This study of the Isaianic Denkschrift (Isaiah 6:1-9:6) is both a traditional and an innovative one. It defends the integrity of the Denkschrift, yet on grounds wholly other than those outlined by the early proponents of the unity of the composition. The present work is founded on an inquiry into the ideological matrix of the composition on one hand and, on the other, on the understanding of the activity of mantic (prophetic) figures in the Near East during the early first millennium BCE that has emerged in recent scholarship. The presentation of Yahweh as a royal character in the Denkschrift is interpreted as an integral part of the symbolic universe promoted by the composition. Several levels of social discourse of the Denkschrift are identified: the author(s) is simultaneously engaged in the creation of Judaean autonomous cultural identity, in polemical activity with the rival Yahwist community (the North, or Samaria) and in the safeguarding of the privileged position of the former Babylonian exiles among the community of Jerusalem and Judah. Two interrelated hypotheses are developed in the book: regarding the historical milieu in which the Denkschrift was composed and regarding the place of the composition in the formation of First Isaiah. As for the first, Prokhorov proposes that the early second-temple community of Yehud matches the profile of a society whose problems the Denkschrift is addressing and reflecting. As for the second, the author maintains the view that the Denkschrift marks one of the final stages of the creation of First Isaiah whose original nucleus consisted of the Hezekiah narrative (now found in chapters 36-39 of Isaiah), which, in turn, modified the respective Deuteronomistic material.
The story of Don Juan first appeared in writing in seventeenth-century Spain, reaching Russia about a century later. Its real impact, however, was delayed until Russia’s most famous poet, Alexander Pushkin, put his own, unique, and uniquely inspirational, spin on the tale. Published in 1830, TheStone Guest is now recognized, with other Pushkin masterpieces, as part of the Russian literary canon. Alexander Burry traces the influence of Pushkin’s brilliant innovations to the legend, which he shows have proven repeatedly fruitful through successive ages of Russian literature, from the Realist to the Silver Age, Soviet, and contemporary periods. Burry shows that, rather than creating a simple retelling of an originally religious tale about a sinful, consummate seducer, Pushkin offered open-ended scenes, re-envisioned and complicated characters, and new motifs that became recursive and productive parts of Russian literature, in ways that even Pushkin himself could never have predicted.
Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.
This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise. Although the material in this book is often described by refined mathematical theories, we have tried to avoid a formal mathematical style. Instead of rigorous proofs, the reader will usually be offered only "demonstrations" (the term used by Prof. V. I. Arnold) to encourage intuitive understanding of a problem and to explain why a particular statement seems plausible. We also refrained from detailing concrete applications in physics or in other scientific fields, so that the book can be used by students of different disciplines. While preparing the lecture course and producing this book, we had intensive discussions with and asked the advice of Prof. V. I. Arnold, Prof. S. Grossmann, Prof. H. Haken, Prof. Yu. L. Klimontovich, Prof. R. L. Stratonovich and Prof. Ya.
Strange Functions in Real Analysis, Third Edition differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In doing so, the book explores a number of important examples and constructions of pathological functions. After introducing basic concepts, the author begins with Cantor and Peano-type functions, then moves effortlessly to functions whose constructions require what is essentially non-effective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, the author considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms. On the whole, the book is devoted to strange functions (and point sets) in real analysis and their applications.
Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary b
New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.
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