Petak, 03. mart 2006. u 14h, sala 2 MI SANU BG:

Prof. Milojica Jacimovic, Prirodno-matematicki fakultet, Podgorica
TEOREMA O ALTERNATIVAMA I PRIMJENE

Sadrzaj: Bice izlozena prva (Farkasova) formulacija teoreme o alternativama koja se odnosi na skupove rjesenja linearnih sistema

Ax=b, x\geq 0, A\in R^{m\times n}, b\in R^m, x\in R^n,

i

A^Tz\leq 0, b^Ty> 0, y\in R^m,

zatim kasnija uopstenja i ideje razlicitih dokaza. Na kraju ce biti pokazane primjene ove teoreme u zadacima optimizacije.

Petak, 10. mart 2006. u 13:30h, sala 2 MI SANU:

Professor Hans G. Feichtinger, University of Vienna, Faculty of Mathematics.
ON THE USEFULNESS OF CERTAIN BANACH GELFAND TRIPLES

Abstract: Most of us know from distribution theory that a good understanding of certain operators requires to make use, aside from the Hilbert space ${\mathcal H} = L^2(R^d)$, of certain spaces of generalized functions. A standard approach is based on the fact that one defines distributions as members of the dual space a space of test functions, which is dense in ${\mathcal H}$. We will show that time-frequency analysis allows the introduction of a Banach spaces $S_0(R^d)$ which is suitable as an algebra of test functions, dense in ${\mathcal H}$. Together with its dual it forms a Gelfand triple of Banach spaces. The Fourier transform is an example: At the level of $S_0$ it is well defined as an integral transform (also the inverse Fourier transform), at the $L^2$-level it is unitary, while one can express at the level distributions that "pure frequencies" are mapped onto Diracs, and that this fact characterizes the Fourier transform as Gelfand tripe isomorphism. Similarly one can view the mapping between the (integral) kernels describing linear mappings and their spreading symbol (a distribution over phase space) as a Gelfand triple isomorphism, characterized by the fact that pure time-frequency shifts are mapped onto corresponding Dirac measures.

Some details about the author:
1. editor in chief to JFAA (Journal of Fourier analysis and Applications)
2. associate editor ACHA, Journ. Approx. Theory,
3. associate editor "Sampling Theory in Signal and Imaging Processing" STSIP
4. associate editor Function Spaces and Applications.

Petak, 17. mart 2006. u 14h, sala 2 MI SANU:

Prof. Bosko Jovanovic, Matematicki fakultet, beograd
NEKI TIPOVI GRANICNIH PROBLEMA S INTERFEJSOM

Sadrzaj: Razmatra se klasa granicnih problema cija resenja imaju prekid parcijalnih izvoda prvog reda duz zadate hiperpovri. Ta hiperpovr se naziva interfejsom i deli oblast na dva disjunktna dela. Opisuju se razliciti nacini zadavanja ovakvih problema (parcijalne jednacine sa singularnim koeficijentima, slabe formulacije, uslovi saglasnosti). Izvode se odgovarajuce apriorne ocene i opisuju funkcionalni prostori koji sadrze njihova resenja. Razmatraju se numericke metode resavanja granicnih problema s interfejsom.

Petak, 24. mart 2006. u 14h, sala 2, MI SANU:

Tatjana Davidovic, Matematicki institut SANU
RASPOREDJIVANJE ZADATAKA NA VISEPROCESORSKE SISTEME PRIMENOM METAHEURISTIKA

Sadrzaj: Razmatra se problem statickog rasporedjivanja zadataka na viseprocesorski sistem proizvoljne strukture. Uzima se u obzir i vreme potrebno za prenos podataka izmedju procesora. Ova varijanta problema rasporedjivanja spada u klasu NP-teskih problema. Stoga je na resavanje ovog problema, primenjeno nekoliko poznatih metaheuristickih metoda. Sve metode implementirane su u odnosu na istu reprezentaciju resenja. Postignuto je znacajno poboljsanje rezultata dobijenih kostruktivnim heuristickim metodama, kao i onih koji predstavljaju njihovu popravku primenom lokalnog pretrazivanja u odnosu na neke okoline. Implementirano je i nekoliko strategija za paralelizaciju jedne od koriscenih metaheuristickih metoda.

Petak, 31. mart 2006. u 14h, sala 718, MF BG:

Bozidar Jovanovic, Matematicki Institut SANU
HAMILTONIZACIJA NEHOLONOMNIH SISTEMA

Rezime: Neholonomni mehanicki sistemi nisu hamiltonovi. U ovom izlaganju prikazace se rezultati dobijeni u saradnji sa Jurijem Fjodorovim (Politehnicki univerzitet, Barselona i Moskovski drzavni univerzitet, Moskva) na pronalazenju prvih visedimenzionih primera capliginovih sistema (kao i novouvedene klase kvazi-capliginovih sistema) koji posle reparametrizacije toka postaju hamiltonovi.

Reference:
[1] Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces. J. Non. Sci., 14, (2004) 341-381, arXiv: math-ph/0307016.
[2] Nonholonomic geodesic flows on compact Lie groups, In: Topological methods in the theory of integrable systems (Bolsinov A.V., Fomenko A.T., Oshemkov A.A. eds) Cambrige Scientific Publ., 2005, pp. 115-152, arXiv: math-ph/0408037.
[3] Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics, to appear in Letters in Mathematical Physics (2006), arXiv: math-ph/0510088.

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