For a compact set A ⊂ R d <m...

We present the STack ARchitecture (STAR) automaton. It is a fixed structure, multiaction, reward-penalty learning automaton, characterized by a star-shaped state transition diagram. Each branch of the star contains D states associated with a particular action. The branches are connected to a central "neutral" state. The most general version of STAR involves probabilistic state transitions in re...

It is shown that each lobe of the figure-eight orbit star-shaped, which indicates corresponding polar angle monotone. In general, it not clear under assumptions a trajectory in minimizer star-shaped. this paper, we study minimizers connecting two fixed-ends (i.e. Bolza problem) planar three-body problem with equal masses. We show if Jacobi coordinates are both orthogonal, then for any minimizer...

The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskĭı, Tsĕıtin, Kreisel, and Lacombe assert the existence of non-empty co-r.e. closed sets devoid of computable points: sets which are even ‘large’ in the sense of positive Lebesgue measure. We observe that a certain size is in fact necessary : every non-empty co-r.e. closed real set without ...