In this study, nearness near-ring, subnearness M-group and ideal are introduced. By considering operations on the set of all near left weak cosets, near-ring cosets homomorphism also presented. Moreover, some properties these structures investigated.

The eukaryotic group II chaperonin TRiC/CCT is a 16-subunit complex with eight distinct but similar subunits arranged in two stacked rings. Substrate folding inside the central chamber is triggered by ATP hydrolysis. We present five cryo-EM structures of TRiC in apo and nucleotide-induced states without imposing symmetry during the 3D reconstruction. These structures reveal the intra- and inter...

We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite st...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

Presented here are two novel open-framework cobalt sulfate-oxalates constructed from molecular and chain-like building blocks. The two compounds have different structures: an hcb-type layer with 20-ring windows and a mog-type framework with 12-ring channels. Amine molecules play dual roles in the two structures: as a chelating ligand and a charge-balancing agent.

Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like struct...

Ring-closing olefin metathesis reactions are used to create intra-molecularly ring closed peptides or inter-molecularly ring-closed peptide dimers based on a designed amyloid peptide sequence. The uncrosslinked peptide self-assembles into high aspect ratio nanotubes, however ring-closing leads to the formation of fibrillar and twisted/helical ribbon structures.