Publications at the Institute of Mathematics

Results: 2072
Created on: Wed, 27 Mar 2024 23:21:46 +0100 in 0.0808 sec


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; Ilchmann, Achim *1956-*; Reis, Timo;
Normal forms, high-gain, and funnel control for linear differential-algebraic systems. - In: Control and optimization with differential-algebraic constraints, (2012), S. 127-164

Cranston, Daniel W.; Pruchnewski, Anja; Tuza, Zsolt; Voigt, Margit
List colorings of K5-minor-free graphs with special list assignments. - In: Journal of graph theory, ISSN 1097-0118, Bd. 71 (2012), 1/2, S. 18-30

https://doi.org/10.1002/jgt.20628
Borowiecki, Piotr; Göring, Frank; Harant, Jochen; Rautenbach, Dieter
The potential of greed for independence. - In: Journal of graph theory, ISSN 1097-0118, Bd. 71 (2012), 3/4, S. 245-259

https://doi.org/10.1002/jgt.20644
Berger, Thomas;
Robustness of stability of time-varying index-1 DAEs. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 44 S., 392,0 KB). - (Preprint ; M12,10)

We study exponential stability and its robustness for time-varying linear index-1 differential-algebraic equations. The effect of perturbations in the leading coefficient matrix is investigated. An appropriate class of allowable perturbations is introduced. Robustness of exponential stability with respect to a certain class of perturbations is proved in terms of the Bohl exponent and perturbation operator. Finally, a stability radius involving these perturbations is introduced and investigated. In particular, a lower bound for the stability radius is derived. The results are presented by means of illustrative examples.



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Pruchnewski, Anja; Voigt, Margit
Weights of induced subgraphs in K1,r-free graphs. - In: Discrete mathematics, Bd. 312 (2012), 16, S. 2429-2432

http://dx.doi.org/10.1016/j.disc.2012.04.025
Berger, Thomas; Trenn, Stephan;
Addition to: the quasi-Kronecker form for matrix pencils. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 7 S., 140,1 KB). - (Preprint ; M12,8)
http://www.db-thueringen.de/servlets/DocumentServlet?id=20641
Eichfelder, Gabriele; Jahn, Johannes
Vector optimization problems and their solution concepts. - In: Recent developments in vector optimization, (2012), S. 1-27

Eichfelder, Gabriele;
Variable ordering structures in vector optimization. - In: Recent developments in vector optimization, (2012), S. 95-126

Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten;
Bounds on the non-real spectrum of differential operators with indefinite weights. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 27 S., 276,8 KB). - (Preprint ; M12,07)

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and infinity are not singular critical points of the unperturbed operator it is shown that a bounded additive perturbation leads to an operator whose non-real spectrum is contained in a compact set and with definite type real spectrum outside this set. The main results are quantitative estimates for this set, which are applied to Sturm-Liouville and second order elliptic partial differential operators with indefinite weights on unbounded domains.



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