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Behrndt, Jussii; Schmitz, Philipp; Trunk, Carsten
Spectral bounds for singular indefinite Sturm-Liouville operators with L1-potentials. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (7 Seiten). - (Preprint. - M17,12)
Im Titel ist "1" hochgestellt

The spectrum of the singular indefinite Sturm-Liouville operator A=sgn(.) (-d^2/dx^2)+q with a real potential q in L^1(R)$ covers the whole real line and, in addition, non-real eigenvalues may appear if the potential q assumes negative values. A quantitative analysis of the non-real eigenvalues is a challenging problem, and so far only partial results in this direction were obtained. In this paper the bound l lambda | <= |q|_{L^1}^2 on the absolute values of the non-real eigenvalues lambda of A is obtained. Furthermore, separate bounds on the imaginary parts and absolute values of these eigenvalues are proved in terms of the L^1-norm of q and its negative part q_-.


http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2017200509
Behrndt, Jussii; Gsell, Bernhard; Schmitz, Philipp; Trunk, Carsten
An estimate on the non-real spectrum of a singular indefinite Sturm-Liouville operator. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (5 Seiten). - (Preprint. - M17,10)

It will be shown with the help of the Birman-Schwinger principle that the non-real spectrum of the singular indefinite Sturm-Liouville operator $\operatorname{sgn}(\cdot)(-\mathrm d^2/\mathrm d x^2 +q)$ with a real potential $q\in L^1\cap L^2$ is contained in a circle around the origin with radius $\|q\|_{L^1}^2$.


https://www.db-thueringen.de/receive/dbt_mods_00032787
Berger, Thomas; Gernandt, Hannes; Trunk, Carsten; Wojtylak, Micha&lstrok;
New lower bound for the distance to singularity of regular matrix pencils. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (5 Seiten). - (Preprint. - M17,10)

For regular matrix pencils $\Ac(s)=sE-A$ the distance to the nearest singular pencil in the Frobenius norm of the coefficients is called the distance to singularity. We derive a new lower bound for this distance by using the spectral theory of tridiagonal Toeplitz matrices.


https://www.db-thueringen.de/receive/dbt_mods_00032786
Bergmann, Jean Pierre; Bielenin, Martin; Herzog, Roland A.; Hildebrand, Jörg; Riedel, Ilka; Schricker, Klaus; Trunk, Carsten; Worthmann, Karl
Prevention of solidification cracking during pulsed laser beam welding. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (7 Seiten). - (Preprint. - M17,05)

We present a mathematical model to describe laser beam welding based on the heat equation. Since the material coeff cients depend on the temperature, this leads to a quasi-linear parabolic partial differential equation. It is our goal to prevent solidif cation cracking. We address this problem by means of optimal control. It is the intensity prof le of the laser beam which acts as the control function. The main challenge is the formulation of a suitable objective function. In particular, high velocities of the solidif cation interface need to be properly penalized in order to deal with and avoid cracking phenomena.


https://www.db-thueringen.de/receive/dbt_mods_00032771
Gernandt, Hannes; Krauße, Dominik; Sommer, Ralf; Trunk, Carsten
A new method for network redesign via rank one updates. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (5 Seiten). - (Preprint. - M17,05)

We present a method to place the eigenvalues of an electrical network towards a prescribed set of complex numbers by inserting an additional capacitance into the network. We use recent results on rank one perturbations of regular matrix pencils and provide an upper bound on the approximation error of the eigenvalues in the chordal distance.


https://www.db-thueringen.de/receive/dbt_mods_00032770
Worthmann, Karl; Mehrez, Mohamed W.; Mann, George K. I.; Gosine, Raymond G.; Pannek, Jürgen
Interaction of open and closed loop control in MPC. - In: Automatica : a journal of IFAC, the International Federation of Automatic Control. - Amsterdam [u.a.] : Elsevier, Pergamon Press, ISSN 00051098, Bd. 82 (2017), S. 243-250
https://doi.org/10.1016/j.automatica.2017.04.038
Müller, Matthias A.; Worthmann, Karl
Quadratic costs do not always work in MPC. - In: Automatica : a journal of IFAC, the International Federation of Automatic Control. - Amsterdam [u.a.] : Elsevier, Pergamon Press, ISSN 00051098, Bd. 82 (2017), S. 269-277
https://doi.org/10.1016/j.automatica.2017.04.058
Fleige, Andreas; Winkler, Henrik
An indefinite inverse spectral problem of Stieltjes type. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 14208989, Bd. 87 (2017), 4, S. 491-514
https://doi.org/10.1007/s00020-017-2358-x
Gernandt, Hannes; Trunk, Carsten
Eigenvalue placement for regular matrix pencils with rank one perturbations. - In: SIAM journal on matrix analysis and applications. - Philadelphia, Pa : Soc, ISSN 10957162, Bd. 38 (2017), 1, S. 134-154
http://dx.doi.org/10.1137/16M1066877
Ilchmann, Achim; Reis, Timo
. - Surveys in differential-algebraic equations ; 4. - Cham : Springer. - ix, 305 Seiten. - (Differential-algebraic equations forum)
http://www.gbv.de/dms/ilmenau/toc/884524973.PDF