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Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.
Here is clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
Engineering Technology and Applications contains the contributions presented at the 2014 International Conference on Engineering Technology and Applications (ICETA 2014, Tsingtao, China, 29-30 April 2014). The book is divided into three main topics: – Civil and environmental engineering – Electrical and computer engineering – Mechanical engineering Considerable attention is also paid to big data, cloud computing, neural network algorithms and social network services. The book will be invaluable to professionals and academics in civil, environmental, electrical, computer and mechanical engineering.
This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly, as bases for the Feller type scheme in terms of the possibilistic integral. These approaches also offer new proofs for the uniform convergence based on a Chebyshev type inequality in the theory of possibility. Researchers in the fields of approximation of functions, signal theory, approximation of fuzzy numbers, image processing, and numerical analysis will find this book most beneficial. This book is also a good reference for graduates and postgraduates taking courses in approximation theory.
The generation and use of megagauss magnetic fields have been subjects of research and development in laboratories around the world for over a quarter of a century. Research goals have included the development of compact, short-pulse, electrical power sources and the production of ultrahigh magnetic field strengths over significant experimental volumes. Energies measured in megajoules, currents in megamperes and timescales of microseconds are not uncommon in such work. Phase changes, insulator breakdowns, and local des truction of the apparatus are also frequently encountered. Some efforts have involved the use of high explosive systems, developing methodologies rather distinct from those of a normal physics laboratory. Manipulation of magnetic flux to exchange energy between high speed, electrically conducting flows and high strength electromagnetic fields remains, of course, a basic interaction of classical physics. The remoteness of the necessary experimental sites (at least in many instances) and the various national concerns for security of defense-related research have often limited the flow of information between investigators of separate organizations, working in common areas of technical concern. Occa sionally, however, it has been possible for the community of scientists and engineers engaged in work on high magnetic fields and related high energy den sity systems to gather together and exchange results and plans, successes and failures. The first such international gathering was in 1965 at the Conference on Megagauss Magnetic Field Generation by Explosives and Related Experi ments, Frascati, Italy.
This textbook follows closely the latest syllabus issued by the Ministry of Education, Singapore. It emphasises the understanding of mathematical concepts using a clear and systematic approach.