Das Thema der Arbeit ist experimentelle Bestimmung der Ausbeute durch Photoaktivierung von Mo-92 mittels Bremsstrahlung des supraleitenden Elektronenlinearbeschleuniger ELBE im Forschungszentrum Dresden-Rossendorf. Mo-92 ist der p-Kern mit der größten Isotopenhäufigkeit und wird in astrophysikalischen Netzwerkrechnungen deutlich unterproduziert. Untersucht wurde dabei insbesondere der (gamma,p)- und (gamma,n)-Kanal, wobei für letzteren wegen der Halbwertszeit des Endkerns (Isomer) von 65 s eine Rohrpost verwendet wurde. Die Aktivierung erfolgte an zwei verschiedenen Bestrahlungsplätzen. Am Kernphysikmessplatz konnte die Photonenfluenz absolut mittels Kernresonanzfluoreszenz an B-11 bestimmt werden. Im Elektronenstrahlfänger wurde die Photodesintegrationsreaktion Au-197(gamma,n) zur Normierung verwendet. Die Endpunktsenergie wurde über den Deuteronenaufbruch durch Messung der Protonenspektren mit Si-Detektoren bestimmt. Die Ergebnisse wurden mit der integralen Ausbeute mit Hauser-Feshbach-Modellrechnungen verglichen. Parasitär konnte auch die Ausbeute der Aktivierung des in natürlichem Mo enthaltenen Isotops Mo-100 untersucht und mit früheren Photoneutronenexperimenten verglichen werden.

We consider the problem of numerical integration, where one aims to approximate an integral of a given continuous function from the function values at given sampling points, also known as quadrature points. A useful framework for such an approximation process is provided by the theory of reproducing kernel Hilbert spaces and the concept of the worst case quadrature error. However, the computation of optimal quadrature points, which minimize the worst case quadrature error, is in general a challenging task and requires efficient algorithms, in particular for large numbers of points. The focus of this thesis is on the efficient computation of optimal quadrature points on the torus T^d, the sphere S^d, and the rotation group SO(3). For that reason we present a general framework for the minimization of the worst case quadrature error on Riemannian manifolds, in order to construct numerically such quadrature points. Therefore, we consider, for N quadrature points on a manifold M, the worst case quadrature error as a function defined on the product manifold M^N. For the optimization on such high dimensional manifolds we make use of the method of steepest descent, the Newton method, and the conjugate gradient method, where we propose two efficient evaluation approaches for the worst case quadrature error and its derivatives. The first evaluation approach follows ideas from computational physics, where we interpret the quadrature error as a pairwise potential energy. These ideas allow us to reduce for certain instances the complexity of the evaluations from O(M^2) to O(M log(M)). For the second evaluation approach we express the worst case quadrature error in Fourier domain. This enables us to utilize the nonequispaced fast Fourier transforms for the torus T^d, the sphere S^2, and the rotation group SO(3), which reduce the computational complexity of the worst case quadrature error for polynomial spaces with degree N from O(N^k M) to O(N^k log^2(N) + M), where k is the dimension of the corresponding manifold. For the usual choice N^k ~ M we achieve the complexity O(M log^2(M)) instead of O(M^2). In conjunction with the proposed conjugate gradient method on Riemannian manifolds we arrive at a particular efficient optimization approach for the computation of optimal quadrature points on the torus T^d, the sphere S^d, and the rotation group SO(3). Finally, with the proposed optimization methods we are able to provide new lists with quadrature formulas for high polynomial degrees N on the sphere S^2, and the rotation group SO(3). Further applications of the proposed optimization framework are found due to the interesting connections between worst case quadrature errors, discrepancies and potential energies. Especially, discrepancies provide us with an intuitive notion for describing the uniformity of point distributions and are of particular importance for high dimensional integration in quasi-Monte Carlo methods. A generalized form of uniform point distributions arises in applications of image processing and computer graphics, where one is concerned with the problem of distributing points in an optimal way accordingly to a prescribed density function. We will show that such problems can be naturally described by the notion of discrepancy, and thus fit perfectly into the proposed framework. A typical application is halftoning of images, where nonuniform distributions of black dots create the illusion of gray toned images. We will see that the proposed optimization methods compete with state-of-the-art halftoning methods.

We consider the problem of numerical integration, where one aims to approximate an integral of a given continuous function from the function values at given sampling points, also known as quadrature points. A useful framework for such an approximation process is provided by the theory of reproducing kernel Hilbert spaces and the concept of the worst case quadrature error. However, the computation of optimal quadrature points, which minimize the worst case quadrature error, is in general a challenging task and requires efficient algorithms, in particular for large numbers of points. The focus of this thesis is on the efficient computation of optimal quadrature points on the torus T^d, the sphere S^d, and the rotation group SO(3). For that reason we present a general framework for the minimization of the worst case quadrature error on Riemannian manifolds, in order to construct numerically such quadrature points. Therefore, we consider, for N quadrature points on a manifold M, the worst case quadrature error as a function defined on the product manifold M^N. For the optimization on such high dimensional manifolds we make use of the method of steepest descent, the Newton method, and the conjugate gradient method, where we propose two efficient evaluation approaches for the worst case quadrature error and its derivatives. The first evaluation approach follows ideas from computational physics, where we interpret the quadrature error as a pairwise potential energy. These ideas allow us to reduce for certain instances the complexity of the evaluations from O(M^2) to O(M log(M)). For the second evaluation approach we express the worst case quadrature error in Fourier domain. This enables us to utilize the nonequispaced fast Fourier transforms for the torus T^d, the sphere S^2, and the rotation group SO(3), which reduce the computational complexity of the worst case quadrature error for polynomial spaces with degree N from O(N^k M) to O(N^k log^2(N) + M), where k is the dimension of the corresponding manifold. For the usual choice N^k ~ M we achieve the complexity O(M log^2(M)) instead of O(M^2). In conjunction with the proposed conjugate gradient method on Riemannian manifolds we arrive at a particular efficient optimization approach for the computation of optimal quadrature points on the torus T^d, the sphere S^d, and the rotation group SO(3). Finally, with the proposed optimization methods we are able to provide new lists with quadrature formulas for high polynomial degrees N on the sphere S^2, and the rotation group SO(3). Further applications of the proposed optimization framework are found due to the interesting connections between worst case quadrature errors, discrepancies and potential energies. Especially, discrepancies provide us with an intuitive notion for describing the uniformity of point distributions and are of particular importance for high dimensional integration in quasi-Monte Carlo methods. A generalized form of uniform point distributions arises in applications of image processing and computer graphics, where one is concerned with the problem of distributing points in an optimal way accordingly to a prescribed density function. We will show that such problems can be naturally described by the notion of discrepancy, and thus fit perfectly into the proposed framework. A typical application is halftoning of images, where nonuniform distributions of black dots create the illusion of gray toned images. We will see that the proposed optimization methods compete with state-of-the-art halftoning methods.

Indiana University-Purdue University Indianapolis (IUPUI) / Steven Millhauser has been recognized for his abilities as both a novelist and a writer of short fiction. Yet, he has evaded definitive categorization because his fiction does not fit into any one category. Millhauser’s fiction has defied clean categorization specifically because of his regular oscillation between the modes of realism and fantasy. Much of Millhauser’s short fiction contains images of labyrinths: wandering narratives that appear to split off or come to a dead end, massive structures of branching, winding paths and complex mysteries that are as deep and impenetrable as the labyrinth itself. This project aims to specifically explore the presence of labyrinthine elements throughout Steven Millhauser’s short fiction. Millhauser’s labyrinths are either described spatially and/or suggested in his narrative form; they are, in other words, spatial and/or discursive. Millhauser’s spatial labyrinths (which I refer to as ‘architecture’ stories) involve the lengthy description of some immense or underground structure. The structures are fantastic in their size and often seem infinite in scale. These labyrinths are quite literal. Millhauser’s discursive labyrinths demonstrate the labyrinthine primarily through a forking, branching and repetitive narrative form. Millhauser’s use of the labyrinth is at once the same and different than preceding generations of short fiction. Postmodern short fiction in the 1960’s and 70’s used labyrinthine elements to draw the reader’s attention to the story’s textuality. Millhauser, too, writes in the experimental/fantastic mode, but to different ends. The devices of metafiction and realism are employed in his short fiction as agents of investigating and expressing two competing visions of reality. Using the ‘tricks’ and techniques of postmodern metafiction in tandem with realistic detail, Steven Millhauser’s labyrinthine fiction adjusts and reapplies the experimental short story to new ends: real-world applications and thematic expression.