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
Japanese punctuation direct HTML equivalent is the codice_1 entity (em-space) which outputs the same fullwidth " " glyph. A fullwidth space may be used where a colon or comma would be used in English: ("Yamato Bank, Osaka Branch"). The resembles a lengthened tilde , which does not exist in JIS X 0208. Uses in Japanese include: The Japanese versions of these punctuation marks are usually full-width characters. A full-width space is usually left after such marks when writing in Japanese. The consists of two equally sized dots centered on the same vertical line. As a rule, a colon informs the reader that