Petak, 07. oktobar 2005. u 14h, sala 2 MI SANU BG:

Miroslav Ciric, University of Nis, Faculty of Sciences and Mathematics
FUZZY RELATIONS AND THEIR APPLICATIONS

Abstract: The concept of a fuzzy relation naturally arose from that of fuzzy set in Zadeh's very first paper on fuzzy sets, and it was further developed in his 1971 paper, where the notions of a fuzzy equivalence relation and fuzzy ordering were introduced. After that, a number of papers dealing with various aspects related with these relations have appeared, and today, the theory of fuzzy binary relations is probably one of the most important and influential branches of fuzzy set theory. By allowing intermediate degrees of relationship, fuzzy relations provide much more freedom to express the subtle nuances of human preferences so they found natural applications in modelling various concepts inherent to so-called ^Soft' sciences like psychology, sociology, linguistics, etc. Here we give a survey of the most interesting results concerning fuzzy equivalence relations, fuzzy quasi-orders, fuzzy tolerance (preference) relations, and their applications in fuzzy cluster analysis, fuzzy control, approximate reasoning etc.

Petak, 14. oktobar 2005. u 14h, sala 2 MI SANU:

Katica (Stevanovic) Hedrih, Masinski fakultet, Nis
SOLUTION OF THE TWO COUPLED PARTIAL FRACTIONAL ORDER DIFFERENTIAL EQUATIONS

Abstract: The solution of the two coupled partial fractional order differential equations of transversal vibrations of a creeping connected double plate homogeneous system have been derived. The analytical solution of system coupled partial fractional differential equations of corresponding dynamical free and forced processes are obtained by using method of Bernoulli's particular integral and Laplace's transform method. By using inverse Laplace's transform it is obtained time series function as a particular components of the solution. By using these components visualizations an analysis of the solution components is done.

Keywords: Fractional order derivative, partial fractional-differential equations, visualization, double plate homogeneous system.

Petak, 21. oktobar 2005. u 14h, sala 2 MI SANU:

Henning Haahr Andersen, Department of Mathematics, Aarhus University, Denmark
TWISTING FUNCTORS ON HIGHEST WEIGHT CATEGORIES

Abstract: Some 35 years ago J. Bernstein, I. M. Gelfand, and S. I. Gelfand introduced a category of highest weight modules for a semisimple complex Lie algebra. In this talk I shall discuss some recent progress in understanding the finer structure of this category via certain twisting functors. These are operations which to standard objects in the category associate modules with the same composition factors but with new and interesting submodule structure. They turn out to be equivalences on the level of derived categories. This fact in turn can be used for instance to give information about their values on simple modules. Our approach works equally well for quantum groups.

Petak, 28. oktobar 2005. u 12h, bibloteka, MI SANU:

Miodrag M. Spalevic, Prirodno-matematicki fakultet, Kragujevac
GRANICE GRESAKA GAUSS-TURAN-ovih KVADRATURNIH FORMULA ZA ANALITICKE FUNKCIJE

Sadrzaj: Cuvene Gaussove kvadraturne formule za aproksimiranje razvijane su u vise pravaca. Jedan od njih je teorija kvadratura sa visestrukim cvorovima, tj. Gauss-Turan-ovih kvadraturnih formula ??? Nas cilj je analiza ostataka u slucaju kada je f analiticka funkcija u nekoj oblasti kompleksne ravni koja u svojoj unutrasnjosti sadrzi interval . U okviru ovog predavanja bice izlozen pregled nedavno dobijenih rezultata (zajedno sa prof. G. V. Milovanovicem).

Petak, 28. oktobar 2005. u 14h, sala 718, MF BG:

Mathieu Dutour Sikiric, Ecole Normale Superieure, Paris, France, (visiting Institut "Rudjer Boskovic" Zagreb)
FACE REGULAR MAPS

Abstract: Call two-faced map and, specifically, (p,q)-map a 3-valent 3-connected map (on sphere or torus) with only p- and q-gonal faces (at least one each), for given integers 3 ( p Here we address the characterization of all weakly face-regular (p,q)-maps on sphere or torus. Examples of obtained results:
1. Any (3,q)-map is 3R0 and have 4 ( q ( 12. It is strongly face-regular for q=4,5 (Prism3 and Barrel3 only) and q=11,12 (only tori, unique for q=12).
2. All such weakly face-regular maps are infitities of polyhedra and tori for each 7 ( q ( 10 and (characterized) infinity of (3,6)-polyhedra.
3. (5,q)-polyhedra 5Rj exist, besides classified case j=2, only for j=3, 6 ( q ( 10.
4. If a (p,q)-polyhedron is qRj, then j( 5. The number of such polyhedra is infinite if and only if q ( 12,10,8,7,7 for j=0,1,2,3,4,5, respectively (except some undecided cases for j=0,3,5). (5,q)-torus 5Rj was found exactly for all cases, when the number of (5,q)-polyhedra qRj was proven to be infinite.
5. In many cases full classification was reached.

We used large computations, variations of Euler formula, analysis of coronae of faces, the decomposition of (p,q)-maps into elementary (p,3)-polycycles and many ad hoc arguments.