We survey and discuss several solution concepts for infinite turn-based multiplayer games with qualitative (i.e. win-lose) objectives of the players. These games generalise in a natural way the common model of games in verification which are two-player, zero-sum games with ω-regular winning conditions. The generalisation is in two directions: our games may have more than two players, and the ob...

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

This paper includes various parts of the theory of mixed type partial differential equations with initial and boundary conditions in fluid mechanics ,such as: The classical dynamical equation of mixed type due to Chaplygin (1904), regularity of solutions in the sense of Tricomi (1923) and in brief his fundamental idea leading to singular integral equations, and the new mixed type boundary value...