Analysis of Weak Associativity in Some Hyper-Algebraic Structures that Represent Dismutation Reactions

Abstract

In this paper, some chemical systems of Tin (Sn), Indium (In) and Vanadium (V) which are represented by hyper-algebraic structures (SSn, ⊕), (SIn, ⊕) and (SV , ⊕) were studied. The analyses of their algebraic properties and the probabilities of elements in dismutation reactions were carried out with the aid of computer codes in Python programming language. It was shown that in the dismutation reactions, the left nuclear (Nλ)-probability, middle nuclear (Nµ)-probability and right nuclear (Nρ)-probability for each of the hyper-algebraic structures (SSn, ⊕), (SIn, ⊕) and (SV , ⊕) is less than 1.000. This implies that, (SSn, ⊕), (SIn, ⊕) and (SV , ⊕) are non-associative hyper-algebraic structures. Also, from the results obtained for FLEX-probability, it was shown that, (SSn, ⊕), (SIn, ⊕) and (SV , ⊕) have flexible elements because the values of their FLEX-probabilities are 1.000 each. Hence, (SSn, ⊕), (SIn, ⊕) and (SV , ⊕) are flexible. Overall, (SV , ⊕) exhibited the lowest measure of weak-associativity, (SSn, ⊕) exhibited lower measure of weak-associativity, and (SIn, ⊕) exhibited a low measure of weak-associativity.