Order of the Precious Crown

The Order of the Precious Crown (宝冠章, Hōkan-shō) is a Japanese order, established on January 4, 1888 by Emperor Meiji of Japan, and the lowest ranking of the Japanese orders currently awarded. Originally the order had five classes, but on April 13, 1896 the sixth, seventh and eighth classes were added.

This Order is conventionally reserved for female recipients; however, men have occasionally been accorded this honour. More often, men have been awarded the Order of the Rising Sun rather than the Order of the Precious Crown. In 1917, medals of the Order of the Crown were bestowed upon twenty-nine Americans who participated in the Russo-Japanese War. This unusual list of honorees was composed of ten women volunteer nurses and nineteen correspondents of American newspapers.

Until 2003, the Order of the Precious Crown ranked below the Order of the Rising Sun but above the Order of the Sacred Treasure, and was bestowed as a female-only version of the Order of the Rising Sun; however, men could also be appointed. In 2003 the Order of the Rising Sun, previously reserved for males, was made available to women as well, and the lowest two classes of the Order of the Precious Crown were abolished. The Order of the Precious Crown is now only bestowed upon female members of the Imperial Family and foreign ladies of distinction.

Big O notation

In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size. In analytic number theory, it is used to estimate the "error committed" while replacing the asymptotic size, or asymptotic mean size, of an arithmetical function, by the value, or mean value, it takes at a large finite argument. A famous example is the problem of estimating the remainder term in the prime number theorem.

Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation.