A first-principles method is presented to calculate elastic constants up the fourth order of crystals with cubic and hexagonal symmetries. The relies on numerical differentiation second Piola-Kirchhoff stress tensor a density functional theory approach Cauchy for list deformed configurations reference state. number strained required independent second, third, 24 37 symmetries, respectively. Her...

in this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. some new positive periodic criteria are given.