Download or read book Vector Fields on Manifolds Phonotape written by and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Vector Fields on Manifolds written by Michael Francis Atiyah and published by Springer. This book was released on 2013-03-09 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle).

Download or read book CANCERGRAM written by and published by . This book was released on 1987 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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Download or read book Flying the Weather Map written by and published by . This book was released on 1945 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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Download or read book Educational Surveys written by Georgia. Department of Education and published by . This book was released on 1915 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Trouble with Genius written by Bob Perelman and published by Univ of California Press. This book was released on 1994-11-02 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Most poets define poetry by creating it. Bob Perelman creates it by defining it, and is thus one step ahead of all the other poets under the sun, one step closer to colliding with Zeno's vanishing point, to merging coyote with road runner, to winning the hand."—John Ashbery "Profound, subtle, and wonderfully written—this is a book from which anyone interested in the twentieth century can learn."—Marjorie Perloff

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Download or read book Hans Christian Andersen written by Jackie Wullschlager and published by University of Chicago Press. This book was released on 2002-06-15 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beloved by generations of children and adults around the world for tales such as "The Ugly Duckling" and "The Emperor's New Clothes," Hans Christian Andersen (1805-1875) revolutionized children's literature. Although others before him had collected and retold folk stories and fairy tales, Andersen was the first to create the stories himself, instilling a previously stilted genre with new humor, wisdom, and pathos. Drawing on letters, diaries, and other original sources (many never before translated from the Danish), Wullschlager shows in this compelling, extensively researched biography how Andersen's writings—darker and more diverse than previously recognized—reflected the complexities of his life, a far cry from the "happily ever after" of a fairy tale. As we follow in his footsteps from Golden Age Copenhagen to the princely courts of Germany and the villas of southern Italy, Andersen becomes a figure every bit as fascinating as a character from one of his stories—a gawky, self-pitying, and desperate man, but also one of the most gifted storytellers the world has ever known.

Download or read book Sister Noon written by Karen Joy Fowler and published by Penguin. This book was released on 2002-05-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Loosely based in historical fact, Sister Noon is a wryly funny, playfully mysterious, and totally subversive novel from the New York Times bestselling author of The Jane Austen Book Club. Lizzie Hayes, a member of the San Francisco elite, is a seemingly docile, middle-aged spinster praised for her volunteer work with the Ladies Relief and Protection Society Home, or "The Brown Ark". All she needs is the spark that will liberate her from the ruling conventions. When the wealthy and well-connected, but ill-reputed Mary Ellen Pleasant shows up at the Brown Ark, Lizzie is drawn to her. It is the beautiful, but mysterious Mary Ellen, an outcast among the women of the elite because of her notorious past and her involvement in voodoo, who will eventually hold the key to unlocking Lizzie's rebellious nature.

Download or read book Radioisotopes in Biology written by Robert J. Slater and published by Practical Approach Series. This book was released on 2002 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to the use of radioactivity in the bioscience laboratory. The text covers general aspects of radioactivity, methods for the detection of radioactivity, radioisotope protocols used to study key cellular processes, and a summary of legislative requirements in the US and European Union. Guidance on safe handling and detailed recipes are provided.