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Titlebook: A Theory of Branched Minimal Surfaces; Anthony Tromba Book 2012 Springer-Verlag Berlin Heidelberg 2012 30B10, 49J50, 49Q05, 53A10, 58E12,

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期刊全稱A Theory of Branched Minimal Surfaces
影響因子2023Anthony Tromba
視頻videohttp://file.papertrans.cn/143/142439/142439.mp4
發(fā)行地址Presents an elementary proof of a very fundamental and beautiful mathematical result.First complete presentation of this results in the mathematical literature.It can be read by almost anyone with a b
學科分類Springer Monographs in Mathematics
圖書封面Titlebook: A Theory of Branched Minimal Surfaces; Anthony Tromba Book 2012 Springer-Verlag Berlin Heidelberg 2012 30B10, 49J50, 49Q05, 53A10, 58E12,
影響因子.One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. .The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet‘s energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet‘s energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated.?.The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education..
Pindex Book 2012
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Very Special Case; The Theorem for ,+1 Even and ,+1 Odd,nterstützen, indem im Buch zun?chst die Inhalte des CRM m?glichst vollst?ndig definiert werden und anschlie?end aufgezeigt wird, wie diese Inhalte von der Theorieschulung über die notwendigen Seminare in das Cockpit übertragen werden k?nnen.978-3-642-15167-5
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,New Brief Proofs of the Gulliver–Osserman–Royden Theorem, aspects of the OR environment?– such as ventilation, door openings, acoustics, and humidity?– are used to illustrate the interactions between work environment and performance. Finally, a number of methods are described that can be deployed to explore these effects.
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