Mathematical Colloquim

PROGRAM

ODELJENJE ZA MATEMATIKU

MATEMATICKOG INSTITUTA SANU

Sastanci Odeljenja za Matematiku odrzavaju se u biblioteci Matematickog Instituta SANU, Kneza Mihaila 35, Beograd, na prvom spratu.

Sastanci se odrzavaju petkom u 11 casova

Molimo da obratite paznju na PROMENU TERMINA. Ubuduce ce sastanci Odeljenja stalno pocinjati u
11 casova (umesto u 12 casova)
kako bi se izbeglo preklapanje sa sednicama na Matematickom fakultetu i omogucilo svima koji zele da prisustvuju obema sednicama.

ODELJENJE ZA MATEMATIKU je opsti seminar sa najduzom tradicijom u Institutu. Predavanja su namenjena sirokom krugu matematicara - i onima koji ne rade u toj oblasti. POSEBNO SU DOBRODOSLI POSTDIPLOMCI I STUDENTI STARIJIH GODINA.

-- PROGRAM ZA APRIL 2003 --

Petak, 04. mart 2003. u 11h:

Marko Nedeljkov (Institut za matematiku, Novi Sad):
DELTA AND SINGULAR SHOCK WAVES

REZIME. Lax, Glimm and others give some important answers on a existence of solutions to Cauchy problems for one dimensional systems of conservation laws in '50s, but for the initial data with small enough total variation. Even Riemann problems for large initial jump are still unsolved in general. In late '70s, Korchinski found some simple system where delta function can occur (by numerical analysis), but there are no reasonable answer when and how they can occur.

In '90s, there are a lot of papers dealing with specific Riemann problems which posses so called "delta shock wave" (Tan, Zheng, Zhang,...). Also, Keyfitz and Kranzer found even more peculiar type of solutions, "singular shock waves", which, roughly speaking, possess a "root of delta function".

We shall try to approach to the question of existence of admissible delta shock waves and singular shock waves in more systematic way. One of the methods uses "splitting" of delta function, and the other uses the generalized function theory started by Colombeau, Oberguggenberger...

First question is when such objects can occur in a fairly general class of systems, and the other is their interactions with other elementary waves. There is no ultimate answer on each of these questions, and we will try to give some possibilities for further work in this field.

Petak, 11. april 2003. u 11h:

Dragan S. Djordjevic (Prirodno-matematicki fakultet, Nis):
PERTURBATIONS OF SPECTRA OF OPERATOR MATRICES

In this talk $M_C$ denotes a $2\times 2$ operator matrix of the form $M_C=\left[\matrix A&C\\0&B\endmatrix\right]$, which is acting on the product of Banach or Hilbert spaces $X\oplus Y$. We investigate sets $\bigcap\limits_{C\in \L(Y,X)}\sigma_\tau(M_C)$, where $\sigma_\tau(M_C)$ can be equal to the left (right), essential, left (right) Fredholm, Weyl or Browder spectrum of $M_C$. Thus, generalizations and extensions of various well-known and recent results of H. Du and J. Pan (Proc. Amer. Math. Soc. {\bf 121} (1994), 761--766), J. K. Han, H. Y. Lee and W. Y. Lee (Proc. Amer. Math. Soc. {\bf 128} (2000), 119--123) and W. Y. Lee (Proc. Amer. Math. Soc. {\bf 12}9 (2000), 131--138) are presented.

Petak, 18. april 2003. u 11h:

Donald McAllister (Northwestern Illinois University and Universidad de Lisboa):
INVERSE SEMIGROUPS AND TILINGS

Inverse semigroups were introduced in the early 1950s to provide a framework for the study of the local symmetries of a mathematical structure. They have an intrinsic beauty of their own and are among the most well understood types of semigroup. In this talk we shall use ideas from the classical theory of inverse semigroups to motivate some recent developments of the theory. The later results have their origin in the attempt to find an algebraic formulation to the study of non-periodic tilings.

Petak, 25. april 2003. u 11h:

Zoran Petric (Matematicki Institut):
BRAUEROVE ALGEBRE I GENERALNOST DOKAZA

Klasican rezultat Riharda Brauera o reprezentaciji grupa ortogonalnih transformacija bice doveden u vezu sa pojmom generalnosti dokaza.

OBAVESTENJA

Ovo obavestenje mozete naci i na Internetu: www.mi.sanu.ac.yu

Ako zelite da se obavestenje o Vasim naucnim skupovima pojave u Newsletter of EMS (European Mathematical Society) i na Internetu na lokaciji EMS, onda se obratite na emsvesti@mi.sanu.ac.yu gde cete dobiti format obavestenja.