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.

We introduced and study fuzzy Γ-hypersemigroups, according to fuzzy semihypergroups as previously defined [33] and prove that results in this respect. In this regard first we introduce fuzzy hyperoperation and then study fuzzy Γ-hypersemigroup. We will proceed by study fuzzy Γ-hyperideals and fuzzy Γ-bihyperideals. Also we study the relation between the classes of fuzzy Γ-hypersemigroups and Γ-...

Intuitively, if two strings S1 and S2 are sufficiently similar and we already have an FM-index for S1 then, by storing a little extra information, we should be able to reuse parts of that index in an FM-index for S2. We formalize this intuition and show that it can lead to significant space savings in practice, as well as to some interesting theoretical problems.