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Hildenbrandt, Regina;
The k-server problem with parallel requests and the compound Harmonic algorithm. - In: Baltic journal of modern computing : BJMC. - [S.l.], ISSN 2255-8950, Bd. 4 (2016), 3, S. 607-629

In this paper the (randomized) compound Harmonic algorithm for solving the generalized k-server problem is proposed. This problem is an online k-server problem with parallel requests where several servers can also be located on one point. In 2000 Bartal and Grove have proved that the well-known Harmonic algorithm is competitive for the (usual) k-server problem. Unfortunately, certain techniques of this proof cannot be used to show that a natural generalization of the Harmonic algorithm is competitive for the problem with parallel requests. The probabilities, which are used by the compound Harmonic algorithm are, finally, derived from a surrogate problem, where at most one server must be moved in servicing the request in each step. We can show that the compound Harmonic algorithm is competitive with the bound of the ratio as which has been proved by Bartal and Grove in the case of the usual problem.



http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2016200094
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)
https://www.db-thueringen.de/receive/dbt_mods_00029270
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.



https://www.db-thueringen.de/receive/dbt_mods_00029271
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.



https://www.db-thueringen.de/receive/dbt_mods_00029233
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

http://dx.doi.org/10.1137/130942413
Eichfelder, Gabriele; Jahn, Johannes;
Vector and set optimization. - In: Multiple criteria decision analysis : state of the art surveys. - New York : Springer, (2016), S. 695-737

This chapter is devoted to recent developments of vector and set optimization. Based on the concept of a pre-order optimal elements are defined. In vector optimization properties of optimal elements and existence results are gained. Further, an introduction to vector optimization with a variable ordering structure is given. In set optimization basic concepts are summed up.



http://dx.doi.org/10.1007/978-1-4939-3094-4_17
Przybyło, Jakub; Schreyer, Jens; Škrabul'áková, Erika;
On the facial Thue choice number of plane graphs via entropy compression method. - In: Graphs and combinatorics - Tokyo : Springer-Verl. Tokyo, ISSN 1435-5914, Bd. 32 (2016), 3, S. 1137-1153

http://dx.doi.org/10.1007/s00373-015-1642-2
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.



https://www.db-thueringen.de/receive/dbt_mods_00029046
Harant, Jochen; Mohr, Samuel;
Maximum weighted induced subgraphs. - In: Discrete mathematics - Amsterdam [u.a.] : Elsevier, Bd. 339 (2016), 7, S. 1954-1559

http://dx.doi.org/10.1016/j.disc.2015.07.013
Worthmann, Karl; Braun, Philipp; Proch, Michael; Schlüchtermann, Jörg; Pannek, Jürgen;
On contractual periods in supplier development. - In: IFAC-PapersOnLine - Frankfurt : Elsevier, ISSN 2405-8963, Bd. 49 (2016), 2, S. 60-65

http://dx.doi.org/10.1016/j.ifacol.2016.03.011