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Die gezielte Einstellung von Randzoneneigenschaften (unter anderem Eigenspannungszustand) beim Unrundschleifen stellt eine Herausforderung dar. In der vorliegenden Arbeit wird die kombinierte Anwendung eines auf dem mikromagnetischen Barkhausenrauschen basierenden Messsystems und einer thermischen Prozessgrenze zur Detektion lokaler Randzonen-beeinflussungen beim Unrundschleifen untersucht. Das Bark-hausenrauschsignal wird unter Berücksichtigung der variieren-den Bauteilkrümmung ausgewertet.

This thesis is concerned with the computation of dimension formulas for special orthogonal modular forms associated with the II_2,10-lattice. For a given arithmetic group, the dimension of the spaces of these orthogonal modular forms is a polynomial of degree 10 in the weight. By using the Hirzebruch-Riemann-Roch theorem and Hirzebruch-Mumford proportionality, this polynomial can be determined up to a geometric error term; this error term is a linear polynomial whose coefficients are given by intersection products of toroidal boundary divisors and certain logarithmic Chern classes. We describe this error term in more detail and determine important components. For this purpose, we construct a special toroidal compactification of the orthogonal moduli variety associated to the II_2,10(N)-lattice and study its geometry. We also describe an essential part of the intersection theory of this compactification, thus reducing the computation of the linear coefficient of the error term to a combinatorial problem. Finally, we give methods to reduce the computation of the constant coefficient of the error term to combinatorial problems; in particular, we can formulate a formulation of the error term without logarithmic Chern classes.