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Prof. Dr. Michael Stiebitz

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Publications at the institute since 1990

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Hildenbrandt, Regina;
A k-server problem with parallel requests and unit distances. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011. - Online-Ressource (PDF-Datei: 11 S., 207,5 KB). . - (Preprint. - M11,16)

In the paper a k-server problem with parallel requests where several servers can also be located on one point is considered. We show that a HARMONIC_p k-server algorithm is competitive against an adaptive online adversary in case of unit distances.
Harant, Jochen;
A lower bound on independence in terms of degrees. - In: Discrete applied mathematics. - [S.l.] : Elsevier, Bd. 159 (2011), 10, S. 966-970
Kuzhel, Sergii; Trunk, Carsten
On a class of J-self-adjoint operators with empty resolvent set. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, ISSN 1096-0813, Bd. 379 (2011), 1, S. 272-289
Snoo, Henk; deWinkler, Henrik; Wojtylak, Michal
Zeros of nonpositive type of generalized Nevanlinna functions with one negative square. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, ISSN 1096-0813, Bd. 382 (2011), 1, S. 399-417
Kostochka, Alexandr V.; Stiebitz, Michael; Woodall, Douglas R.
Ohba's conjecture for graphs with independence number five. - In: Discrete mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 311 (2011), 12, S. 996-1005
Geletu, Abebe; Hoffmann, Armin; Klöppel, Michael; Li, Pu
Monotony analysis and sparse-grid integration for nonlinear chance constrained process optimization. - In: Engineering optimization. - London : Taylor & Francis, ISSN 1029-0273, Bd. 43 (2011), 10, S. 1019-1041
Löwenstein, Christian; Pedersen, Anders Sune; Rautenbach, Dieter; Regen, Friedrich
Independence, odd girth, and average degree. - In: Journal of graph theory. - New York, NY [u.a.] : Wiley, ISSN 1097-0118, Bd. 67 (2011), 2, S. 96-111
Babovsky, Hans;
Kinetic lattice group models: structure and numerics. - In: AIP conference proceedings. - Melville, NY : Inst, ISSN 15517616, Bd. 1333 (2011), S. 63-68
Azizov, Tomas Ya.; Trunk, Carsten
PT symmetric, hermitian and P-self-adjoint operators related to potentials in PT quantum mechanics. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011. - Online-Ressource (PDF-Datei: 28 S., 189,9 KB). . - (Preprint. - M11,15)

In the recent years a generalization H=p^2 + x^2(ix)^\epsilon of the harmonic oscillator using a complex deformation was investigated, where \epsilon is a real parameter. Here, we will consider the most simple case: \epsilon even and x real. We will give a complete characterization of three different classes of operators associated with the differential expression H: The class of all self-adjoint (Hermitian) operators, the class of all PT symmetric operators and the class of all P-self-adjoint operators. Surprisingly, some of the PT symmetric operators associated to this expression have no resolvent set.
Berger, Thomas; Ilchmann, Achim; Reis, Timo
Normal forms, high-gain and funnel control for linear differential-algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011. - Online-Ressource (PDF-Datei: 35 S., 563,1 KB). . - (Preprint. - M11,14)

We consider linear differential-algebraic m-input m-output systems with positive strict relative degree or proper inverse transfer function; in the single-input single-output case these two disjoint classes make the whole of all linear DAEs without feedthrough term. Structural properties - such as normal forms (i.e. the counterpart to the Byrnes-Isidori form for ODE systems), zero dynamics, and high-gain stabilizability - are analyzed for two purposes: first, to gain insight into the system classes and secondly, to solve the output regulation problem by funnel control. The funnel controller achieves tracking of a class of reference signals within a pre-specified funnel; this means in particular, the transient behaviour of the output error can be specified and the funnel controller does neither incorporate any internal model for the reference signals nor any identification mechanism, it is simple in its design. The results are illuminated by position and velocity control of a mechanical system encompassing springs, masses, and dampers.