These are the lecture notes of the seminar "Mathematische Theorie der finiten Element- und Randelementmethoden" organized by the "Deutsche Mathematiker-Vereinigung" and held in Dusseldorf from 07. - 14. of June 1987. Finite element methods and the closely related boundary element methods nowadays belong to the standard routines for the computation of solutions to boundary and initial boundary value problems of partial differential equations with many applications as e.g. in elasticity and thermoelasticity, fluid mechanics, acoustics, electromagnetics, scatter- ing and diffusion. These methods...
These are the lecture notes of the seminar "Mathematische Theorie der finiten Element- und Randelementmethoden" organized by the "Deutsche Mathematike...
These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.
These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin...
The mathematical study of the Bose gas goes back to the ?rst quarter of the twentieth century, with the invention of quantum mechanics. The name refers to the Indian physicist S.N. Bose who realized in 1924 that the statistics governing photons(essentiallyinventedbyMaxPlanckin1900)isdetermined(usingmodern terminology) by restricting the physical Hilbert space to be the symmetric tensor product of single photon states. Shortly afterwards, Einstein applied this idea to massive particles, such as a gas of atoms, and discovered the phenomenon that we now call Bose-Einstein condensation. At that...
The mathematical study of the Bose gas goes back to the ?rst quarter of the twentieth century, with the invention of quantum mechanics. The name refer...
Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key...
Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides d...
This book is based on the lectures given at the Oberwolfach Seminar on Tropical Algebraic Geometry in October 2004. Tropical Geometry ?rst appeared as a subject of its own in 2002, while its roots can be traced back at least to Bergman s work 1] on logarithmic limit sets. Tropical Geometry is now a rapidly developing area of mathematics. It is int- twined with algebraic and symplectic geometry, geometric combinatorics, in- grablesystems, and statistical physics. Tropical Geometry can be viewed as a sort of algebraic geometry with the underlying algebra based on the so-called tropical...
This book is based on the lectures given at the Oberwolfach Seminar on Tropical Algebraic Geometry in October 2004. Tropical Geometry ?rst appeared as...
The following notes grew out oflectures held during the DMV-Seminar on Random Media in November 1999 at the Mathematics Research Institute of Oberwolfach, and in February-March 2000 at the Ecole Normale Superieure in Paris. In both places the atmosphere was very friendly and stimulating. The positive response of the audience was encouragement enough to write up these notes. I hope they will carryover the enjoyment of the live lectures. I whole heartedly wish to thank Profs. Matthias Kreck and Jean-Franc;ois Le Gall who were respon sible for these two very enjoyable visits, Laurent Miclo for...
The following notes grew out oflectures held during the DMV-Seminar on Random Media in November 1999 at the Mathematics Research Institute of Oberwolf...
Dieses Buchlein ist aus den vier doppelstOndigen Vorlesungen her vorgegangen, die die Autoren anlaBlich des DMV-Seminars gleichen Titels auf der Jahrestagung der DMV 1979 in Hamburg gehalten haben. Sein Text enthalt zwar wesentlich mehr Details als die Vorlesungen. Dennoch war es nicht unsere Absicht, ein "luckenloses" Textbuch zu schreiben. Viel mehr haben wir lediglich versucht, dem Leser ein moglichst ubersicht liches Bild neuerer Ergebnisse und Methoden in der Theorie der Konvexitat in der komplexen Analysis zu geben. Wir wollten damit zum einen dem Inter esse desjenigen Nichtspezialisten...
Dieses Buchlein ist aus den vier doppelstOndigen Vorlesungen her vorgegangen, die die Autoren anlaBlich des DMV-Seminars gleichen Titels auf der Jahre...
Vom 1. bis 8. Oktober 1989 fand im Kloster Neresheim das DMV-Seminar "Stochastische Geometrie" statt. Das Ziel dieser Veranstaltung war es, die Stochastische Geometrie, die sich in den letzten Jahren lebhaft entwickelt hat und die auch fur Anwendungen in der Bildverarbeitung, der Stereologie und der Statistik von raumlichen Daten eine grundlegende Bedeutung bekommen hat, einem breiteren Kreis von Mathematikern nahe zu bringen. Dabei sollte auch das Zusammenwirken geometrischer Ideen und stochastischer Modelle exemplarisch aufgezeigt werden. Die Vortrage uber Integralgeometrie (R. Schneider),...
Vom 1. bis 8. Oktober 1989 fand im Kloster Neresheim das DMV-Seminar "Stochastische Geometrie" statt. Das Ziel dieser Veranstaltung war es, die Stocha...
This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers.
In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities,...
This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology...
