Mathematical Colloquim
Mathematical Colloquim
PROGRAM
ODELJENJE ZA MATEMATIKU
MATEMATICKOG INSTITUTA SANU
Sastanci se odrzavaju petkom u 11 casova
(OBRATITE PAZNJU NA PROMENU TERMINA).
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
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