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Veröffentlichungen am Institut für Mathematik seit 1990

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Winkler, Henrik; Woracek, Harald
Reparametrizations of non trace-normed Hamiltonians. - In: Spectral theory, mathematical system theory, evolution equations, differential and difference equations. - Basel : Birkhäuser, (2012), S. 667-690

Golembewski, René; Schäfer, Günter; Gerlach, Tobias
Efficient communication for large-scale robust image processing with smart camera devices. - In: IEEE Symposium on Computational Intelligence for Security and Defense Applications (CISDA), 2012 : 11 - 13 July 2012, Ottawa, Canada.. - Piscataway, NJ : IEEE, ISBN 978-1-4673-1417-6, (2012), insges. 8 S.

http://dx.doi.org/10.1109/CISDA.2012.6291526
Werner, Jürgen; Zhao, Mingcheng; Hillenbrand, Matthias; Sinzinger, Stefan
RBF-based optical surfaces. - In: DGaO-Proceedings. - Erlangen-Nürnberg: Dt. Gesellschaft für angewandte Optik, ISSN 1614-8436, Bd. 113.2012, P39, insges. 2 S.

Freeform optical surfaces offer additional degrees of freedom for designing imaging systems without rotational symmetry. This allows for a reduction in the number of optical elements, leading to more compact and lightweight systems, while at the same time improving the image quality. This also enables new areas of application. Commonly used representations for freeform surfaces are x-y-polynomials, Zernike polynomials and NURBS. Radial basis functions (RBF) have been used for many years e.g. in artificial neural networks and functional approximation and can also be used to describe optical surfaces. In this contribution we investigate properties specific to RBF-based optical surfaces and compare the performance of RBF-based surfaces to other representations in selected optical imaging systems. Interesting aspects include the dependency on the number of RBF that are summed to form the surface, the locality structure and its effects on optimization.



http://www.db-thueringen.de/servlets/DocumentServlet?id=21333
Alt-Epping, Bernd; Stäritz, Anke E.; Simon, Steffen T.; Altfelder, Nadine; Hotz, Thomas; Lindena, Gabriele; Nauck, Friedemann
What is special about patients with lung cancer and pulmonary metastases in palliative care? : results from a nationwide survey. - In: Journal of palliative medicine. - Larchmont, NY : Liebert, ISSN 1557-7740, Bd. 15 (2012), 9, S. 971-977

http://dx.doi.org/10.1089/jpm.2011.0434
Eichfelder, Gabriele;
Cone-valued maps in optimization. - In: Applicable analysis : an international journal.. - London [u.a.] : Taylor & Francis, ISSN 1563-504X, Bd. 91 (2012), 10, S. 1831-1846

Cone-valued maps are special set-valued maps where the image sets are cones. Such maps play an important role in optimization, for instance in optimality conditions or in the context of Bishop-Phelps cones. In vector optimization with variable ordering structures, they have recently attracted even more interest. We show that classical concepts for set-valued maps as cone-convexity or monotonicity are not appropriate for characterizing cone-valued maps. For instance, every convex or monotone cone-valued map is a constant map. Similar results hold for cone-convexity, sublinearity, upper semicontinuity or the local Lipschitz property. Therefore, we also propose new concepts for cone-valued maps.



http://dx.doi.org/10.1080/00036811.2011.616499
Babovsky, Hans;
Discrete kinetic models in the fluid dynamic limit. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 27 S., 395,4 KB). . - (Preprint. - M12,13)

We investigate discrete kinetic models in the Fluid dynamic limit described by the Euler system and the Navier-Stokes correction obtained by the Chapman Enskog procedure. We show why reliable "small" systems can be expected only for small Mach numbers and derive a calculus for designing models for given Prandtl numbers.



http://www.db-thueringen.de/servlets/DocumentServlet?id=21218
Scheide, Diego; Stiebitz, Michael
The maximum chromatic index of multigraphs with given [Delta] and [mu]. - In: Graphs and combinatorics. - Tokyo : Springer-Verl. Tokyo, ISSN 1435-5914, Bd. 28 (2012), 5, S. 717-722

http://dx.doi.org/10.1007/s00373-011-1068-4
Behrndt, Jussi; Möws, Roland; Trunk, Carsten
On finite rank perturbations of selfadjoint operators in Krein spaces and eigenvalues in spectral gaps. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 10 S., 150,6 KB). . - (Preprint. - M12,12)

It is shown that the finiteness of eigenvalues in a spectral gap of a definitizable or locally definitizable selfadjoint operator in a Krein space is preserved under finite rank perturbations. This results is applied to a class of singular Sturm-Liouville operators with an indefinite weight function.



http://www.db-thueringen.de/servlets/DocumentServlet?id=20974
Philipp, Friedrich; Trunk, Carsten
The numerical range of non-negative operators in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 21 S., 177,7 KB). . - (Preprint. - M12,11)

We define and characterize the Krein space numerical range W(A) and the Krein space co-numerical range W_{\rm co}(A) of a non-negative operator A in a Krein space. It is shown that the non-zero spectrum of A is contained in the closure of W(A)\cap W_{\rm co}(A).



http://www.db-thueringen.de/servlets/DocumentServlet?id=20973
Berger, Thomas; Ilchmann, Achim; Reis, Timo
Normal forms, high-gain, and funnel control for linear differential-algebraic systems. - In: Control and optimization with differential-algebraic constraints. - Philadelphia, Pa. : SIAM, Soc. for Industrial and Applied Mathematics, (2012), S. 127-164