{"title":"Lectures In Mathematics Eth Zürich","description":null,"products":[{"product_id":"numerical-methods-for-conservation-laws-book-randall-j-leveque-9783764327231","title":"Numerical Methods for Conservation Laws","description":"These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de­ veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un­ derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present­ ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. Without the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are. not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50065385292049,"sku":"CIN3764327235G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":51334568280337,"sku":"CIN3764327235VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3764327235.jpg?v=1751190510"},{"product_id":"spatial-branching-processes-random-snakes-and-partial-differential-equations-book-jean-francois-le-gall-9783764361266","title":"Spatial Branching Processes, Random Snakes and Partial Differential Equations","description":"In these lectures, we give an account of certain recent developments of the theory of spatial branching processes. These developments lead to several fas­ cinating probabilistic objects, which combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial dif­ ferential equations. Our first objective is to give a short self-contained presentation of the measure­ valued branching processes called superprocesses, which have been studied extensively in the last twelve years. We then want to specialize to the important class of superprocesses with quadratic branching mechanism and to explain how a concrete and powerful representation of these processes can be given in terms of the path-valued process called the Brownian snake. To understand this representation as well as to apply it, one needs to derive some remarkable properties of branching trees embedded in linear Brownian motion, which are of independent interest. A nice application of these developments is a simple construction of the random measure called ISE, which was proposed by Aldous as a tree-based model for random distribution of mass and seems to play an important role in asymptotics of certain models of statistical mechanics. We use the Brownian snake approach to investigate connections between super­ processes and partial differential equations. These connections are remarkable in the sense that almost every important probabilistic question corresponds to a significant analytic problem.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51062857629969,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51062860775697,"sku":"NIN9783764361266","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/B01CMUND5Y.jpg?v=1751317780"},{"product_id":"gradient-flows-book-luigi-ambrosio-9783764387211","title":"Gradient Flows","description":"The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51062934274321,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51062937092369,"sku":"NIN9783764387211","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/B01CMY8P30.jpg?v=1750731024"},{"product_id":"topics-in-combinatorial-group-theory-book-gilbert-baumslag-9783764329211","title":"Topics in Combinatorial Group Theory","description":"Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. 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These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51064077746449,"sku":"NIN9783764329211","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3764329211.jpg?v=1751065294"},{"product_id":"splinefunktionen-book-carl-de-boor-9783764325145","title":"Splinefunktionen","description":"Der Begriff der Splinefunktionen wurde von I. J. Schoenberg 1946 eingefUhrt. \"Spline\" ist der Name eines Zeichengerates, welches auf mechanischem Weg Interpolatio- aufgaben lost. Dieses Gerat besteht aus einer flexiblen, oft mehrere Meter langen Latte, die auf dem Zeichenbrett aufliegt und dort an bestimmten Stellen durch Gewichte festgehalten wird. Die Form, die die Latte annimmt, hangt von den Elastizitatseigenschaften der Latte abo -, \" , , , , , , \\ , \\ \\ I , , , ,\" -\"', , , , , J::\u0026gt;----\" , I I , I I I , , , , , , , , , , , \" ) Fig. 1: Latteninterpo1ation Po1ynominterpo1ation _ - - - - - - - --0 Wir konnen natUrlich versuchen, ein mathematisches Modell fUr dieses mechanische Zeichengerat zu machen, d. h. die Gestalt solcher Kurven mathematisch zu erfassen. - 2 - Die Theorie der Balkenbiegung verlangt, dass die mittlere 2 K quadratische KrUmmung, (\"strain energy\", Spannungs- J energie) minimiert wird. Lasst sich die Kurve als Graph einer Funktion f auf dem Intervall [a,b] schreiben, so erhalt man mit dem bekannten Ausdruck fUr die Krlimmung K [f\" (t) P --------------dt ~ min (1) t [1 +f' (t)2J5\/2 a Statt dieses schwierige Extremalproblem zu losen, begnUgt man sich damit, (2) zu minimieren. Die Extremalfunktion fUr das Funktional (2) ist stUckweise ein kubisches Polynom; die Polyn- stUcke gehen an den Bruchstellen so glatt ineinander Uber, dass die Funktion zweimal stetig differenzierbar ist.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144113123601,"sku":"NLS9783764325145","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764325145.jpg?v=1757587471"},{"product_id":"cardinal-functions-on-boolean-algebras-book-monk-9783764324957","title":"Cardinal Functions on Boolean Algebras","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52454734790929,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52454735544593,"sku":"NLS9783764324957","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764324957.jpg?v=1759372065"},{"product_id":"singularitaten-book-horst-knrrer-9783034897198","title":"Singularitäten","description":"1 Klassifikation der einfachen Hyperftachen-Singularitaten . . . . . . . . . . . . . . 2 1. 1 Abbildungskeime, Rechtsaquivalenz, Einfachheit . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 2 Endlich bestimmte FUnktionskeime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 1. 3 Klassifikation der einfachen Singularitaten in C ---- ------------. -. . . --. - 11 1. 4 Beweis des verallgemeinerten Morse-Lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1. 5 Klassifikation der einfachen Singularitaten in C . . . . . . . . . . . . . . . . . . . . . . . . 19 3 2 Die einfachen Flachensingularitaten in C als Quotientensingularitaten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. 1 Die endlichen Untergruppen von SL(2, C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. 2 Quotientensingularitaten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2 2. 3 C jG, wo G eine endliche Untergruppe von SL(2, C) ist . . . . . . . . . . . . . . . . . 27 2. 4 Die Rationalitat der Quotientensingularitaten . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 Die Auflosung der einfachen zweidimensionalen Hyperftachensingularitaten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3. 1 Das Auflosen von Kurvensingularitaten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2 3. 2 Das Auflosen von C jG, wo G eine endliche Untergruppe von SL(2, C) ist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4 Elementare lokale Eigenschaften von Singularitaten . . . . . . . . . . . . . . . . . . 49 4. 1 Der Umgebungsrand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4. 2 Gute Reprasentanten von Abbildungskeimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4. 3 Monodromie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4. 4 Die Monodromie einer quadratischen Singularitat (lokaler Fall) . . . . . . . . . . 65 5 Die U ntersuchung von Milnorfasern . . . . . . . . . . . . . . . . . -. . . -. . --. - -. . . . . . . 73 5. 1 Milnorfasem von ebenen Kurvensingularitaten . . . . . . -. . -. . . -. . -. . . . . . . . . 73 5. 2 Milnorfasem von Hyperfia. chensingularitaten . . . . . . . . . . . . . . -. . -. . . . . . . . . . 81 6 Die Beec r hnung d er M o n oro d mie . . . . . . . . . . . . . . . . . . . -. . . . . . -. . - . . . . . . . . . 87 6. 1 Die Morsifikation . . . ., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -. . . . . . . 87 6. 2 Die Monodromie der ebenen Kurvensingularitaten in Cl. . . . . . . . . . 88 6. 3 Dynkin-Dia. gramm und Monodromiegruppe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6. 4 Die Monodromie beim Addieren von FUnktionskeimen . . . . . . . . . . . . .","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52660644512017,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52660645691665,"sku":"NLS9783034897198","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783034897198.jpg?v=1762265677"}],"url":"https:\/\/www.worldofbooks.com\/en-ie\/collections\/lectures-in-mathematics-eth-zurich-book-series.oembed","provider":"World of Books ","version":"1.0","type":"link"}