Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators

The main objective of our paper is to focus on the study sequences (finite or countable) groups and hypergroups linear differential operators decreasing orders. By using a suitable ordering preordering we construct hypercompositional structures operators. Moreover, actions rings polynomials one real variable including diagrams actions–considered as special automata. Finally, obtain examples, choose explain theoretical results with, fall within theory artificial neurons infinite cyclic groups.