the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.

We present an additively homomorphic commitment scheme with hardness based on the Ring-SIS problem. Our construction is statistically hiding as well as computationally binding and allows to commit to a vector of ring elements at once. We show how to instantiate efficient zero-knowledge protocols that can be used to prove a number of relations among these commitments, and apply these in the cont...

Bis-spiropryran molecules were grafted onto the surface of upconverting nanoparticles. Fluorescence resonance energy transfer from the upconverting nanoparticles to the surface bis-spiropyran molecules triggered the transformation of the ring-closed bis-spiropyran to the ring-open bis-merocyanine forms.

A highly efficient Cu-catalyzed ring expansion reaction of 2H-azirines with terminal alkynes has been developed. This transformation provides a powerful method for the synthesis of 3-alkynyl polysubstituted pyrroles under mild conditions in good yields. The direct transformation process, specific selectivity, and good tolerance to a variety of substituents make it an alternative approach to the...

Abstract Vinyl aziridines are versatile starting materials toward ring-expansion transformations. Such processes widely used to give various medium or larger N-heterocycles of synthetic interest. This letter describes a copper-catalyzed ring expansion vinyl 3-pyrrolines by using Cu(I) salt [(CuOTf)2·toluene Cu(MeCN)4·PF6]. In particular, this transformation occurs under mild conditions (THF, rt).