Petak, 17. januar 2003. u 12h :

Miroljub Jevtic (Matematicki fakultet):
Teoreme o srednjoj vrednosti hiper-harmonijskih funkcija

REZIME. Predavanje ce biti posveceno nekim teoremama o srednjoj vrednosti hiper-harmonijskih funkcija,a posebno jednoj od njih, koja je predmet rada "Fixed points of an integral operator", koji je prihvacen za stampu u casopisu Journal dAnalyse Mathematique.

Petak, 24. januar 2003. u 11h :



OBRATITE PAZNJU NA TERMIN!!!

11-12 Sandi Klav\v{z}ar (Univerzitet u Mariboru, Slovenia):
The cube polynomial and its derivatives: the case of median graphs

(This is a joint work with Bo\v{s}tjan Bre\v{s}ar and Riste \v Skrekovski)
Abstract. For $i\geq 0$, the $i$-cube $Q_i$ is the graph on $2^i$ vertices representing $0/1$ tuples of length $i$, where two vertices are adjacent whenever the tuples differ in exactly one position. (In particular, $Q_0 = K_1$.) Let $\alpha_i(G)$ be the number of induced $i$-cubes of a graph $G$. Then the cube polynomial $c(G,x)$ of $G$ is introduced as $\sum_{i\geq 0} \alpha_i(G) x^i$. It is shown that any function $f$ with two related, natural properties, is up to the factor $f(Q_0,x)$ the cube polynomial. The derivation $\partial\, G$ of a median graph $G$ is introduced and it is proved that the cube polynomial is the only function $f$ with the property $f'(G,x)= f(\partial\, G, x)$ provided that $f(G,0)=|V(G)|$. As the main application of the new concept, several relations that widely generalize previous such results for median graphs are proved. For instance, it is shown that for any $s\geq 0$ we have $c^{(s)}(G,x+1) = \sum_{i\geq s}\,\frac {c^{(i)}(G,x)} {(i-s)!}\,,$ where certain derivatives of the cube polynomial coincide with well-known invariants of median graphs.

12-14 Otvoreni sastanak Komisije za matematiku i mehaniku, II deo
NASTAVAK SASTANKA OD 10.01.2003.

Obrazlozenje
Na sastanku Odeljenja 10. januara, posle zanimljive diskusije veceg broja nasih istaknutih matematicara i mehanicara, dogovoren je nastavak sastanka sa temama koje se odnose na probleme u naucnom radu, organizovanju naucnog rada, poslediplomskim studijama,...

OBAVESTENJA

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