An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

Cohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,bin R.$ The reversible property is an important role in noncommutative ring theory‎. ‎Recently‎, ‎Abdul-Jabbar et al‎. ‎studied the reversible ring property on nilpotent elements‎, ‎introducing‎ the concept of commutativity of nilpotent elements at zero (simply‎, ‎a CNZ ring)‎. ‎In this paper‎, ‎we extend the CNZ pr...

A synthetic approach to the preparation of [2]rotaxanes (1-5·6PF(6)) incorporating bispyridinium derivatives and two 1,5-dioxynaphthalene (DNP) units situated in the rod portions of their dumbbell components that are encircled by a single cyclobis(paraquat-p-phenylene) tetracationic (CBPQT(4+)) ring has been developed. Since the π-electron-deficient bispyridinium units are introduced into the d...

In this paper, an effective synthesis method for sparse uniformly excited concentric ring array (CRA) element positions featuring a minimum sidelobe level (SLL) is presented. This based on the chaos sparrow search algorithm (CSSA), which can optimal solution under multiple constraints. By improving constraint number of elements each ring, range further reduced, and global ability effectively im...

Athermal silicon ring resonators are experimentally demonstrated by overlaying a polymer cladding on narrowed silicon wires. The ideal width to achieve athermal condition for the TE mode of 220 nm-height SOI waveguides is found to be around 350 nm. After overlaying a polymer layer, the wavelength temperature dependence of the silicon ring resonator is reduced to less than 5 pm/degrees C, almost...

The importance of the double bonds in the furan ring of avocadofurans with relation to their insecticidal activity was examined. The insecticidal activity of two naturally occurring avocadofurans, 2-(pentadecyl)furan and 2-(heptadecyl)furan, was compared to the toxicity of five tetrahydrofurans with alkyl chains at position 2 and varying side chains from 14 to 18 carbons. We found that eliminat...