Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that.
One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, inversion, and complementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.
Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two. For example, musicians use the terms transposition and inversion where mathematicians would use translation and reflection. Furthermore, where musical set theory refers to ordered sets, mathematics would normally refer to tuples or sequences (though mathematics does speak of ordered sets, and although these can be seen to include the musical kind in some sense, they are far more involved).
The 2007 New Zealand raids were a series of armed police arrests conducted on Monday, 15 October 2007, in response to the discovery of an alleged paramilitary training camp in the Urewera mountain range near the town of Ruatoki in the eastern Bay of Plenty.
About 300 police, including members of the Armed Offenders Squad and Special Tactics Group, were involved in the arrests in which four guns and 230 rounds of ammunition were seized and 17 people arrested, all but one of them charged with firearms offences. According to police, the raids were a culmination of more than a year of surveillance that uncovered and monitored the training camps. Search warrants were executed under the Summary Proceedings Act to search for evidence relating to potential breaches of the Terrorism Suppression Act and the Arms Act.
On 29 October, police referred evidence gathered during the raids to the Solicitor-General to consider whether charges should be laid under the Terrorism Suppression Act. Authorisation for prosecutions under the Act is given by the Attorney-General though he has delegated this responsibility to Solicitor-General David Collins. On 8 November the Solicitor-General declined to press charges under the Terrorism Suppression Act, because of inadequacies of the legislation. According to Helen Clark, the Prime Minister at the time of the raids, one of the reasons police tried to lay charges under anti-terror legislation was because they could not use telephone interception evidence in prosecutions under the Arms Act.
Operation 40 was the code name for a Central Intelligence Agency-sponsored counterintelligence group composed of Cuban exiles. The group was formed to seize control of the Cuban government after the Bay of Pigs Invasion. Operation 40 continued to operate unofficially until it disbanded in 1970 due to allegations that an aircraft that was carrying cocaine and heroin in support of the group crashed in California.
It was approved by President Dwight D. Eisenhower in March 1960, after the January 1959 Cuban Revolution, and was presided over by Vice-president Richard Nixon. The group included Frank Sturgis (who would later become one of the Watergate burglars); Felix Rodriguez (a CIA officer who later was involved in the capture and summary execution of Che Guevara); Luis Posada Carriles (held in the US in 2010 on charges of illegal immigration, he is demanded by Venezuela for his key role in the execution of the 1976 Cubana Flight 455 bombing); Orlando Bosch (founder of the counterrevolutionary Coordination of United Revolutionary Organizations, that organized the 1976 murder of Chilean former minister Orlando Letelier); Rafael 'Chi Chi' Quintero; Virgilio Paz Romero; Pedro Luis Diaz Lanz; Bernard Barker; and Porter Goss.
The one hundred euro note (€100) is one of the higher value euro banknotes and has been used since the introduction of the euro (in its cash form) in 2002. The note is used daily by some 332 million Europeans and in the 23 countries which have it as their sole currency (with 22 legally adopting it).
It is the third largest note measuring 147 millimetres (5.8 in) × 82 millimetres (3.2 in) and has a green colour scheme. The hundred euro notes depict bridges and arches/doorways in the Baroque and Rococo style (between the 17th and 18th century).
The hundred euro note contains several complex security features such as watermarks, invisible ink, holograms and microprinting that document its authenticity. In May 2012, there were approximately 1,652,287,100 hundred euro banknotes in circulation in the eurozone.
The euro was founded on 1 January 1999, when it became the currency of over 300 million people in Europe. For the first three years of its existence it was an invisible currency, only used in accountancy. Euro cash was not introduced until 1 January 2002, when it replaced the national banknotes and coins of the countries in eurozone 12, such as the French franc and the Spanish peseta.
The ten euro note (€10) is the second-lowest value euro banknote and has been used since the introduction of the euro (in its cash form) in 2002. The note is used in the 23 countries which have it as their sole currency (with 22 legally adopting it); with a population of about 332 million.
It is the second-smallest note measuring 127x67mm with a red colour scheme. The ten euro banknotes depict bridges and arches/doorways in Romanesque architecture (between the 11th and 12th centuries).
The ten euro note contains several complex security features such as watermarks, invisible ink, holograms and microprinting that document its authenticity. In September 2011, there were approximately 2,005,149,600 ten euro banknotes in circulation around the eurozone.
The euro was founded on 1 January 1999, when it became the currency of over 300 million people in Europe. For the first three years of its existence it was an invisible currency, only used in accountancy. Euro cash was not introduced until 1 January 2002, when it replaced the national banknotes and coins of the countries in eurozone 12, such as the Italian lira and the German mark.
The 2 euro coin (€2) is the highest value euro coin and has been used since the introduction of the euro (in its cash form) in 2002. The coin is used in the 22 countries not including the vatican coin which have it as their sole currency (with 20 legally adopting it); with a population of about 332 million. The coin is made of two alloys: the inner part of nickel brass, the outer part of copper-nickel. All coins have a common reverse side and country-specific national sides. The coin has been used since 2002, with the present common side design dating from 2007.
The €2 coin is the coin subject to legal-tendercommemorative issues and hence there is a large number of national sides, including three issues of identical commemorative sides by all eurozone members.
The coin dates from 2002, when euro coins and notes were introduced in the 12 member eurozone and its related territories. The common side was designed by Luc Luycx, a Belgian artist who won a Europe-wide competition to design the new coins. The designs of the one and two-euro coins were intended to show the European Union (EU) as a whole with the then 15 countries more closely joined together than on the 10 to 50-cent coins (the 1-cent to 5-cent coins showed the EU as one, though intending to show its place in the world).
The Irish History Junior Certificate Examination is an achievement test offered in Ireland. It is one of a suite of Junior Certificate Examinations the country uses to assess students. It has two difficulty levels, Higher and Ordinary. This subject is not required at a national level. However, many schools make it compulsory. Most students choose to complete the Higher Level exam.
The Ordinary Level exam lasts 90 minutes. It includes four questions. The maximum score is 180.
The exam lasts 150 minutes. It includes six questions. The maximum score is 270.
Questions 1, 2 and 5 are mandatory. Only 10 of the 20 sub-questions in Question 3 are required. Question 4 includes two sections. One sub-question from each section must be answered. In Question 6, only two of four possible sub-questions need to be completed. The four sub-question topics are: