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
Last antecedent rule in fact operates remotely on all the antecedents, binding them to the modifier. Nothing in the general literature on punctuation suggests such a mechanism. The last antecedent rule is also applied to contract interpretation. Last antecedent rule The last antecedent rule is a doctrine of interpretation of a statute, by which "Referential and qualifying phrases, where no contrary intention appears, refer solely to the last antecedent." The rule is typically bound by "common sense" and is flexible enough to avoid application that "would involve an absurdity, do violence to the plain intent of the language, or if the context for