in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

A Kohn-Sham (KS) inversion determines a KS potential and orbitals corresponding to given electron density, procedure that has applications in developing evaluating functionals used density functional theory. Despite the utility of inversions, application these methods among research community is disproportionately small. We implement Zhao-Morrison-Parr Wu-Yang framework simplifies analysis conv...

Background: In randomized controlled trials (RCTs), the power is often ‘reverse engineered’ based on number of participants that can realistically be achieved. An attractive alternative planning a new trial conditional available evidence; design particular interest in RCTs use sham control arm (sham-RCTs). Methods: We explore sham-...