The association between hyperstructures and binary relations had been intensively studied 5,6,10,11,2,4,20 . Chvalina 5,6 and Hort 2 use ordered structures for the construction of semigroups and hypergroups. Rosenberg 4 associated with any binary relation of full domain, a hypergroupoid and found conditions on , such that is a hypergroup. Corsini and Leoreanu 16 study hypergroups and binary rel...

Mathematical models can be used in several sciences as a tool to organize the research in such a way that the results could be transferred into other sciences. Here we go on with a method how to organise some results, which do not seem to have any relation with mathematics in a strictly algebraic way. The topic of algebra used is called Hv-structures, the largest class of hyperstructures. Our e...

The largest class of hyperstructures is the one which satisfies the  weak properties. We connect the theory of P-hopes, a large class of  hyperoperations, with the Lie-Santilli admissibility used in  Hardonic Mechanics. This can be achieved by a kind of Ree,  sandwich hyperoperation.

A salt metathesis reaction is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. Hyperstructure theory is studied from the theoretical point of view and for its applications. In this paper, we provide some examples of hyperstructures associated with salt m...

One from classical constructions of algebraic binary hyperstructures (semihypergroups and hypergroups) from ordered algebraic systems is based on a certain Lemma on principal ends generated by products of pairs of elements – shortly termed as Ends-Lemma. First version of this auxiliary lemma was obtained in the monography [3]. The mentioned lemma is applied not only in case of hyperstructures c...

‎In this paper first we define the morphism between geometric spaces in two different types‎. ‎We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎The relation between hypergroups and geometric spaces is studied‎. ‎By constructing the category $qh$ of $H_{v}$-groups we answer the question...

Chromosome separation and segregation must be executed within a bacterial cell in which the membrane and cytoplasm are highly structured. Here, we develop a strand-specific model based on each of the future daughter chromosomes being associated with a different set of structures or hyperstructures in an asymmetric cell. The essence of the segregation mechanism is that the genes on the same stra...

Hyperstructures and binary relations have been studied by many researchers, for instance, Chvalina 1, 2 , Corsini and Leoreanu 3 , Feng 4 , Hort 5 , Rosenberg 6 , Spartalis 7 , and so on. A partial hypergroupoid 〈H, ∗〉 is a nonempty setH with a function fromH×H to the set of subsets of H. A hypergroupoid is a nonempty set H, endowed with a hyperoperation, that is, a function fromH ×H to P H , t...

It is recognized in cognitive informatics [10, 12-14, 20, 25, 29, 30] that the core scientific knowledge of the mankind is mainly archived in mathematical forms [1, 2, 5-9, 10-39]. The entire set o f fundamental and long-lasting problems in contemporary disciplines, such as, inter alia, intelligence science, robotics, knowledge science, information science, brain science, system science, softwa...

To answer both the growth of world’s urban population and climate changes, new structural systems with high prefabrication levels renewable materials need to be developed. A novel system that could enable use modular light-frame construction in high-rise buildings was modeled analyzed. This achieved by having a hyperstructure carrying loads four-story superposed substructures. Two 20-story hype...