Physical Sciences and Mathematics Commons^™

Nidus Idearum. Scilogs, Xi: In-Turns And Out-Turns, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this eleventh book of scilogs – called in-turns and out-turns –, one may find new and old questions and solutions, referring mostly to topics on Neutrosophy, but also Multispace, with miscellaneous addition of topics on Physics, Mathematics, or Sociology – email messages to research colleagues, or replies, notes about authors, articles, or books, spontaneous ideas, and so on.

Superhyperfunction, Superhyperstructure, Neutrosophic Superhyperfunction And Neutrosophic Superhyperstructure: Current Understanding And Future Directions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The n-th PowerSet of a Set {or Pn(S)} better describes our real world, because a system S (which may be a company, institution, association, country, society, set of objects/plants/animals/beings, set of concepts/ideas/propositions, etc.) is formed by sub-systems, which in their turn by sub-sub-systems, and so on. We prove that the SuperHyperFunction is a generalization of classical Function, SuperFunction, and HyperFunction. And the SuperHyperAlgebra, SuperHyperGraph are part of the SuperHyperStructure. Almost all structures in our real world are Neutrosophic SuperHyperStructures since they have indeterminate/incomplete/uncertain/conflicting data.

Neutrosophic Superhyperalgebra And New Types Of Topologies, Florentin Smarandache, Memet Sahin, Derya Bakbak, Vakkas Uluçay, Abdullah Kargı

Branch Mathematics and Statistics Faculty and Staff Publications

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P^2(S) } and so on.

That’s why the n-th PowerSet of a Set S { defined recursively and denoted by P^n(S) = P(P^(n-1)(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world.

The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order …