I. Relocated Analytic Beer

Motto:	He who goes for salt gets the beer
Place and time:	Snezna, 27.2.-1.3.1987

Attendance:

Jiri Hrdina
Ales Nekvinda
Lubos Pick
Mirko Rokyta
Jan Rehacek

J.Hrdina: OPTIMAL CONTROL
Minimization of the functional describing the optimal control with constraints by the method of associated tasks.
A.Nekvinda: PEANO CURVE
Investigation of properties of Peano curves with respect to the number of pre-images.
L.Pick: BROUWER THEOREM
An elementary proof of the theorem about the retraction of the ball to the sphere using the direct computation of the volume of the n-dim 1-ball.
M.Rokyta: TRANSCENDENTALITY OF e
A proof of the transcendentality of "e" based on certain properties of the integral giving values of the Gamma function for integers.
J. Rehacek: BANACH ALGEBRAS
Definition of the spectrum in BA. A proof that spectrum is a non-empty compact set. Specification of algebras isomorfic to C.

Pearls of the seminar:	-
Problems:	(i) continuity of the inverse mapping between metric spaces (ii) Is there f:[0,1] -> [0,1]^2 cont., with exactly 2 pre-images? (iii) df(x)/dx=f(x+1) (iv) Retraction theorem implies Brouwer Thm.? (v) Definition of analytic functions in Banach Algebras.
Awards/Remarks:	Award for the best talk: Jan Rehacek