75th Analytic Beer

Abstract program:

1. "3n+1 problem" - let f be a discrete dynamical system defined as f(n)=n/2 for n even and f(n)=3n+1 for n odd. The question is whether all initial conditions (positive integers) converge to the cycle 4-2-1? It is supposedly unsolved and quite difficult. (JR)
2. Various remarks about Diophantine problems (JR, MR)
3. Is the maximal operator from Lp(x) to Lp(x) bounded for p(x)=2+x on (0,1)? The norm in Lp(x) is defined as infimum of positive lambdas such that the integral of |f(x)|^p(x) / lambda dx < 1. (AN, LP)

Concrete program:

• 10^o Staropramen, coffee, soda
• pork on mushrooms+fries, chicken nuggets, fried cheese, croquets, fries

1. Rum, gentlemen, is quite a thing, as I have noticed (LP)
2. I think that better way of becoming famous would be to get naked and go to the main square (JR)