In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications were soon extended beyond linear operators. In approximation theory, however, applications were limited to linear operators mainly by the fact that the notion of singularity of an integral operator was closely connected with its linearity. This book represents the first attempt at a comprehensive treatment of approximation theory by means of nonlinear integral operators in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed in order to obtain consistent approximation results. Applications to nonlinear summability, nonlinear integral equations and nonlinear sampling theory are given. In particular, the study of nonlinear sampling operators is important since the results permit the reconstruction of several classes of signals. In a wider context, the material of this book represents a starting point for new areas of research in nonlinear analysis. For this reason the text is written in a style accessible not only to researchers but to advanced students as well.
Establishing a factual basis on which to apply the law can be an extraordinarily challenging process, and perhaps more so in international arbitration than in any other proceedings, due to the very different notions of fact-finding that prevail among jurisdictions. This important book assesses, for the first time, the contours of an emerging transnational law of fact-finding that promises to greatly enhance the efficiency and reliability of this crucial arbitral procedure. In his analysis, focusing on bases that reflect current (but fluid) transnational practice, the author assembles a viable lex evidentiae from an in-depth examination and synthesis of the following bodies of source material: published arbitration proceedings and awards; the general framework of fact-finding issues as provided for under the arbitration acts of England and Wales, the United States, Germany, Brazil, Spain, Switzerland, Austria, and Italy, as well as under the Model Law; fact-finding stipulations under UNCITRAL Arbitration Rules as well as under various institutional rules; soft law (such as the IBA Rules, Prague Rules, ALI/UNIDROIT Principles of Transnational Civil Procedure); best practices as captured by legal commentary; and investment arbitration proceedings, where many decisions and awards are nowadays publicly available. In the course of the analysis, a comprehensive description and analysis of what fact-finding entails, including both gathering of facts and taking of evidence, is fully elaborated. Given that it is an essential task of international arbitration proceedings to define the disagreements between the parties and seek to determine the truth, the international arbitration community must be able to rely on a robust, consistent, and predictable, albeit flexible and adaptive, set of fact-finding rules. Against this background, the present study not only provides a stocktaking of current practice but also makes a signal contribution to meeting the need for legal certainty and reliability in international arbitration.
Films like Welcome to the Dollhouse and Happiness established Todd Solondz as independent cinema's premier satirist. Blending a trademark black humor into atmospheres of grueling bleakness, Solondz repeatedly takes moviegoers into a bland suburban junk space peopled by the damaged, the neglected, and the depraved.Julian Murphet appraises the career of the controversial, if increasingly ignored, indie film auteur. Through close readings and a discussion with the director, Murphet dissects how Solondz's themes and techniques serve stories laden with hot-button topics like pedophilia, rape, and family and systemic cruelty. Solondz's uncompromising return to the same motifs, stylistic choices, and characters reject any idea of aesthetic progression. Instead, he embraces an art of diminishing returns that satirizes the laws of valuation sustaining what we call cinema. It also reflects both Solondz's declining box office fortunes and the changing economics of independent film in an era of financial contraction.
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