avila and molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). this work is a further investigation of generalized weak structures due to avila and molina. further we introduce the structures ro(g) and rc(g) and study the properties of the structur...

Abstract. This investigation studies nonemptiness problems of plane square tiling. In the edge coloring (or Wang tiles) of a plane, unit squares with colored edges of p colors are arranged side by side such that adjacent tiles have the same colors. Given a set of Wang tiles B, the nonemptiness problem is to determine whether or not Σ(B) = ∅, where Σ(B) is the set of all global patterns on Z2 th...

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...