Sreda, 06.10.2010. u 13 sati:
Manfred Droste, Leipzig University
WEIGHTED AUTOMATA AND QUANTITATIVE LOGICS

Abstract: In automata theory, a classical result of Bhi states that the recognizable languages are precisely the ones definable by sentences of monadic second order logic. We will present a generalization of this result to the context of weighted automata. A weighted automaton is a classical nondeterministic automaton in which each transition carries a weight describing e.g. the resources used for its execution, the length of time needed, or its reliability. The behavior (language) of such a weighted automaton is a function associating to each word the weight of its execution. We develop syntax and semantics of a quantitative logic; the semantics counts 'how often' a formula is true. Our main results show that if the weights are taken either in an arbitrary semiring or in an arbitrary bounded lattice, then the behaviors of weighted automata are precisely the functions definable by sentences of our quantitative logic. The methods also apply to recent quantitative automata model of Henzinger et al. where weights of paths are determined, e.g., as the average of the weights of the path's transitions. Bhi's result follows by considering the classical Boolean algebra {0,1}. Joint work with Paul Gastin (ENS Cachan), Heiko Vogler (TU Dresden), resp. Ingmar Meinecke (Leipzig).

Petak, 08.10.2010. u 14h sala 2 SANU
Prof. dr Pavle Pandzic, Matematicki odjel PMF-a, Zagreb
DIRACOVI OPERATORI I UNITARNE REPREZENTACIJE

Abstract: U prvom dijelu predavanja dati cu kratak pregled teorije reprezentacija Liejevih grupa i pripadnih (g,K)-modula, s naglaskom na problem unitarnosti. Zatim cu definirati Diracov operator na (g,K)-modulima i objasniti njegovu ulogu u proucavanju unitarnosti.

Petak, 22.10.2010. u 14h, sala 2, MI SANU, BGD

Prof. dr Danilo Rastovic, Control systems group, Zagreb
NEKI PRISTUPI VARIJACIONOJ METODI U TEORIJI REAKTORA FUZIJE

Abstract: U predavanju daje se pregled rezultata predavaca iz matematickih problema reaktora fuzije. Vlasov-Poisson-Fokker-Planck jednadba iona se stabilizira pomocu izucavanja Boltzmannove jednadbe za neutrone. Metodama fazi logickih kontrolera izvodi se pracenje deterministickog ponasanja distribucije iona i elektrona, a pomocu maximuma entropije za stohasticki slucaj. To sve omogucava primjenu Ott-Grebogi-York metode na upravljanje procesom smjestavanja plazme kod tokamaka.

Petak, 29.10.2010. u 14h, sala 2, SANU, BGD

Prof G\"unther H\"ormann, Fakult\"at f\"ur Mathematik, Universit\"at Wien
ON THE ELASTO-GRAVITATIONAL EQUATIONS OF MOTION FOR THE ROTATING EARTH

Abstract: We discuss the derivation of the equations of motion of a uniformly rotating, elastic, and self-gravitating earth model based on a variational principle and under low regularity assumptions on the material parameters. The underlying geometric-physical assumptions allow for an aspheric, inhomogeneous, and anisotropic earth model with non-C^1 ``interior boundaries''. Such models and equations lie at the heart of global seismology and the study of the so-called free oscillations of the Earth. We establish existence and uniqueness of solutions to the resulting system of integro-differential equations of motion with spatial Sobolev regularity.