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- ItemSimple vector bundles on plane degenerations of an elliptic curve(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Bodnarchuk, Lesya; Drozd, Yuriy; Greuel, Gert-MartinIn 1957 Atiyah classifed simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classifcation by describing the simple vector bundles on all reduced plane cubic curves. Our main result states that a simple vector bundle on such a curve is completely determined by its rank, multidegree and determinant. Our approach, based on the representation theory of boxes, also yields an explicit description of the corresponding universal families of simple vector bundles.
- ItemHeuristic parameter selection based on functional minimization : optimality and model function approach(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Lu, Shuai; Mathé, KarstenWe analyze some parameter choice strategies in regularization of inverse problems, in particular the (modified) L-curve method and a variant of the Hanke-Raus rule. These are heuristic rules, free of the noise level, and they are based on minimization of some functional. We analyze these functionals, and we prove some optimality results under general smoothness conditions. We also devise some numerical approach for finding the minimizers, which uses model functions. Numerical experiments indicate that this is an efficient numerical procedure.
- ItemHomological properties of piecewise hereditary algebras(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Happel, Dieter; Zacharia, DanLet Delta be a finite dimensional algebra over an algebraically closed field k. We will investigate homological properties of piecewise hereditary algebras Delta. In particular we give lower and upper bounds of the strong global dimension, show the behavior of the strong global under one point extensions and tilting. Moreover we show that the pieces of mod Delta have Auslander-Reiten sequence.
- ItemGeneSys Horstberg II - Methoden und Konzepte zur Erderwärmung aus gering permeablen Sedimentgesteinen : Abschlussbericht(Hannover : Technische Informationsbibliothek (TIB), 2009) Schellschmidt, Rüdiger[no abstract available]
- ItemAnnual report 2008 // Institute of Radiochemistry(Dresden : Forschungszentrum Dresden-Rossendorf, 2009) Bernhard, Gert[no abstract available]
- ItemMinimal Riesz energy on the sphere for axis-supported external fields(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Brauchart, J.S.; Dragnev, P.D.; Saff, E.B.We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere Sd in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials |x−y|−s with d−2 s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on Sd is determined. The special case s = d − 2 yields interesting phenomena, which we investigate in detail. A weak∗ asymptotic analysis is provided as s ! (d − 2)+.
- ItemRationales Design poröser Katalysatorfilme im Nanometerbereich - DEPOKAT : Schlussbericht ; Berichtszeitraum: 01.06.2007 - 30.04.2009(Hannover : Technische Informationsbibliothek (TIB), 2009) Krähnert, Ralph[no abstract available]
- ItemA priori error analysis for state constrained boundary control problems : Part I: Control discretization(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Krumbiegel, Klaus; Meyer, Christian; Rösch, ArndThis is the first of two papers concerned with a state-constrained optimal control problems with boundary control, where the state constraints are only imposed in an interior subdomain. We apply the virtual control concept introduced in [20] to regularize the problem. The arising regularized optimal control problem is discretized by finite elements and linear and continuous ansatz functions for the boundary control. In the first part of the work, we investigate the errors induced by the regularization and the discretization of the boundary control. The second part deals with the error arising from discretization of the PDE. Since the state constraints only appear in an inner subdomain, the obtained order of convergence exceeds the known results in the field of a priori analysis for state-constrained problems
- ItemMachbarkeitsstudie für ein industrieorientiertes, innovatives Applikationslabor zum Transfer von Röntgentechnologien höchster räumlicher und zeitlicher Auflösung(Hannover : Technische Informationsbibliothek (TIB), 2009) MBI[no abstract available]
- ItemCollision in a cross-shaped domain(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Linke, AlexanderIn the numerical simulation of the incompressible Navier-Stokes equations different numerical instabilities can occur. While instability in the discrete velocity due to dominant convection and instability in the discrete pressure due to a vanishing discrete LBB constant are well-known, instability in the discrete velocity due to a poor mass conservation at high Reynolds numbers sometimes seems to be underestimated. At least, when using conforming Galerkin mixed finite element methods like the Taylor-Hood element, the classical grad-div stabilization for enhancing discrete mass conservation is often neglected in practical computations. Though simple academic flow problems showing the importance of mass conservation are well-known, these examples differ from practically relevant ones, since specially designed force vectors are prescribed. Therefore we present a simple steady Navier-Stokes problem in two space dimensions at Reynolds number 1024, a colliding flow in a cross-shaped domain, where the instability of poor mass conservation is studied in detail and where no force vector is prescribed.