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
Uptick rule on 2009-04-08. A modified form of the rule was adopted on 2010-02-24. In 1938, the U.S. Securities and Exchange Commission (SEC) adopted the uptick rule, more formally known as "rule 10a-1", after conducting an inquiry into the effects of concentrated short selling during the market break of 1937. The original rule was implemented when Joseph P. Kennedy, Sr. was SEC commissioner. In 1994, the NASD and Nasdaq adopted their own short sale price tests, known as NASD Rule 3350, based on the last bid rather than on the last reported sale. In 1978, the purpose of the uptick rule was