The shilling is a unit of currency used in Austria, in the United Kingdom, New Zealand and other British Commonwealth countries. The shilling is used as a currency in four east African countries: Kenya, Tanzania and Somalia; the east African community additionally plans to introduce an east African shilling. The word shilling comes from old English "Scilling", a monetary term meaning twentieth of a pound, from the Proto-Germanic root skiljaną meaning'to separate, divide.' The word "Scilling" is mentioned in the earliest recorded Germanic law codes, those of Æthelberht of Kent. Slang terms for the old shilling coins include "bob" and "hog". While the derivation of "bob" is uncertain, John Camden Hotten in his 1864 Slang Dictionary says the original version was "bobstick" and speculates that it may be connected with Sir Robert Walpole. One abbreviation for shilling is s, it was represented by a solidus symbol, which may have stood for a long s or ſ, thus 1/9 would be one shilling and ninepence. A price with no pence was sometimes written with a solidus and a dash: 11/–.

The solidus symbol is still used for the Kenyan shilling, rather than sh. During the Great Recoinage of 1816, the mint was instructed to coin one troy pound of standard silver into 66 shillings, or its equivalent in other denominations; this set the weight of the shilling, its subsequent decimal replacement 5 new pence coin, at 87.2727 grains or 5.655 grams from 1816 until 1990, when a new smaller 5p coin was introduced. In the past, the English world has had various myths about the shilling. One myth was that it was deemed to be the value of a cow in a sheep elsewhere. A shilling was a coin used in England from the reign of Henry VII; the shilling continued in use after the Acts of Union of 1707 created a new United Kingdom from the Kingdoms of England and Scotland, under Article 16 of the Articles of Union, a common currency for the new United Kingdom was created. The term shilling was in use in Scotland from early medieval times; the common currency created in 1707 by Article 16 of the Articles of Union continued in use until decimalisation in 1971.

In the traditional pounds and pence system, there were 20 shillings per pound and 12 pence per shilling, thus there were 240 pence in a pound. Three coins denominated in multiple shillings were in circulation at this time, they were: two shillings, which adopted the value of 10 new pence at decimalisation. At decimalisation in 1971, the shilling coin was superseded by the new five-pence piece, of identical size and weight and had the same value, inherited the shilling's slang name of a bob. Shillings remained in circulation until the five pence coin was reduced in size in 1991. Between 1701 and the unification of the currencies in 1825, the Irish shilling was valued at 13 pence and known as the "black hog", as opposed to the 12-pence English shillings which were known as "white hogs". In the Irish Free State and Republic of Ireland the shilling coin was issued as scilling in Irish, it was worth 1/20th of an Irish pound, was interchangeable at the same value to the British coin, which continued to be used in Northern Ireland.

The coin featured a bull on the reverse side. The first minting, from 1928 until 1941, contained 75% silver, more than the equivalent British coin; the original Irish shilling coin was withdrawn from circulation on 1 January 1993, when a smaller five pence coin was introduced. Australian shillings, twenty of which made up one Australian pound, were first issued in 1910, with the Australian coat of arms on the reverse and King Edward VII on the face; the coat of arms design was retained through the reign of King George V until a new ram's head design was introduced for the coins of King George VI. This design continued until the last year of issue in 1963. In 1966, Australia's currency was decimalised and the shilling was replaced by a ten cent coin, where 10 shillings made up one Australian dollar; the slang term for a shilling coin in Australia was "deener". The slang term for a shilling as currency unit was "bob", the same as in the United Kingdom. After 1966, shillings continued to circulate, as they were replaced by 10-cent coins of the same size and weight.

New Zealand shillings, twenty of which made up one New Zealand pound, were first issued in 1933 and featured the image of a Maori warrior carrying a taiaha "in a warlike attitude" on the reverse. In 1967, New Zealand's currency was decimalised and the shilling was replaced by a ten cent coin of the same size and weight. Ten cent coins minted through the remainder of the 1960s included the legend "ONE SHILLING" on the reverse. Smaller 10-cent coins were introduced in 2006. Shillings were used in Malta, prior to decimalisation in 1972, had a face value of five Maltese cents. In British Ceylon, an shilling was equivalent to eight fanams. With the replacement of the rixdollar by the rupee in 1852, a shilling was deemed to be equivalent to half a rupee. On the decimalisation of the currency in 1869, a shilling was deemed to be equivalent to 50 Ceylon cents; the term continued to be u

Four Million Smiles

Four Million Smiles was the theme of an advertising campaign in Singapore by the Singapore 2006 Organising Committee, sponsored by the government of Singapore. The advertising campaign encouraged Singaporeans to smile more in preparation for the 61st Annual Meetings of the International Monetary Fund, World Bank Group and their 16,000 delegates, it was launched by Prime Minister Lee Hsien Loong on 8 July 2006. A mural was created to welcome the visitors. Singaporeans were encouraged to submit photographs of them smiling through an official website or by Multimedia Messaging Service; these were compiled into the mural, those submitting had a chance of winning several lucky draws. While some agree that Singaporeans are cold in public and there needs to be encouragement of more visible goodwill in society, others saw the campaign as a form of social control. Critics argued that the campaign perpetuated racial discrimination and self-degradation of Singaporeans by encouraging them to smile in the presence of delegates just because they happen to be "ang mo" foreigners.

This includes a Straits Times article featuring recruitment calls by escort agencies for young, athletic girls between 18 and 20 to offer themselves for the expected spike in demand for escort services, sparking outrage from women's rights organisations. As parodies, Four Million Frowns and 400 Frowns projects were started online, but the police arrested a man over the latter. Welcome the world with a smile for Singapore 2006 - Channel NewsAsia

Covering relation

In mathematics order theory, the covering relation of a ordered set is the binary relation which holds between comparable elements that are immediate neighbours. The covering relation is used to graphically express the partial order by means of the Hasse diagram. Let X be a set with a partial order ≤; as usual, let < be the relation on X such that x < y if and only if x ≤ y and x ≠ y. Let x and y be elements of X. Y covers x, written x ⋖ y, if x < y and there is no element z such that x < z < y. Equivalently, y covers x if the interval is the two-element set; when x ⋖ y, it is said. Some authors use the term cover to denote any such pair in the covering relation. In a finite linearly ordered set, i + 1 covers i for all i between 1 and n − 1. In the Boolean algebra of the power set of a set S, a subset B of S covers a subset A of S if and only if B is obtained from A by adding one element not in A. In Young's lattice, formed by the partitions of all nonnegative integers, a partition λ covers a partition μ if and only if the Young diagram of λ is obtained from the Young diagram of μ by adding an extra cell.

The Hasse diagram depicting the covering relation of a Tamari lattice is the skeleton of an associahedron. The covering relation of any finite distributive lattice forms a median graph. On the real numbers with the usual total order ≤, the cover set is empty: no number covers another. If a ordered set is finite, its covering relation is the transitive reduction of the partial order relation; such ordered sets are therefore described by their Hasse diagrams. On the other hand, in a dense order, such as the rational numbers with the standard order, no element covers another. Knuth, Donald E; the Art of Computer Programming, Volume 4, Fascicle 4, Addison-Wesley, ISBN 0-321-33570-8. Stanley, Richard P. Enumerative Combinatorics, 1, Cambridge University Press, ISBN 0-521-55309-1. Brian A. Davey.