Spectral bounds for singular indefinite Sturm-Liouville operators with L1-potentials. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 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
Degree sequences and edge connectivity. - In: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, ISSN 1865-8784, Bd. 87 (2017), 2, S. 343-355
https://doi.org/10.1007/s12188-016-0171-0
Decision uncertainty in multiobjective optimization. - In: Journal of global optimization, ISSN 1573-2916, Bd. 69 (2017), 2, S. 485-510
In many real-world optimization problems, a solution cannot be realized in practice exactly as computed, e.g., it may be impossible to produce a board of exactly 3.546 mm width. Whenever computed solutions are not realized exactly but in a perturbed way, we speak of decision uncertainty. We study decision uncertainty in multiobjective optimization problems and we propose the concept of decision robust efficiency for evaluating the robustness of a solution in this case. This solution concept is defined by using the framework of set-valued maps. We prove that convexity and continuity are preserved by the resulting set-valued maps. Moreover, we obtain specific results for particular classes of objective functions that are relevant for solving the set-valued problem. We furthermore prove that decision robust efficient solutions can be found by solving a deterministic problem in case of linear objective functions. We also investigate the relationship of the proposed concept to other concepts in the literature.
https://doi.org/10.1007/s10898-017-0518-9
An estimate on the non-real spectrum of a singular indefinite Sturm-Liouville operator. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 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
New lower bound for the distance to singularity of regular matrix pencils. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 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
Prevention of solidification cracking during pulsed laser beam welding. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (7 Seiten). - (Preprint ; M17,09)
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
A new method for network redesign via rank one updates. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (5 Seiten). - (Preprint ; M17,08)
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
Interaction of open and closed loop control in MPC. - In: Automatica, ISSN 0005-1098, Bd. 82 (2017), S. 243-250
https://doi.org/10.1016/j.automatica.2017.04.038
Quadratic costs do not always work in MPC. - In: Automatica, ISSN 0005-1098, Bd. 82 (2017), S. 269-277
https://doi.org/10.1016/j.automatica.2017.04.058
An indefinite inverse spectral problem of Stieltjes type. - In: Integral equations and operator theory, ISSN 1420-8989, Bd. 87 (2017), 4, S. 491-514
https://doi.org/10.1007/s00020-017-2358-x