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Prof. Dr. Achim Ilchmann

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Škalikov, Andrej Andreevič; Trunk, Carsten;
Ob ustojčivosti zamknutosti i samosoprjažennosti dlja 2 x 2 operator-matric. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (6 Seiten). . - (Preprint. - M16,07)

Consider an operator which is defined in Banach or Hilbert space by a 2x2 matrix with entries A, B, C, D which where linear operators and which are assumed to be unbounded. In the case when the operators C and B are relatively bounded with respect to the operators A and D, respectively, new conditions of the closeness or closability are obtained for the operator L. For the operator L acting in a Hilbert space the analogs of Rellich-Kato theorems on the stability of self-adjointness are obtained.
Ilchmann, Achim;
EAGLE-Starthilfe Mathematik und Gesellschaft : zur Funktion der angewandten Mathematik. - Leipzig : Edition am Gutenbergplatz Leipzig, 2016. - 97 Seiten. . - (Eagle. - 093. Eagle-Starthilfe) ISBN 978-3-95922-093-4
- Literaturverzeichnis: Seite 91-94

Leben, Leslie;
Non-negative operators in Krein spaces and rank one perturbations. - Ilmenau : Universitätsverlag Ilmenau, 2016. - Online-Ressource (116 Seiten, 6.65 MB).
Technische Universität Ilmenau, Dissertation 2016

In der vorliegenden Arbeit werden eindimensionale Störungen von nichtnegativen Operatoren in Kreinräumen betrachtet. Dabei wird untersucht wie sich die Anzahl der Eigenwerte und deren Vielfachheit in einer Lücke des essentiellen Spektrums unter einer Störung ändern können. Zudem wird beschrieben wie sich an einem Eigenwert die Anzahl und die Länge der linear unabhängigen Jordanketten ändern können.
Worthmann, Karl; Proch, Michael; Braun, Philipp; Schlüchtermann, Jörg; Pannek, Jürgen;
Towards dynamic contract extension in supplier development. - In: Logistics research. - Berlin : Springer, ISSN 1865-0368, Bd. 9.2016, Article 14, insg. 12 Seiten

We consider supplier development within a supply chain consisting of a single manufacturer and a single supplier. Because investments in supplier development are usually relationship-specific, safeguard mechanisms against the hazards of partner opportunism have to be installed. Here, formal contracts are considered as the primary measure to safeguard investments. However, formal contracts entail certain risks, e.g., a lack of flexibility, particular in an ambiguous environment. We propose a receding horizon control scheme to mitigate possible contractual drawbacks while significantly enhancing the supplier development process and, thus, to increase the overall supply chain profit. Our findings are validated by a numerical case study.
Worthmann, Karl; Mehrez, Mohamed W.; Zanon, Mario; Mann, George K. I.; Gosine, Raymond G.; Diehl, Moritz;
Model predictive control of nonholonomic mobile robots without stabilizing constraints and costs. - In: IEEE transactions on control systems technology : a publication of the IEEE Control Systems Society.. - New York, NY : IEEE, ISSN 1558-0865, Bd. 24 (2016), 4, S. 1394-1406
Büttner, Florian; Trunk, Carsten;
Limit-point/limit-circle classification of second-order differential operators arising in PT quantum mechanics. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (6 Seiten). . - (Preprint. - M16,03)
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten;
Bounds on the non-real spectrum of a singular indefinite Sturm-Liouville operator on R. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (4 Seiten). . - (Preprint. - M16,05)

A simple explicit bound on the absolute values of the non-real eigenvalues of a singular indefinite Sturm-Liouville operator on the real line with the weight function sgn(&hahog;) and an integrable, continuous potential q is obtained.
Gernandt, Hannes; Trunk, Carsten;
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (8 Seiten). . - (Preprint. - M16,04)

We study the eigenvalues of rank one perturbations of regular matrix pencils depending linearly on a complex parameter. We prove properties of the corresponding eigenvalue sets including a convergence result as the parameter tends to infinity and an eigenvalue interlacing property for real valued pencils having real eigenvalues only.
Ilchmann, Achim; Selig, Tilman; Trunk, Carsten;
The Byrnes-Isidori form for infinite-dimensional systems. - In: SIAM journal on control and optimization. - Philadelphia, Pa. : Soc., ISSN 1095-7138, Bd. 54 (2016), 3, S. 1504-1534
Behrndt, Jussi; Möws, Roland; Trunk, Carsten;
Eigenvalue estimates for operators with finitely many negative squares. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (14 Seiten). . - (Preprint. - M16,02)

Let A and B be selfadjoint operators in a Krein space. Assume that the re- solvent difference of A and B is of rank one and that the spectrum of A consists in some interval I of isolated eigenvalues only. In the case that A is an operator with finitely many negative squares we prove sharp estimates on the number of eigenvalues of B in the interval I. The general results are applied to singular indefinite Sturm-Liouville problems.