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The Yang-Mills heat equation with finite action in three dimensions
The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over
eBook
Personal Liberty and Public Good
Blame for the putative failure of liberalism in late-nineteenth-century Japan and China has often been placed on an insufficient grasp of modernity among East Asian leaders or on their cultural commitments to traditional values. InPersonal Liberty and Public Good, Douglas Howland refutes this view, turning to the central text of liberalism in that era: John Stuart Mill?sOn Liberty.
Howland offers absorbing analyses of the translations of the book into Japanese and Chinese, which at times reveal astonishing emendations. As with their political leaders, Mill?s Japanese and Chinese translators feared individual liberty could undermine the public good and standards for public behaviour, and so introduced their own moral values ? Christianity and Confucianism, respectively? intoOn Liberty, filtering its original meaning. Howland mirrors this mistrust of individual liberty in Asia with critiques of the work in England, which itself had trouble adopting liberalism.
Personal Liberty and Public Goodis a compelling addition to the corpus of writing on the work of John Stuart Mill. It will be of great interest to historians of political thought, liberalism, and translation, as well as scholars of East Asian studies.
eBook
Mill and paternalism
\"Many discussions of J. S. Mill's concept of liberty focus too narrowly on On Liberty and fail to acknowledge that his treatment of related issues elsewhere may modify its leading doctrines. Mill and Paternalism demonstrates how a contextual reading suggests that in Principles of Political Economy, and also his writings on Ireland, India and on domestic issues like land reform, Mill proposed a substantially more interventionist account of the state than On Liberty seems to imply. This helps to explain Mill's sympathies for socialism after 1848, as well as his Malthusianism and feminism, which, in conjunction with Harriet Taylor's views, are central to his later discussions of the family and marriage. Feminism, indeed, is shown to provide the answer to the problem which most agitated Mill, overpopulation. Thus Gregory Claeys sheds new lights on many of Mill's overarching preoccupations, including the theory of liberty at the heart of On Liberty\"-- Provided by publisher.
Book
Global regularity for the Yang–Mills equations on high dimensional Minkowski space
This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on (6 1) and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space H˙(n−4)/2A. Regularity is obtained through a certain \"\"microlocal geometric renormalization\"\" of the equations which is implemented via a family of approximate null Crönstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic Lp spaces, and also proving some bilinear estimates in specially constructed square-function spaces.
eBook
John Stuart Mill
Nicholas Capaldi's 2004 biography of John Stuart Mill traces the ways in which Mill's many endeavours are related and explores the significance of Mill's contribution to metaphysics, epistemology, ethics, social and political philosophy, the philosophy of religion, and the philosophy of education. He shows how Mill was groomed for his life by both his father James Mill, and Jeremy Bentham, the two most prominent philosophical radicals of the early nineteenth century. Yet Mill revolted against this education and developed friendships with both Thomas Carlyle and Samuel Taylor Coleridge, who introduced him to Romanticism and political conservatism. A special feature of this biography is the attention devoted to his relationship with Harriet Taylor. No one exerted a greater influence than the woman he was eventually to marry. Nicholas Capaldi reveals just how deep her impact was on Mill's thinking about the emancipation of women.
eBook
John Stuart Mill : a very short introduction
\"John Stuart Mill (1806-73) is widely regarded as the leading liberal philosopher, economist, and political theorist of nineteenth century Britain. In his lifetime he was best known for his System of Logic (1843) and the Principles of Political Economy (1848). Today Mill is chiefly identified with On Liberty (1859), perhaps the definitive text of modern liberal statement of its subject, and probably the single most important work of modern political thought. Mill was also the first major male feminist thinker of the period (author of The Subjection of Women, 1869), and the first, as an MP, to introduce a bill for female enfranchisement before Parliament. This Very Short Introduction offers a brief survey of the life and key ideas of this most influential Victorian British writer. Moving chronologically, Gregory Claeys outlines the philosophical background out of which Mill developed, chiefly through the ideas of Jeremy Bentham and James Mill. He demonstrates how Mill's personal life, especially his 'mental crisis' of 1827, and his relationship with Harriet Taylor, were integral to his intellectual development. Throughout Claeys considers Mill's key works set within the context of his lesser writings and correspondence, and discusses the more controversial aspects of his thought concerning religion, secularism, and birth control.\"
Book
Yang-Mills connections on orientable and nonorientable surfaces
In \"\"The Yang-Mills equations over Riemann surfaces\"\", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In \"\"Yang-Mills Connections on Nonorientable Surfaces\"\", the authors study Yang-Mills functional on the space of connections on a principal $G_{\\mathbb{R}}$-bundle over a closed, connected, nonorientable surface, where $G {\\mathbb{R}}$ is any compact connected Lie group. In this monograph, the authors generalize the discussion in \"\"The Yang-Mills equations over Riemann surfaces\"\" and \"\"Yang-Mills Connections on Nonorientable Surfaces\"\". They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.
eBook