In the present work, we have considered a modified gravity model dubbed as ‘logarithmicf (T) gravity’ as reported by Bamba et al. (J. Cosmol. Astropart. Phys 1101: 21, 2011) and investigated the behavior of Ricci dark energy interacting with pressureless Dark Matter. We have chosen the interaction term in the form Q=3 Hdrm and investigated the behavior of the Hubble parameter H as a function of the redshift z. For this reconstructed H, we have investigated the behavior of the fractional density contribution due to the Ricci dark energy and torsion. Subsequently, we investigated the equation of state parameter w RDE which is found to have a phantom-like behavior for all choices of c 2 in the Ricci dark energy density.

Using fixed point methods, we prove the stability of orthogonally RING homomorphism and orthogonally RING derivation in Banach algebras.

The concept of fuzzy soft G-RING is introduced; and some properties of fuzzy soft G-RINGs are given. Then the definitions of fuzzy soft G-ideals are proposed and some of their theories are considered.

In this paper the transmittance of metal-insulator-metal (MIM) waveguides containing semi-circular RING shaped and rectangular RING shaped grooves are investigated theoretically in the 500 nm to 1700 nm wavelength range. By varying groove parameters their effects on the transmittance of the MIM waveguides are investigated. The results show that the transmittance spectra of the waveguides have maximum and minimum points, and by using appropriate parameters for the grooves it is possible to make the transmittance maximum or minimum at a required frequency. Therefore by using the RING shaped grooves in the MIM waveguides a frequency splitter is designed. The results show that the efficiency of an MIM waveguide containing the RING shaped groove for filteRING a required frequency is higher than the efficiency of an MIM waveguide containing tooth shaped groove.

Let A be a commutative RING with unity. The annihilating graph of A, denoted by Gð AÞ , is a graph whose vertices are all non-trivial ideals of A and two distinct vertices I and J are adjacent if and only if Annð IÞ Annð JÞ ¼ 0. For every commutative RING A, we study the diameter and the girth of Gð AÞ . Also, we prove that if Gð AÞ is a triangle-free graph, then Gð AÞ is a bipartite graph. Among other results, we show that if Gð AÞ is a tree, then Gð AÞ is a star or a double star graph. Moreover, we prove that the annihilating graph of a commutative RING cannot be a cycle. Let n be a positive integer number. We classify all integer numbers n for which Gð ZnÞ is a complete or a planar graph. Finally, we compute the domination number of Gð ZnÞ .