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Prof. Dr. rer. nat. habil. Matthias Kriesell


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Veröffentlichungen am Institut für Mathematik seit 1990

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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.
Bang-Jensen, Jørgen; Kriesell, Matthias; Maddaloni, Alessandro; Simonsen, Sven;
Arc-disjoint directed and undirected cycles in digraphs. - In: Journal of graph theory - New York, NY [u.a.] : Wiley, ISSN 1097-0118, Bd. 83 (2016), 4, S. 406-420
Meierott, Stefan; Hotz, Thomas; Néel, Nicolas; Kröger, Jörg;
Asymmetry parameter of peaked Fano line shapes. - In: Review of scientific instruments : a monthly journal devoted to scientific instruments, apparatus, and techniques. - [S.l.] : American Institute of Physics, ISSN 1089-7623, Bd. 87 (2016), 10, S. 103901, insges. 7 S.

The spectroscopic line shape of electronic and vibrational excitations is ubiquitously described by a Fano profile. In the case of nearly symmetric and peaked Fano line shapes, the fit of the conventional Fano function to experimental data leads to difficulties in unambiguously extracting the asymmetry parameter, which may vary over orders of magnitude without degrading the quality of the fit. Moreover, the extracted asymmetry parameter depends on initially guessed values. Using the spectroscopic signature of the single-Co Kondo effect on Au(110) the ambiguity of the extracted asymmetry parameter is traced to the highly symmetric resonance profile combined with the inevitable scattering of experimental data. An improved parameterization of the conventional Fano function is suggested that enables the nonlinear optimization in a reduced parameter space. In addition, the presence of a global minimum in the sum of squared residuals and thus the independence of start parameters may conveniently be identified in a two-dimensional plot. An angular representation of the asymmetry parameter is suggested in order to reliably determine uncertainty margins via linear error propagation.
Hotz, Thomas; Kelma, Florian; Wieditz, Johannes;
Non-asymptotic confidence sets for circular means. - In: Entropy : an international and interdisciplinary journal of entropy and information studies. - Basel : MDPI, ISSN 1099-4300, Bd. 18 (2016), 10, 375, insges. 13 S.
Adamaszek, Anna; Adamaszek, Michal; Mnich, Matthias; Schmidt, Jens M.;
Lower bounds for locally highly connected graphs. - In: Graphs and combinatorics - Tokyo : Springer-Verl. Tokyo, ISSN 1435-5914, Bd. 32 (2016), 5, S. 1641-1650
Neundorf, Werner;
Die mathematische Zauberkiste : Mathematik für alle : mathematische Knobeleien : Zeige mal, was du kannst!
Um ein Drittel erweiterte Ausgabe - Ilmenau : Unicopy-Campus-Ed., 2016 - V, 538 Seiten. . - (Ilmenauer Editionen)
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

Harant, Jochen; Kemnitz, Arnfried;
Lower bounds on the sum choice number of a graph. - In: Electronic notes in discrete mathematics - Amsterdam : Elsevier Science, ISSN 15710653, Bd. 53 (2016), S. 421-431
Eichfelder, Gabriele; Krüger, Corinna; Schöbel, Anita;
Decision uncertainty in multiobjective optimization - Ilmenau : Technische Universität, Institut für Mathematik, 2016 - 1 Online-Ressource (27 Seiten). . - (Preprint. - M16,06)

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 decision robust efficiency for evaluating the robustness of a solution in this case. Therefore, we address decision uncertainty within the framework of set-valued maps. First, we prove that convexity and continuity are preserved by the resulting set-valued mappings. Second, 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.
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.