Universität Stuttgart
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Item Open Access Fibrations of spheres by great spheres over division algebras and their differentiability(1990) Grundhöfer, Theo; Hähl, HermannThe authors answer the natural question: When is the fibration of S {2n-1} by great (n-1)-spheres determined by a division algebra differentiable? They show that this happens only for the classical Hopf fibrations, which are determined by the classical division algebras R, C, H and O.Item Open Access Item Open Access General interface problems. 1(1994) Nicaise, Serge; Sändig, Anna-MargareteWe study transmission problems for elliptic operators of order 2m with general boundary and interface conditions, introducing new covering conditions. This allows to prove solvability, regularity and asymptotics of solutions in weighted Sobolev spaces. We give some numerical examples for the location of the singular exponents.Item Open Access A new estimate for the Ginzburg-Landau approximation on the real axis(1994) Schneider, GuidoModulation equations play an essential role in the understanding of complicated systems near the threshold of instability. For scalar parabolic equations for which instability occurs at nonzero wavelength, we show that the associated Ginzburg-Landau equation dominates the dynamics of the nonlinear problem locally, at least over a long timescale. We develop a method which is simpler than previous ones and allows initial conditions of lower regularity. It involves a careful handling of the critical modes in the Fourier-transformed problem and an estimate of Gronwall's type. As an example, we treat the Kuramoto-Shivashinsky equation. Moreover, the method enables us to handle vector-valued problems.Item Open Access Topologische Ovale(1981) Buchanan, Thomas; Hähl, Hermann; Löwen, RainerDer Ausgangspunkt für die hier dargestellten Untersuchungen war die Frage, ob es lokalkompakte topologische Laguerreebenen gibt, in denen die topologische Dimension des Punktraums größer ist als vier. Im Zusammenhang damit galt es zu klären, ob es in kompakten topologischen projektiven Ebenen einer Dimension größer als vier Ovale geben kann, die in topologischer Hinsicht gutartig sind. In dieser Arbeit werden wir beide Fragen verneinend entscheiden (wobei wir allerdings die betrachteten Ebenen als endlichdimensional voraussetzen); dabei genügt als topologische Voraussetzung an die Ovale ihre Abgeschlossenheit im Punktraum.Item Open Access Kriterien für lokalkompakte topologische Quasikörper(1982) Hähl, HermannAnliegen dieser Note ist die Aufstellung von notwendigen und hinreichenden Kriterien, die es erlauben, mit möglichst geringem Aufwand zu verifizieren, daß eine vorgelegte topologisch-algebraische Struktur ein lokalkompakter topologischer Quasikörper ist.Item Open Access Ovale und Kegelschnitte in der komplexen projektiven Ebene(1979) Buchanan, ThomasDie Kegelschnitte der komplexen projektiven Ebene werden in dieser Arbeit durch ihre geometrischen und toplogischen Eigenschaften charakterisiert - genauer, durch die Ovaleigenschaft und die topologische Abgeschlossenheit.Item Open Access Embedding a non-embeddable stable plane(1993) Stroppel, MarkusIn [4], K. Strambach describes a 2-dimensional stable plane R admitting Σ=SL2 R as a group of automorphisms such that there exists no Σ-equivarient embedding into a 2-dimensional projective plane. R. Löwen [3] has given a 4-dimensional analogue C, admitting Δ=SL2Copf. He posed the question whether there are embeddings of Strambach's plane R into C. We show that such embeddings exist, in fact we determine all -Σ-equivariant embeddings of 2-dimensional stable planes admitting Σ as atransitive group of automorphisms.Item Open Access Endomorphisms of stable planes(1992) Stroppel, MarkusEndomorphisms of stable planes are introduced, and it is shown that these are injective, locally constant or collapsed. Examples are studied, and it is shown that there are stable planes admitting "substantially more" endomorphisms than automorphisms.Item Open Access Photogrammetry and projective geometry : an historical survey(1993) Buchanan, ThomasGeneral Jean-Victor Poncelet published his treatise on projective geometry in 1822. This was the start of an enormous development in geometry in the 19th century. During this period geometry in the plane and in 3-dimensional space was studied in particular detail. The development culminated in the publishing of the Encyclopedia of Mathematics, which appeared in irregular installments from 1900 to 1934. Photogrammetry - the use of photographic images for surveying, mapping and reconnaissance - began in the second half of the 19th century. By the 1890's substantial theoretical contributions were made by Sebastian Finsterwalder. Finsterwalder reported on his foundational work in a keynote address to the German Mathematical Society in 1897; he also contributed an article on photogrammetry to the Encyclopedia of Mathematics. Among other things Finsterwalder observed that Rudolf Sturm's analysis of the "homography problem" (1869) can be used to solve the problem of 3D-reconstruction using point matches in two images. Subsequently, important theoretical advances were made by mathematicians at the Technical University of Vienna. An excellent reference for geometry and its relationship to photogrammetry is a book of Emil Muller on constructive geometry, which appeared in 1923. Muller's assistent and successor Erwin Kruppa established the "structure-from-motion" theorem in 1913. This theorem was rediscovered by Shimon Ullman in 1977.