Recently, we have introduced six types of composition ternary fuzzy relations. These compositions are close in spirit to the binary Based on these composition, several transitivity a relation and investigated their basic properties. In this paper, prove additional properties characterizations relation. Also, provide representation theorem for relations satisfying transitivity. Finally, focus pr...

Capsules provide a clean algebraic representation of the state of a computation in higherorder functional and imperative languages. They play the same role as closures or heapor stack-allocated environments but are much simpler. A capsule is essentially a finite coalgebraic representation of a regular closed λ-coterm. One can give an operational semantics based on capsules for a higher-order pr...

The closures of the pre-images associated with families of mappings in different topologies of normed spaces are considered. The question of finding a description of these closures by means of families of the same kind as original ones is studied. It is shown that for the case of the weak topology this question may be reduced to finding an appropriate closure of a given family. There are discus...

closely related to closures since they too can be nested in methods and classes. Their translation scheme follows the scheme described for closures. They are crucial for implementing iterators efficiently. Iterators are quite valuable as they permit encapsu-lation of iteration strategies within containers. In other words, the iteration algorithm, complete with its initialization code and termin...