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Veröffentlichungen am Institut für Mathematik seit 1990

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Bruhn, Henning; Diestel, Reinhard; Kriesell, Matthias; Pendavingh, Rudi; Wollan, Paul;
Axioms for infinite matroids. - In: Advances in mathematics. - Amsterdam [u.a.] : Elsevier, ISSN 1090-2082, Bd. 239 (2013), S. 18-46

http://dx.doi.org/10.1016/j.aim.2013.01.011
Göring, Frank; Harant, Jochen
Prescribed edges and forbidden edges for a cycle in a planar graph. - In: Discrete applied mathematics. - [S.l.] : Elsevier, Bd. 161 (2013), 12, S. 1734-1738

http://dx.doi.org/10.1016/j.dam.2011.08.020
Berger, Thomas; Reis, Timo
Zero dynamics and funnel control for linear electrical circuits. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 25 S., 217,2 KB). . - (Preprint. - M13,07)
http://www.db-thueringen.de/servlets/DocumentServlet?id=22165
Behrndt, Jussi; Hassi, Seppo; Snoo, Henk; Wietsma, Rudi; Winkler, Henrik
Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator. - In: Complex analysis and operator theory. - Cham (ZG) : Springer International Publishing AG, ISSN 1661-8262, Bd. 7 (2013), 2, S. 331-362

http://dx.doi.org/10.1007/s11785-011-0197-3
Eichfelder, Gabriele; Kasimbeyli, Refail
Properly optimal elements in vector optimization with variable ordering structures. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 27 S., 311,4 KB). . - (Preprint. - M13,05)

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.



http://www.db-thueringen.de/servlets/DocumentServlet?id=22044
Winkler, Henrik; Woracek, Harald
Symmetry in de Branges almost Pontryagin spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 33 S., 303,1 KB). . - (Preprint. - M13,06)

In many examples of de Branges spaces symmetry appears naturally. Presence of symmetry gives rise to a decomposition of the space into two parts, the "even" and the "odd" part, which themselves can be regarded as de Branges spaces. The converse question is to decide whether a given space is the "even" part or the "odd" part of some symmetric space, and, if yes, to describe the totality of all such symmetric spaces. We consider this question in an indefinite (almost Pontryagin space) setting, and give a complete answer. Interestingly, it turns out that the answers for the "even" and "odd" cases read quite differently; the latter is significantly more complex.



http://www.db-thueringen.de/servlets/DocumentServlet?id=22048
Bomze, Immanuel M.; Eichfelder, Gabriele;
Copositivity detection by difference-of-convex decomposition and [omega]-subdivision. - In: Mathematical programming : Series A, Series B ; a publication of the Mathematical Programming Society.. - Berlin : Springer, ISSN 1436-4646, Bd. 138 (2013), 1/2, S. 365-400

We present three new copositivity tests based upon difference-of-convex (d.c.) decompositions, and combine them to a branch-and-bound algorithm of [omega]-subdivision type. The tests employ LP or convex QP techniques, but also can be used heuristically using appropriate test points. We also discuss the selection of efficient d.c. decompositions and propose some preprocessing ideas based on the spectral d.c. decomposition. We report on first numerical experience with this procedure which are very promising.



https://doi.org/10.1007/s10107-012-0543-x
Berger, Thomas;
Zero dynamics and funnel control of general linear differential-algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 44 S., 438 KB). . - (Preprint. - M13,04)
http://www.db-thueringen.de/servlets/DocumentServlet?id=21790
Philipp, Friedrich; Trunk, Carsten
The numerical range of non-negative operators in Krein spaces. - In: Linear algebra and its applications : LAA.. - New York, NY : American Elsevier Publ., Bd. 438 (2013), 5, S. 2542-2556

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://dx.doi.org/10.1016/j.laa.2012.10.048
Behrndt, Jussi; Luger, Annemarie; Trunk, Carsten
On the negative squares of a class of self-adjoint extensions in Krein spaces. - In: Mathematische Nachrichten. - [S.l.] : Wiley-VCH, ISSN 1522-2616, Bd. 286 (2013), 2/3, S. 118-148

A description of all exit space extensions with finitely many negative squares of a symmetric operator of defect one is given via Krein's formula. As one of the main results an exact characterization of the number of negative squares in terms of a fixed canonical extension and the behaviour of a function $\tau$ (that determines the exit space extension in Krein's formula) at zero and at infinity is obtained. To this end the class of matrix valued $\mathcal D_\kappa^{n\times n}$-functions is introduced and, in particular, the properties of the inverse of a certain $\mathcal D_\kappa^{2\times 2}$-function which is closely connected with the spectral properties of the exit space extensions with finitely many negative squares is investigated in detail. Among the main tools here are the analytic characterization of the degree of non-positivity of generalized poles of matrix valued generalized Nevanlinna functions and some extensions of recent factorization results.



http://dx.doi.org/10.1002/mana.201000154