The topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. In this version every player can...

Organic Rankine Cycle (ORC) power plants have become very popular and have found their applications in systems with renewable sources of energy. So far their overall efficiencies are not very impressive and only for the upper temperature of about 300 °C do they exceed 20%. A drawback of these cycles is the limitation of the cycle upper temperature due to the heat exchanger technology and the materials used. However, it is possible...

Consider a game played on the edge set of the infinite clique by two players, Builder and Painter. In each round, Builder chooses an edge and Painter colours it red or blue. Builder wins by creating either a red copy of $G$ or a blue copy of $H$ for some fixed graphs $G$ and $H$. The minimum number of rounds within which Builder can win, assuming both players play perfectly, is the \emph{on-line Ramsey number} $\tilde{r}(G,H)$. In...

Organic Rankine cycles (ORC) are quite popular, but the overall efficiencies of these plants are rather very low. Numerous studies have been conducted in many scientific centers and research centers to improve the efficiency of such cycles. The research concerns both the modification of the cycle and the increase in the parameters of the medium at the inlet to the turbine. However, the efficiency of even these modified cycles rarely...