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
Phonological rule most general way possible. Thus, the intervocalic alveolar flapping described above can be formalized as The rule given above for intervocalic alveolar flapping describes what sound is changed, what the sound changes to, and where the change happens (in other words, what the "environment" is that triggers the change). The illustration below presents the same rule, with each of its parts labelled and described. Taken together and read from left to right, this notation of the rule for intervocalic alveolar flapping states that any alveolar stop consonant (/t/ or /d/) becomes a tap ([ɾ]) in the environment where it is