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Eichfelder, Gabriele;
Numerical procedures in multiobjective optimization with variable ordering structures. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 24 S., 365 KB). . - (Preprint. - M12,05)

Multiobjective optimization problems with a variable ordering structure instead of a partial ordering have recently gained interest due to several applications. In the last years a basic theory has been developed for such problems. The difficulty in their study arises from the fact that the binary relations of the variable ordering structure, which are defined by a cone-valued map which associates to each element of the image space a pointed convex cone of dominated or preferred directions, are in general not transitive. - In this paper we propose numerical approaches for solving such optimization problems. For continuous problems a method is presented using scalarization functionals which allows the determination of an approximation of the infinite optimal solution set. For discrete problems the Jahn-Graef-Younes method known from multiobjective optimization with a partial ordering is adapted to allow the determination of all optimal elements with a reduced effort compared to a pairwise comparison.



http://www.db-thueringen.de/servlets/DocumentServlet?id=20485
Berger, Thomas; Halikias, George; Karcanias, Nicos
Effects of dynamic and non-dynamic element changes in RLC networks. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 27 S., 328 KB). . - (Preprint. - M12,04)

The paper deals with the redesign of passive electric networks by changes of single dynamic and non-dynamic elements which may retain, or affect the natural topology of the network. It also deals with the effect of such changes on the natural dynamics of the network, the natural frequencies. The impedance and admittance modeling for passive electrical networks is used which provides a structured, symmetric, integral-differential description, which in the special cases of RC and RL networks is reduced to matrix pencil descriptions. The transformations on the network are expressed as those preserving, or modifying the two natural topologies of the network, the impedance graph and the admittance graph topologies. For the special cases of RC and RL networks we consider the problem of the effect of changes of a single dynamic, or non-dynamic element on the natural frequencies. Using the Determinantal Assignment Framework, it is shown that the family of single parameter variation problems is reduced to equivalent Root Locus problems with the possibility of fixed modes. An explicit characterization of the fixed modes is given and a number of interesting properties of the spectrum are derived such as the interlacing property of poles and zeros for the entire family of Root Locus problems.



http://www.db-thueringen.de/servlets/DocumentServlet?id=20479
Berger, Thomas; Ilchmann, Achim; Trenn, Stephan
The quasi-Weierstraß form for regular matrix pencils. - In: Linear algebra and its applications : LAA.. - New York, NY : American Elsevier Publ., Bd. 436 (2012), 10, S. 4052-4069

http://dx.doi.org/10.1016/j.laa.2009.12.036
Harant, Jochen; Kemnitz, Arnfried; Saito, Akira; Schiermeyer, Ingo
Closures, cycles, and paths. - In: Journal of graph theory. - New York, NY [u.a.] : Wiley, ISSN 1097-0118, Bd. 69 (2012), 3, S. 314-323

http://dx.doi.org/10.1002/jgt.20584
Ilchmann, Achim; Pham Huu Anh, Ngoc
Stability and robust stability of positive Volterra systems. - In: International journal of robust and nonlinear control : IFAC affiliated journal.. - New York, NY [u.a.] : Wiley, ISSN 1099-1239, Bd. 22 (2012), 6, S. 604-629

http://dx.doi.org/10.1002/rnc.1712
Schreyer, Jens; Škrabul'áková, Erika
On the facial Thue choice index of plane graphs. - In: Discrete mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 312 (2012), 10, S. 1713-1721

http://dx.doi.org/10.1016/j.disc.2012.01.023
Berger, Thomas; Reis, Timo
Controllability of linear differential-algebraic systems - a survey. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 48 S., 501 KB). . - (Preprint. - M12,03)

Different concepts related to controllability of differential-algebraic equations are described. The class of systems considered consists of linear differential-algebraic equations with constant coefficients. Regularity, which is, loosely speaking, a concept related to existence and uniqueness of solutions for any inhomogeneity, is not required in this article. The concepts of impulse controllability, controllability at infinity, behavioral controllability, strong and complete controllability are described and defined in time-domain. Equivalent criteria that generalize the Hautus test are presented and proved. - Special emphasis is placed on normal forms under state space transformation and, further, under state space, input and feedback transformations. Special forms generalizing the Kalman decomposition and Brunovsky form are presented. Consequences for state feedback design and geometric interpretation of the space of reachable states in terms of invariant subspaces are proved.



http://www.db-thueringen.de/servlets/DocumentServlet?id=20281
Kostochka, Alexandr V.; Rabern, Landon; Stiebitz, Michael
Graphs with chromatic number close to maximum degree. - In: Discrete mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 312 (2012), 6, S. 1273-1281

http://dx.doi.org/10.1016/j.disc.2011.12.014
Azizov, Tomas Ya.; Trunk, Carsten
PT symmetric, Hermitian and P-self-adjoint operators related to potentials in PT quantum mechanics. - In: Journal of mathematical physics. - College Park, Md. : American Inst. of Physics, ISSN 1089-7658, Bd. 53 (2012), 1, S. 012109, insges. 18 S.

http://dx.doi.org/10.1063/1.3677368
Süße, Roland; Marx, Bernd
Variationsrechnung und Maxwellsche Gleichungen. - Theoretische Elektrotechnik ; Bd. 1
2., überarb. und erw. Ausg.. - Langewiesen : Wiss.-Verl. Thüringen, 2012. - XXXVIII, 264 S.. - Literaturverz. S. 255 - 257