This comprehensive resource is designed to guide professionals in product compliance and safety in order to develop more profitable products, contribute to customer satisfaction, and reduce the risk of liability. This book analyzes the principles and methods of critical standards, highlighting how they should be applied in the field. It explores the philosophy of electrical product safety and analyzes the concepts of compliance and safety, perception of risk, failure, normal and abnormal conditions, and redundancy. Professionals find valuable information on power sources, product construction requirements, markings, compliance testing, and manufacturing of safe electrical products.
It is known that certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments have diffusive scaling limits. Here, in the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was first developed by Le Jan and Raimond, who showed that each such flow is characterized by its -point motions. The authors' work focuses on a class of stochastic flows of kernels with Brownian -point motions which, after their inventors, will be called Howitt-Warren flows. The authors' main result gives a graphical construction of general Howitt-Warren flows, where the underlying random environment takes on the form of a suitably marked Brownian web. This extends earlier work of Howitt and Warren who showed that a special case, the so-called "erosion flow", can be constructed from two coupled "sticky Brownian webs". The authors' construction for general Howitt-Warren flows is based on a Poisson marking procedure developed by Newman, Ravishankar and Schertzer for the Brownian web. Alternatively, the authors show that a special subclass of the Howitt-Warren flows can be constructed as random flows of mass in a Brownian net, introduced by Sun and Swart. Using these constructions, the authors prove some new results for the Howitt-Warren flows.
Famed mathematician Alexander Grothendieck, in his Resume, set forth his plan for the study of the finer structure of Banach spaces. He used tensor products as a foundation upon which he built the classes of operators most important to the study of Banach spaces and established the importance of the "local" theory in the study of these operators and the spaces they act upon. When Lintenstrauss and Pelczynski addressed his work at the rebirth of Banach space theory, they shed his Fundamental Inequality in the trappings of operator ideals by shedding the tensorial formulation. The authors of this book, however, feel that there is much of value in Grothendieck's original formulations in the Resume and here endeavor to "expose the Resume" by presenting most of Grothendieck's arguments using the mathematical tools that were available to him at the time.
Grothendieck's Resume is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical Banach spaces ($C(K)$'s, Hilbert spaces, and the spaces of integrable functions) fit naturally within the mosaic that Grothendieck constructed.
This beautiful and important book highlights the collection of European drawings at the Yale University Art Gallery, one of America's premier university museums. From intimate studies to exquisite finished compositions, this selection of works documents the history of European drawing practices beginning with late-medieval model books and progressing to the verge of the modern period. The accompanying text--written by a team of scholars--offers a unique introduction to various critical and technical aspects of the study of master drawings, brought to life through drawings from a range of national schools and in a variety of media. Among the drawings examined in this handsomely produced volume are an animated pen and ink sketch by Giulio Romano, a pastoral landscape by Claude Lorrain, a forceful and humorous caricature by Guercino, a scene from the epic poem Orlando Furioso by Jean-Honoré Fragonard, and a delicate portrait by Edgar Degas.
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