logo 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

Main talks (28.2.):

  1. J.Hrdina: OPTIMAL CONTROL
    Minimization of the functional describing the optimal control with constraints by the method of associated tasks.
  2. A.Nekvinda: PEANO CURVE
    Investigation of properties of Peano curves with respect to the number of pre-images.
  3. 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.
  4. 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.
  5. 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

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