in this paper a linear fuzzy fredholm integral equation(ffie) with arbitrary fuzzy function input and symmetric triangular (fuzzy interval) output is considered. for each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (ffie).

Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...

We show that for any spacetime dimension greater than or equal to four, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime, irrespective of the mode of perturbations. Our starting point is the gauge-invariant formalism for perturbations in an arbitrary dimension...

The effective one-body method provides a framework to apply the black hole perturbation theory binary system where two masses can be comparable. We study gravitational-wave equation in background of for spinless binary, which is general available with spherically symmetric as well. obtain gauge conditions decoupled wave equation, and also give solutions terms metric special case, extends result...

A Correction to this paper has been published: https://doi.org/10.1007/s10883-021-09575-w