical structures has been included. The sequence of chapters follows what is seen as the historical development of the subject.
The book is directed at graduate students and professional economists who may have an interest in constructing or applying general equilibrium models. The exercises and readings in the book provide a comprehensive introduction to applied general equilibrium modeling. To enable the reader to acquire hands-on experience with computer implementations of the models which are described in the book, a companion set of diskettes is available.
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.
Computer algebra systems have the potential to revolutionize the teaching of and learning of science. Not only can students work thorough mathematical models much more efficiently and with fewer errors than with pencil and paper, they can also work with much more complex and computationally intensive models. Thus, for example, in studying the flight of a golf ball, students can begin with the simple parabolic trajectory, but then add the effects of lift and drag, of winds, and of spin. Not only can the program provide analytic solutions in some cases, it can also produce numerical solutions and graphic displays.
On Fracture Mechanics A major objective of engineering design is the determination of the geometry and dimensions of machine or structural elements and the selection of material in such a way that the elements perform their operating function in an efficient, safe and economic manner. For this reason the results of stress analysis are coupled with an appropriate failure criterion. Traditional failure criteria based on maximum stress, strain or energy density cannot adequately explain many structural failures that occurred at stress levels considerably lower than the ultimate strength of the material. On the other hand, experiments performed by Griffith in 1921 on glass fibers led to the conclusion that the strength of real materials is much smaller, typically by two orders of magnitude, than the theoretical strength. The discipline of fracture mechanics has been created in an effort to explain these phenomena. It is based on the realistic assumption that all materials contain crack-like defects from which failure initiates. Defects can exist in a material due to its composition, as second-phase particles, debonds in composites, etc. , they can be introduced into a structure during fabrication, as welds, or can be created during the service life of a component like fatigue, environment-assisted or creep cracks. Fracture mechanics studies the loading-bearing capacity of structures in the presence of initial defects. A dominant crack is usually assumed to exist.
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