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Isaac N. Arnold
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Introduction to Arnold’s Proof of the Kolmogorov–Arnold–Moser Theorem
INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREM This book provides an accessible step-by-step account of Arnold’s classical proof of the Kolmogorov–Arnold–Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville–Arnold theorem for integrable systems and introduces Kneser’s tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold’s proof, before the second half of the book walks the reader through a detailed account of Arnold’s proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to resear...
The History of Mental Illness in Criminal Cases: The English Tradition
Whether the accused is competent to stand trial, whether the plaintiff is competent to accuse, or whether a witness is competent to testify has had a long legal history. Such questions draw legal reasoning into areas of ethical reflection and scientific debate deeply rooted in the moral history of the United States. Mental competence has come to play a central and controversial role in proving guilt, and in evaluating the severity of a crime and its corresponding punishment. This compendium brings together the major legal precedents and legal commentaries that have defined the role of mental illness in criminal trials throughout U.S. history. The reprint collection considers, among other issues, the evolution of the Supreme Court's position on the insanity defense and mental retardation, how these affect one's competency to stand trial or be executed, and how these affect culpability and punishment. Each volume begins with an introductory essay, and includes both cases and commentary. Scholars as well as students will find these volumes a useful research tool.
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