Hyperfine interactions in R x Gd1− x Fe3 intermetallics R = Tb, Y

2-D skew constacyclic codes over R[x, y; ρ, θ]

For a finite field $mathbb{F}_q$, the bivariate skew polynomial ring $mathbb{F}_q[x,y;rho,theta]$ has been used to study codes cite{XH}. In this paper, we give some characterizations of the ring $R[x,y;rho,theta]$, where $R$ is a commutative ring. We investigate 2-D skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $R[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ A...

( R = Y , La , Sm , Tb , Yb ,

ANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X]

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...

Fuzzy rules for fuzzy $overline{X}$ and $R$ control charts

Statistical process control ($SPC$), an internationally recognized technique for improving product quality and productivity, has been widely employed in various industries. $SPC$ relies on the use of control charts to monitor a manufacturing process for identifying causes of process variation and signaling the necessity of corrective action for the process. Fuzzy data exist ubiquitously in the ...

Derivations having divergence zero on R [ X , Y ]