Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Two-barrier rule Two-barrier rule The two barrier rule is a policy of safety for work on piping carrying high pressure and/or high temperature fluids. It is commonly used by oil companies. The rule simply states that for any work that must be done on a section of piping, which involves breaking containment, there must be at least two barriers separating the fluids from the broken area. The purpose behind specifying two barriers is to ensure redundancy. The risk of a total loss of containment is reduced if there are two independent isolations as it is highly improbable they would both fail at