@phdthesis{Trumpf2002,
  author    = {Trumpf, Jochen},
  title     = {On the geometry and parametrization of almost invariant subspaces and observer theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-5034},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2002},
  abstract  = {In my Ph.D. thesis "On the geometry and parametrization of almost invariant subspaces and observer theory" I consider the set of almost conditioned invariant subspaces of fixed dimension for a given fixed linear finite-dimensional time-invariant observable control system in state space form. Almost conditioned invariant subspaces were introduced by Willems. They generalize the concept of a conditioned invariant subspace requiring the invariance condition to hold only up to an arbitrarily small deviation in the metric of the state space. One of the goals of the theory of almost conditioned invariant subspaces was to identify the subspaces appearing as limits of sequences of conditioned invariant subspaces. An example due to {\"O}zveren, Verghese and Willsky, however, shows that the set of almost conditioned invariant subspaces is not big enough. I address this question in a joint paper with Helmke and Fuhrmann (Towards a compactification of the set of conditioned invariant subspaces, Systems and Control Letters, 48(2):101-111, 2003). Antoulas derived a description of conditioned invariant subspaces as kernels of permuted and truncated reachability matrices of controllable pairs of the appropriate size. This description was used by Helmke and Fuhrmann to construct a diffeomorphism from the set of similarity classes of certain controllable pairs onto the set of tight conditioned invariant subspaces. In my thesis I generalize this result to almost conditioned invariant subspaces describing them in terms of restricted system equivalence classes of controllable triples. Furthermore, I identify the controllable pairs appearing in the kernel representations of conditioned invariant subspaces as being induced by corestrictions of the original system to the subspace. Conditioned invariant subspaces are known to be closely related to partial observers. In fact, a tracking observer for a linear function of the state of the observed system exists if and only if the kernel of that function is conditioned invariant. In my thesis I show that the system matrices of the observers are in fact the corestrictions of the observed system to the kernels of the observed functions. They in turn are closely related to partial realizations. Exploring this connection further, I prove that the set of tracking observer parameters of fixed size, i.e. tracking observers of fixed order together with the functions they are tracking, is a smooth manifold. Furthermore, I construct a vector bundle structure for the set of conditioned invariant subspaces of fixed dimension together with their friends, i.e. the output injections making the subspaces invariant, over that manifold. Willems and Trentelman generalized the concept of a tracking observer by including derivatives of the output of the observed system in the observer equations (PID-observers). They showed that a PID-observer for a linear function of the state of the observed system exists if and only if the kernel of that function is almost conditioned invariant. In my thesis I replace PID-observers by singular systems, which has the advantage that the system matrices of the observers coincide with the matrices appearing in the kernel representations of the subspaces. In a second approach to the parametrization of conditioned invariant subspaces Hinrichsen, M{\"u}nzner and Pr{\"a}tzel-Wolters, Fuhrmann and Helmke and Ferrer, F. Puerta, X. Puerta and Zaballa derived a description of conditioned invariant subspaces in terms of images of block Toeplitz type matrices. They used this description to construct a stratification of the set of conditioned invariant subspaces of fixed dimension into smooth manifolds. These so called Brunovsky strata consist of all the subspaces with fixed restriction indices. They constructed a cell decomposition of the Brunovsky strata into so called Kronecker cells. In my thesis I show that in the tight case this cell decomposition is induced by a Bruhat decomposition of a generalized flag manifold. I identify the adherence order of the cell decomposition as being induced by the reverse Bruhat order.},
  subject      = {Invarianter Unterraum},
  language  = {en}
}
@phdthesis{Baumann2009,
  author    = {Baumann, Sabine Christine},
  title     = {Mapping, analysis, and interpretation of the glacier inventory data from Jotunheimen, South Norway, since the maximum of the 'Little Ice Age'},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-46320},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {Glacier outlines during the 'Little Ice Age' maximum in Jotunheimen were mapped by using remote sensing techniques (vertical aerial photos and satellite imagery), glacier outlines from the 1980s and 2003, a digital terrain model (DTM), geomorphological maps of individual glaciers, and field-GPS measurements. The related inventory data (surface area, minimum and maximum altitude) and several other variables (e.g. slope, range) were calculated automatically by using a geographical information system. The length of the glacier flowline was mapped manually based on the glacier outlines at the maximum of the 'Little Ice Age' and the DTM. The glacier data during the maximum of the 'Little Ice Age' were compared with the Norwegian glacier inventory of 2003. Based on the glacier inventories during the maximum of the 'Little Ice Age', the 1980s and 2003, a simple parameterization after HAEBERLI \& HOELZLE (1995) was performed to estimate unmeasured glacier variables, as e.g. surface velocity or mean net mass balance. Input data were composed of surface glacier area, minimum and maximum elevation, and glacier length. The results of the parameterization were compared with the results of previous parameterizations in the European Alps and the Southern Alps of New Zealand (HAEBERLI \& HOELZLE 1995; HOELZLE et al. 2007). A relationship between these results of the inventories and of the parameterization and climate and climate changes was made.},
  subject      = {Gletscher},
  language  = {en}
}