title: Richmond Palace

text: Richard II was the first English king to make Sheen his main residence in 1383. He took his bride Anne of Bohemia there. Twelve years later Richard was so distraught at the death of Anne at the age of 28, that he, according to Holinshed, "caused it [the manor] to be thrown down and defaced; whereas the former kings of this land, being wearied of the citie, used customarily thither to resort as to a place of pleasure, and serving highly to their recreation." For almost 20 years it lay in ruins until Henry V undertook rebuilding work in 1414. The first, pre-Tudor, version of the palace was known as "Sheen Palace". It was positioned roughly at , in what is now the garden of Trumpeters' House, between Richmond Green and the River. In 1414 Henry V also founded a Carthusian monastery there known as Sheen Priory, adjacent on the N. to the royal residence.


title: Richmond Palace

text: Henry VI continued the rebuilding in order that the palace might be worthy of the reception of his queen, Margaret of Anjou. Edward IV granted it to his queen for life.


title: Richmond Palace

text: In 1492, a great tournament was held at the Palace by Henry VII. On 23 December 1497 a fire destroyed most of the wooden buildings. Henry rebuilt it and named the new palace "Richmond" Palace after his title of Earl of Richmond. The earldom was seated at Richmond Castle, Yorkshire, from which it took its name. In 1502, the new palace witnessed the betrothal of Princess Margaret, daughter of Henry VII, to King James IV of Scotland. From this line eventually came the House of Stuart. In 1509 Henry VII died at Richmond Palace.


title: Richmond Palace

text: At Christmastide 1497 a great fire broke out in the king's private chambers, destroying a large portion of the palace. The Milanese ambassador, Raimondo Soncino, witnessed the blaze, and estimated the damage at 60,000 ducats, in modern money about $10 million or approximately £7 million. The fire lasted three hours and tore through the rest of the palace, causing panic and hundreds to flee. Hammerbeam roofs of the Middle Ages were a structural necessity as much as they were pretty architecture as they kept the heavy timbered roofs from caving in; they were the carpenter's equivalent of the stone vaulting found in Gothic cathedrals of the Middle Ages because as in famous examples, like Westminster Hall, they allowed the architect greater ability to achieve higher heights with thinner walls and evenly distributed the lateral weight. In as large a fire as described by Soncino the English oak beams of the great hall, a centrepiece of a royal Christmas, would have stood no chance of remaining upright and intact. They would have been engulfed in flames in the high temperatures well exceeding 270 °C. Much of the tapestry work of earlier ages was burnt to cinders, and losses included crown jewels and much of the royal wardrobe including a large amount of cloth of gold, at this time a luxury item only wearable by royalty and in the case of Sheen Palace it was a feature of the bedding.


title: Richmond Palace

text: Accounts refer to Henry Tudor, his mother, Margaret Beaufort, and his wife, Queen Elizabeth, running for their lives, with the king barely making it out in time: one of the corridors nearly collapsed on top of him. As it was the time of the Christmas revels, also present during the disaster were all but one of the royal children, and all under the age of 10: Margaret, Mary, and a six-year-old Henry VIII, each of them described as being hurried out in the arms of their nursemaids. For Queen Elizabeth, this would have been a horrible blow: records show that as a child in the 1470s this was where she spent much of her childhood and otherwise this palace would have had strong associations with her mother Elizabeth Woodville: Edward IV left Sheen to his wife in his will. Soncino reports all of the events outlined above, and also states in his accounts that the king "does not attach much importance to this loss. He purposes to build the chapel all in stone, and much finer than before."


title: Richmond Palace

text: Construction on the new palace began in 1498. Henry named his creation Richmond Palace, in honour of the title he held before acceding to the throne and the title he inherited from his father: Earl of Richmond. Though the palace did not survive the English Civil War, fragments of the edifice still remain along the bank of the Thames, as does Richmond Park, originally a royal hunting reserve that Henry Tudor and all members of the Tudors and early Stuarts used for their personal entertainment. Henry Tudor built a large and grand palace that became the centre of royal life for many years to come, a very important centre of the court of each Tudor monarch and James I. Drawings and descriptions of the palace survive as does the documentation of a 1970s excavation of the grounds, thus posterity has a fairly accurate idea of what the contents and features of the building were.


title: Richmond Palace

text: Richmond Palace was largely a building of brick and white stone in the latest styles of the times, with geometric octagonal towers, pepper-pot chimney caps, and ornate weathervanes made of brass. Though it retained the layout of Sheen Palace, new additions that would mark the Renaissance were to be found in this palace, for example, long galleries to display sculpture and portraiture. Henry VII also established a library and a richly appointed chapel. The windows were panelled, built to bring in more light than the tiny slit-like windows of a castle, built for defence. From its earliest it had inner courtyards designed for leisure, with several portions built for the royal family overlooking a large green. Richmond Palace covered ten acres of land and was large and well appointed enough to have its own orchards and walled gardens. It is known that Henry Tudor decorated his home with many gifts he accepted from Italian bankers in Venice, and the evidence for this and the other accoutrements survives in a 17th-century inventory taken of the palace that is now located in the British National Archives. The inventory also describes new tapestries he commissioned to replace the ones lost in the fire.


title: Richmond Palace

text: Later the same year, Henry VIII celebrated Christmas to Twelfth Night at Richmond with the first of his six wives, Catherine of Aragon. During those celebrations, says Mrs. A. T. Thomson, in her "Memoirs of the Court of Henry the Eighth":


title: Richmond Palace

text: On the night of the Epiphany (1510), a pageant was introduced into the hall at Richmond, representing a hill studded with gold and precious stones, and having on its summit a tree of gold, from which hung roses and pomegranates. From the declivity of the hill descended a lady richly attired, who, with the gentlemen, or, as they were then called, children of honour, danced a morris before the king. On another occasion, in the presence of the court, an artificial forest was drawn in by a lion and an antelope, the hides of which were richly embroidered with golden ornaments; the animals were harnessed with chains of gold, and on each sat a fair damsel in gay apparel. In the midst of the forest, which was thus introduced, appeared a gilded tower, at the end of which stood a youth, holding in his hands a garland of roses, as the prize of valour in a tournament which succeeded the pageant!"


title: Richmond Palace

text: Henry's son, Henry, Duke of Cornwall, was born there on New Year's Day, 1511, but died on 22 February. Some years later, the king received a present of Hampton Court from Wolsey, and in return the cardinal received permission to reside at the royal manor of Richmond, where he kept up so much state as to increase the growing ill-feeling against him. When he fell into disfavour he took up his residence at the Lodge in the 'great' park, and subsequently moved to the Priory.


title: Richmond Palace

text: In 1533 Richmond became the principal residence of Henry's daughter Mary after she was evicted from her previous residence of Beaulieu. Mary stayed at the palace until December of that year when she was ordered to Hatfield House to wait on the newly born Princess Elizabeth.


title: Richmond Palace

text: In 1540 Henry gave the palace to his fourth wife, Anne of Cleves, as part of her annulment settlement.


title: Richmond Palace

text: In 1554 Queen Mary I married Philip II of Spain. Forty-five years after her mother Catherine of Aragon had spent Christmas at Richmond Palace, they spent their honeymoon there (and at Hampton Court). Later that same year, her sister Elizabeth was taken to Richmond as a prisoner on her way to Woodstock.


title: Richmond Palace

text: Once Elizabeth became queen she spent much of her time at Richmond, as she enjoyed hunting stags in the "Newe Parke of Richmonde" (now the Old Deer Park). Elizabeth died there on 24 March 1603.


title: Richmond Palace

text: King James I preferred the Palace of Westminster to Richmond, but his eldest son Prince Henry was able to commission water-works for the garden designed by the French Huguenot, Salomon de Caus, and the Florentine Costantino de' Servi, shortly before his death in 1612. Before he became king, Charles I owned Richmond Palace and started to build his art collection whilst living there. Like Elizabeth, Charles enjoyed hunting stags, and in 1637 created a new area for this now known as Richmond Park, renaming Elizabeth's "Newe Parke" the "Old Deer Park". There continue to be red deer in Richmond Park today, possibly descendants of the original herd, free from hunting and relatively tame.


title: Richmond Palace

text: Charles I gave the palace with the manor to Queen Henrietta Maria, probably in 1626, and it became the home of the royal children. Within months of the execution of the king in 1649, Richmond Palace was surveyed by order of Parliament to see what it could fetch in terms of raw materials, and was sold for £13,000. Over the next ten years it was largely demolished, the stones being re-used as building materials.


title: Richmond Palace

text: Following the Restoration of the Monarchy in 1660, the Palace and manor were restored to Queen Henrietta Maria (d.1669), the mother of King Charles II and widow of the beheaded King Charles I, who during the Civil War had lived in exile in France. It was then in a dismantled condition, having suffered much dilapidation during the inter-regnum. The ruined palace was never rebuilt.


title: Richmond Palace

text: All the accounts which have come down to us describe the furniture and decorations of Richmond Palace as superb, exhibiting in tapestries the deeds of kings and heroes.


title: Richmond Palace

text: The survey taken in 1649 affords a minute description of the palace. The great hall was in length, and in breadth, having a screen at the lower end, over which was "fayr foot space in the higher end thereof, the pavement of square tile, well lighted and seated; at the north end having a turret, or clock-case, covered with lead, which is a special ornament to this building." The prince's lodgings are described as a "freestone building, three stories high, with "fourteen turrets" covered with lead," being "a very graceful ornament to the whole house, and perspicuous to the county round about." A round tower is mentioned, called the "Canted Tower," with a staircase of 124 steps. The chapel was long and broad, with cathedral-seats and pews. Adjoining the prince's garden was an open gallery, long, over which was a close gallery of similar length. Here was also a royal library. Three pipes supplied the palace with water, one from the white conduit in the new park, another from the conduit in the town fields, and the third from a conduit near the alms-houses in Richmond.


title: Richmond Palace

text: During 1997 the site was investigated in the Channel 4 programme "Time Team" which was broadcast in January 1998.


title: Richmond Palace

text: This palace was one of the first buildings in history to be equipped with a flushing lavatory, invented by Elizabeth I's godson, Sir John Harington. Henry VIII had earlier installed flushing latrines at Hampton Court.


title: Richmond Palace

text: Structures of the former palace that have survived include the Wardrobe, Trumpeters' House and the Gate House, all three of which are Grade I listed. The Gate House was built in 1501, and was let on a 65-year lease by the Crown Estate Commissioners in 1986. It has five bedrooms.


title: Angst

text: Angst is fear or anxiety ("anguish" is its Latinate equivalent, and the words "anxious" and "anxiety" are of similar origin). The dictionary definition for angst is a feeling of anxiety, apprehension, or insecurity.


title: Angst

text: The word "angst" was introduced into English from the Danish, Norwegian, and Dutch word and the German word . It is attested since the 19th century in English translations of the works of Søren Kierkegaard and Sigmund Freud. It is used in English to describe an intense feeling of apprehension, anxiety, or inner turmoil.


title: Angst

text: In other languages (with words from the Latin for "fear" or "panic"), the derived words differ in meaning; for example, as in the French and . The word "angst" has existed since the 8th century, from the Proto-Indo-European root "", "restraint" from which Old High German developed. It is pre-cognate with the Latin , "tensity, tightness" and , "choking, clogging"; compare to the Ancient Greek () "strangle".


title: Angst

text: In existentialist philosophy, the term "angst" carries a specific conceptual meaning. The use of the term was first attributed to Danish philosopher Søren Kierkegaard (1813–1855). In "The Concept of Anxiety" (also known as "The Concept of Dread"), Kierkegaard used the word "Angest" (in common Danish, "angst", meaning "dread" or "anxiety") to describe a profound and deep-seated condition. Where non-human animals are guided solely by instinct, said Kierkegaard, human beings enjoy a freedom of choice that we find both appealing and terrifying. It is the anxiety of understanding of being free when considering undefined possibilities of one's life and the immense responsibility of having the power of choice over them. Kierkegaard's concept of angst reappeared in the works of existentialist philosophers who followed, such as Friedrich Nietzsche, Jean-Paul Sartre, and Martin Heidegger, each of whom developed the idea further in individual ways. While Kierkegaard's angst referred mainly to ambiguous feelings about moral freedom within a religious personal belief system, later existentialists discussed conflicts of personal principles, cultural norms, and existential despair.


title: Angst

text: Existential angst makes its appearance in classical musical composition in the early twentieth century as a result of both philosophical developments and as a reflection of the war-torn times. Notable composers whose works are often linked with the concept include Gustav Mahler, Richard Strauss (operas ' and '), Claude Debussy (opera "", ballet "Jeux"), Jean Sibelius (especially the Fourth Symphony), Arnold Schoenberg ("A Survivor from Warsaw"), Alban Berg, Francis Poulenc (opera "Dialogues of the Carmelites"), Dmitri Shostakovich (opera "Lady Macbeth of Mtsensk", symphonies and chamber music), Béla Bartók (opera "Bluebeard's Castle"), and Krzysztof Penderecki (especially "Threnody to the Victims of Hiroshima").


title: Angst

text: Angst began to be discussed in reference to popular music in the mid- to late 1950s, amid widespread concerns over international tensions and nuclear proliferation. Jeff Nuttall's book "Bomb Culture" (1968) traced angst in popular culture to Hiroshima. Dread was expressed in works of folk rock such as Bob Dylan's "Masters of War" (1963) and "A Hard Rain's a-Gonna Fall". The term often makes an appearance in reference to punk rock, grunge, nu metal, and works of emo where expressions of melancholy, existential despair, or nihilism predominate.


title: Nuclear disarmament

text: Nuclear disarmament is the act of reducing or eliminating nuclear weapons. Its end state can also be a nuclear-weapons-free world, in which nuclear weapons are completely eliminated. The term denuclearization is also used to describe the process leading to complete nuclear disarmament.


title: Nuclear disarmament

text: Disarmament and non-proliferation treaties have been agreed upon because of the extreme danger intrinsic to nuclear war and the possession of nuclear weapons.


title: Nuclear disarmament

text: Proponents of nuclear disarmament say that it would lessen the probability of nuclear war occurring, especially accidentally. Critics of nuclear disarmament say that it would undermine deterrence and make conventional wars more common.


title: Nuclear disarmament

text: Nuclear disarmament groups include the Campaign for Nuclear Disarmament, Peace Action, Pugwash Conferences on Science and World Affairs, Greenpeace, Soka Gakkai International, International Physicians for the Prevention of Nuclear War, Mayors for Peace, Global Zero, the International Campaign to Abolish Nuclear Weapons, and the Nuclear Age Peace Foundation. There have been many large anti-nuclear demonstrations and protests. On June 12, 1982, one million people demonstrated in New York City's Central Park against nuclear weapons and for an end to the cold war arms race. It was the largest anti-nuclear protest and the largest political demonstration in American history.


title: Nuclear disarmament

text: In recent years, some U.S. elder statesmen have also advocated nuclear disarmament. Sam Nunn, William Perry, Henry Kissinger, and George Shultz have called upon governments to embrace the vision of a world free of nuclear weapons, and in various op-ed columns have proposed an ambitious program of urgent steps to that end. The four have created the Nuclear Security Project to advance this agenda. Organisations such as Global Zero, an international non-partisan group of 300 world leaders dedicated to eliminating all nuclear weapons, have also been established.


title: Nuclear disarmament

text: In 1945 in the New Mexico desert, American scientists conducted "Trinity," the first nuclear weapons test, marking the beginning of the atomic age. Even before the Trinity test, national leaders debated the impact of nuclear weapons on domestic and foreign policy. Also involved in the debate about nuclear weapons policy was the scientific community, through professional associations such as the Federation of Atomic Scientists and the Pugwash Conference on Science and World Affairs.


title: Nuclear disarmament

text: On August 6, 1945, towards the end of World War II, the "Little Boy" device was detonated over the Japanese city of Hiroshima. Exploding with a yield equivalent to 12,500 tonnes of TNT, the blast and thermal wave of the bomb destroyed nearly 50,000 buildings (including the headquarters of the 2nd General Army and Fifth Division) and killed 70,000–80,000 people outright, with total deaths being around 90,000–146,000. Detonation of the "Fat Man" device exploded over the Japanese city of Nagasaki three days later on August 9, 1945, destroying 60% of the city and killing 35,000–40,000 people outright, though up to 40,000 additional deaths may have occurred over some time after that. Subsequently, the world’s nuclear weapons stockpiles grew.


title: Nuclear disarmament

text: In 1946 the Truman administration commissioned the Acheson-Lilienthal Report, which proposed the international control of the nuclear fuel cycle, revealing atomic energy technology to the USSR, and the decommissioning of all existing nuclear weapons through the new United Nations (UN) system, via the United Nations Atomic Energy Commission (UNAEC). With key modifications, the report became US policy in the form of the Baruch Plan, which was presented to the UNAEC during its first meeting in June 1946. As Cold War tensions emerged, it became clear that Stalin wanted to develop his own atomic bomb and that the United States insisted on an enforcement regime that would have overridden the UN Security Council veto. This soon led to deadlock in the UNAEC.


title: Nuclear disarmament

text: Operation Crossroads was a series of nuclear weapon tests conducted by the United States at Bikini Atoll in the Pacific Ocean in the summer of 1946. Its purpose was to test the effect of nuclear weapons on naval ships. Pressure to cancel Operation Crossroads came from scientists and diplomats. Manhattan Project scientists argued that further nuclear testing was unnecessary and environmentally dangerous. A Los Alamos study warned "the water near a recent surface explosion will be a 'witch's brew' of radioactivity". To prepare the atoll for the nuclear tests, Bikini's native residents were evicted from their homes and resettled on smaller, uninhabited islands where they were unable to sustain themselves.


title: Nuclear disarmament

text: Radioactive fallout from nuclear weapons testing was first drawn to public attention in 1954 when a hydrogen bomb test in the Pacific contaminated the crew of the Japanese fishing boat "Lucky Dragon". One of the fishermen died in Japan seven months later. The incident caused widespread concern around the world and "provided a decisive impetus for the emergence of the anti-nuclear weapons movement in many countries". The anti-nuclear weapons movement grew rapidly because for many people the atomic bomb "encapsulated the very worst direction in which society was moving".


title: Nuclear disarmament

text: Peace movements emerged in Japan and in 1954 they converged to form a unified "Japanese Council Against Atomic and Hydrogen Bombs". Japanese opposition to the Pacific nuclear weapons tests was widespread, and "an estimated 35 million signatures were collected on petitions calling for bans on nuclear weapons". In the United Kingdom, the first Aldermaston March organised by the Direct Action Committee and supported by the Campaign for Nuclear Disarmament took place on Easter 1958, when several thousand people marched for four days from Trafalgar Square, London, to the Atomic Weapons Research Establishment close to Aldermaston in Berkshire, England, to demonstrate their opposition to nuclear weapons. CND organised Aldermaston marches into the late 1960s when tens of thousands of people took part in the four-day events.


title: Nuclear disarmament

text: On November 1, 1961, at the height of the Cold War, about 50,000 women brought together by Women Strike for Peace marched in 60 cities in the United States to demonstrate against nuclear weapons. It was the largest national women's peace protest of the 20th century.


title: Nuclear disarmament

text: In 1958, Linus Pauling and his wife presented the United Nations with the petition signed by more than 11,000 scientists calling for an end to nuclear-weapon testing. The "Baby Tooth Survey," headed by Dr Louise Reiss, demonstrated conclusively in 1961 that above-ground nuclear testing posed significant public health risks in the form of radioactive fallout spread primarily via milk from cows that had ingested contaminated grass. Public pressure and the research results subsequently led to a moratorium on above-ground nuclear weapons testing, followed by the Partial Test Ban Treaty, signed in 1963 by John F. Kennedy and Nikita Khrushchev. On the day that the treaty went into force, the Nobel Prize Committee awarded Pauling the Nobel Peace Prize, describing him as "Linus Carl Pauling, who ever since 1946 has campaigned ceaselessly, not only against nuclear weapons tests, not only against the spread of these armaments, not only against their very use, but against all warfare as a means of solving international conflicts." Pauling started the International League of Humanists in 1974. He was president of the scientific advisory board of the World Union for Protection of Life and also one of the signatories of the Dubrovnik-Philadelphia Statement.


title: Nuclear disarmament

text: In the 1980s, a movement for nuclear disarmament again gained strength in the light of the weapons build-up and statements of US President Ronald Reagan. Reagan had "a world free of nuclear weapons" as his personal mission, and was largely scorned for this in Europe. Reagan was able to start discussions on nuclear disarmament with Soviet Union. He changed the name "SALT" (Strategic Arms Limitation Talks) to "START" (Strategic Arms Reduction Talks).


title: Nuclear disarmament

text: On June 3, 1981, William Thomas launched the White House Peace Vigil in Washington, D.C. He was later joined on the vigil by anti-nuclear activists Concepcion Picciotto and Ellen Benjamin.


title: Nuclear disarmament

text: On June 12, 1982, one million people demonstrated in New York City's Central Park against nuclear weapons and for an end to the cold war arms race. It was the largest anti-nuclear protest and the largest political demonstration in American history. International Day of Nuclear Disarmament protests were held on June 20, 1983 at 50 sites across the United States. In 1986, hundreds of people walked from Los Angeles to Washington, D.C. in the Great Peace March for Global Nuclear Disarmament. There were many Nevada Desert Experience protests and peace camps at the Nevada Test Site during the 1980s and 1990s.


title: Nuclear disarmament

text: On May 1, 2005, 40,000 anti-nuclear/anti-war protesters marched past the United Nations in New York, 60 years after the atomic bombings of Hiroshima and Nagasaki. In 2008, 2009, and 2010, there have been protests about, and campaigns against, several new nuclear reactor proposals in the United States.


title: Nuclear disarmament

text: There is an annual protest against U.S. nuclear weapons research at Lawrence Livermore National Laboratory in California and in the 2007 protest, 64 people were arrested. There have been a series of protests at the Nevada Test Site and in the April 2007 Nevada Desert Experience protest, 39 people were cited by police. There have been anti-nuclear protests at Naval Base Kitsap for many years, and several in 2008.


title: Nuclear disarmament

text: In 2017, the International Campaign to Abolish Nuclear Weapons was awarded the Nobel Peace Prize "for its work to draw attention to the catastrophic humanitarian consequences of any use of nuclear weapons and for its ground-breaking efforts to achieve a treaty-based prohibition of such weapons".


title: Nuclear disarmament

text: One of the earliest peace organisations to emerge after the Second World War was the World Peace Council, which was directed by the Communist Party of the Soviet Union through the Soviet Peace Committee. Its origins lay in the Communist Information Bureau's (Cominform) doctrine, put forward 1947, that the world was divided between peace-loving progressive forces led by the Soviet Union and warmongering capitalist countries led by the United States. In 1949, Cominform directed that peace "should now become the pivot of the entire activity of the Communist Parties", and most western Communist parties followed this policy. Lawrence Wittner, a historian of the post-war peace movement, argues that the Soviet Union devoted great efforts to the promotion of the WPC in the early post-war years because it feared an American attack and American superiority of arms at a time when the USA possessed the atom bomb but the Soviet Union had not yet developed it.


title: Nuclear disarmament

text: In 1950, the WPC launched its Stockholm Appeal calling for the absolute prohibition of nuclear weapons. The campaign won support, collecting, it is said, 560 million signatures in Europe, most from socialist countries, including 10 million in France (including that of the young Jacques Chirac), and 155 million signatures in the Soviet Union – the entire adult population. Several non-aligned peace groups who had distanced themselves from the WPC advised their supporters not to sign the Appeal.


title: Nuclear disarmament

text: The WPC had uneasy relations with the non-aligned peace movement and has been described as being caught in contradictions as "it sought to become a broad world movement while being instrumentalized increasingly to serve foreign policy in the Soviet Union and nominally socialist countries." From the 1950s until the late 1980s it tried to use non-aligned peace organizations to spread the Soviet point of view. At first there was limited co-operation between such groups and the WPC, but western delegates who tried to criticize the Soviet Union or the WPC's silence about Russian armaments were often shouted down at WPC conferences and by the early 1960s they had dissociated themselves from the WPC.


title: Nuclear disarmament

text: After the 1986 Reykjavik Summit between U.S. President Ronald Reagan and the new Soviet General Secretary Mikhail Gorbachev, the United States and the Soviet Union concluded two important nuclear arms reduction treaties: the INF Treaty (1987) and START I (1991). After the end of the Cold War, the United States and the Russian Federation concluded the Strategic Offensive Reductions Treaty (2003) and the New START Treaty (2010). The US withdrew from the INF Treaty in 2019 under president Donald Trump, and launched the United States–Russia Strategic Stability Dialogue (SSD) in 2021 under president Joe Biden.


title: Nuclear disarmament

text: When the extreme danger intrinsic to nuclear war and the possession of nuclear weapons became apparent to all sides during the Cold War, a series of disarmament and nonproliferation treaties were agreed upon between the United States, the Soviet Union, and several other states throughout the world. Many of these treaties involved years of negotiations, and seemed to result in important steps in arms reductions and reducing the risk of nuclear war.


title: Nuclear disarmament

text: Only one country (South Africa) has been known to ever dismantle an indigenously-developed nuclear arsenal completely. The apartheid government of South Africa produced half a dozen crude fission weapons during the 1980s, but they were dismantled in the early 1990s.


title: Nuclear disarmament

text: In its landmark resolution 1653 of 1961, "Declaration on the prohibition of the use of nuclear and thermo-nuclear weapons," the UN General Assembly stated that use of nuclear weaponry “would exceed even the scope of war and cause indiscriminate suffering and destruction to mankind and civilization and, as such, is contrary to the rules of international law and to the laws of humanity”.


title: Nuclear disarmament

text: The UN Office for Disarmament Affairs (UNODA) is a department of the United Nations Secretariat established in January 1998 as part of the United Nations Secretary-General Kofi Annan's plan to reform the UN as presented in his report to the General Assembly in July 1997.


title: Nuclear disarmament

text: Its goal is to promote nuclear disarmament and non-proliferation and the strengthening of the disarmament regimes in respect to other weapons of mass destruction, chemical and biological weapons. It also promotes disarmament efforts in the area of conventional weapons, especially land mines and small arms, which are often the weapons of choice in contemporary conflicts.


title: Nuclear disarmament

text: Following the retirement of Sergio Duarte in February 2012, Angela Kane was appointed as the new High Representative for Disarmament Affairs.


title: Nuclear disarmament

text: On July 7, 2017, a UN conference adopted the Treaty on the Prohibition of Nuclear Weapons with the backing of 122 states. It opened for signature on September 20, 2017.


title: Nuclear disarmament

text: Despite a general trend toward disarmament in the early 2000s, the George W. Bush administration repeatedly pushed to fund policies that would allegedly make nuclear weapons more usable in the post–Cold War environment. To date the U.S. Congress has refused to fund many of these policies. However, some feel that even considering such programs harms the credibility of the United States as a proponent of nonproliferation.


title: Nuclear disarmament

text: Former U.S. officials Henry Kissinger, George Shultz, Bill Perry, and Sam Nunn (aka 'The Gang of Four' on nuclear deterrence) proposed in January 2007 that the United States rededicate itself to the goal of eliminating nuclear weapons, concluding: "We endorse setting the goal of a world free of nuclear weapons and working energetically on the actions required to achieve that goal." Arguing a year later that "with nuclear weapons more widely available, deterrence is decreasingly effective and increasingly hazardous," the authors concluded that although "it is tempting and easy to say we can't get there from here, [...] we must chart a course toward that goal." During his presidential campaign, former U.S. President Barack Obama pledged to "set a goal of a world without nuclear weapons, and pursue it."


title: Nuclear disarmament

text: The United States has taken the lead in ensuring that nuclear materials globally are properly safeguarded. A popular program that has received bipartisan domestic support for over a decade is the Cooperative Threat Reduction Program (CTR). While this program has been deemed a success, many believe that its funding levels need to be increased so as to ensure that all dangerous nuclear materials are secured in the most expeditious manner possible. The CTR program has led to several other innovative and important nonproliferation programs that need to continue to be a budget priority in order to ensure that nuclear weapons do not spread to actors hostile to the United States.


title: Nuclear disarmament

text: While the vast majority of states have adhered to the stipulations of the Nuclear Nonproliferation Treaty, a few states have either refused to sign the treaty or have pursued nuclear weapons programs while not being members of the treaty. Many view the pursuit of nuclear weapons by these states as a threat to nonproliferation and world peace.


title: Nuclear disarmament

text: The precise use of terminology in the context of disarmament may have important implications for political Signaling theory. In the case of North Korea, "denuclearization" has historically been interpreted as different from "disarmament" by including withdrawal of American nuclear capabilities from the region. More recently, this term has become provocative due to its comparisons to the after disarmament. The Biden Administration has been criticized for its reaffirming of a strategy of denuclearization with Korea and Japan, as opposed to a "freeze" or "pause" on new nuclear developments.


title: Nuclear disarmament

text: Similarly, the term "irreversible" has been argued to set an impossible standard for states to disarm.


title: Nuclear disarmament

text: Eliminating nuclear weapons has long been an aim of the pacifist left. But now many mainstream politicians, academic analysts, and retired military leaders also advocate nuclear disarmament. Sam Nunn, William Perry, Henry Kissinger, and George Shultz have called upon governments to embrace the vision of a world free of nuclear weapons, and in three "Wall Street Journal" opeds proposed an ambitious program of urgent steps to that end. The four have created the Nuclear Security Project to advance this agenda. Nunn reinforced that agenda during a speech at the Harvard Kennedy School on October 21, 2008, saying, "I’m much more concerned about a terrorist without a return address that cannot be deterred than I am about deliberate war between nuclear powers. You can’t deter a group who is willing to commit suicide. We are in a different era. You have to understand the world has changed." In 2010, the four were featured in a documentary film entitled "Nuclear Tipping Point". The film is a visual and historical depiction of the ideas laid forth in the Wall Street Journal op-eds and reinforces their commitment to a world without nuclear weapons and the steps that can be taken to reach that goal.


title: Nuclear disarmament

text: Global Zero is an international non-partisan group of 300 world leaders dedicated to achieving nuclear disarmament. The initiative, launched in December 2008, promotes a phased withdrawal and verification for the destruction of all devices held by official and unofficial members of the nuclear club. The Global Zero campaign works toward building an international consensus and a sustained global movement of leaders and citizens for the elimination of nuclear weapons. Goals include the initiation of United States-Russia bilateral negotiations for reductions to 1,000 total warheads each and commitments from the other key nuclear weapons countries to participate in multilateral negotiations for phased reductions of nuclear arsenals. Global Zero works to expand the diplomatic dialogue with key governments and continue to develop policy proposals on the critical issues related to the elimination of nuclear weapons.


title: Nuclear disarmament

text: The International Conference on Nuclear Disarmament took place in Oslo in February 2008, and was organized by The Government of Norway, the Nuclear Threat Initiative and the Hoover Institute. The Conference was entitled "Achieving the Vision of a World Free of Nuclear Weapons" and had the purpose of building consensus between nuclear weapon states and non-nuclear weapon states in relation to the Nuclear Non-proliferation Treaty.


title: Nuclear disarmament

text: The Tehran International Conference on Disarmament and Non-Proliferation took place in Tehran in April 2010. The conference was held shortly after the signing of the New START, and resulted in a call of action toward eliminating all nuclear weapons. Representatives from 60 countries were invited to the conference. Non-governmental organizations were also present.


title: Nuclear disarmament

text: Among the prominent figures who have called for the abolition of nuclear weapons are "the philosopher Bertrand Russell, the entertainer Steve Allen, CNN’s Ted Turner, former Senator Claiborne Pell, Notre Dame president Theodore Hesburgh, South African Bishop Desmond Tutu and the Dalai Lama".


title: Nuclear disarmament

text: Others have argued that nuclear weapons have made the world relatively safer, with peace through deterrence and through the stability–instability paradox, including in south Asia. Kenneth Waltz has argued that nuclear weapons have created a nuclear peace, and further nuclear weapon proliferation might even help avoid the large scale conventional wars that were so common prior to their invention at the end of World War II. In the July 2012 issue of Foreign Affairs Waltz took issue with the view of most U.S., European, and Israeli, commentators and policymakers that a nuclear-armed Iran would be unacceptable. Instead Waltz argues that it would probably be the best possible outcome, as it would restore stability to the Middle East by balancing Israel's regional monopoly on nuclear weapons. Professor John Mueller of Ohio State University, the author of "Atomic Obsession", has also dismissed the need to interfere with Iran's nuclear program and expressed that arms control measures are counterproductive. During a 2010 lecture at the University of Missouri, which was broadcast by C-SPAN, Dr. Mueller has also argued that the threat from nuclear weapons, especially nuclear terrorism, has been exaggerated, both in the popular media and by officials.


title: Nuclear disarmament

text: Former Secretary Kissinger says there is a new danger, which cannot be addressed by deterrence: "The classical notion of deterrence was that there was some consequences before which aggressors and evildoers would recoil. In a world of suicide bombers, that calculation doesn’t operate in any comparable way". George Shultz has said, "If you think of the people who are doing suicide attacks, and people like that get a nuclear weapon, they are almost by definition not deterrable".


title: Nuclear disarmament

text: Andrew Bacevich wrote that there is no feasible scenario under which the US could sensibly use nuclear weapons:For the United States, they are becoming unnecessary, even as a deterrent. Certainly, they are unlikely to dissuade the adversaries most likely to employ such weapons against us -- Islamic extremists intent on acquiring their own nuclear capability. If anything, the opposite is true. By retaining a strategic arsenal in readiness (and by insisting without qualification that the dropping of atomic bombs on two Japanese cities in 1945 was justified), the United States continues tacitly to sustain the view that nuclear weapons play a legitimate role in international politics ... .In "The Limits of Safety", Scott Sagan documented numerous incidents in US military history that could have produced a nuclear war by accident. He concluded:while the military organizations controlling U.S. nuclear forces during the Cold War performed this task with less success than we know, they performed with more success than we "should" have reasonably predicted. The problems identified in this book were not the product of incompetent organizations. They reflect the inherent limits of organizational safety. Recognizing that simple truth is the first and most important step toward a safer future.


title: Nuclear disarmament

text: On 3 January 2022, the permanent members of the United Nations Security Council, China, France, Russia, Britain, and the United States issued a statement on prevention of nuclear war, affirming that "a nuclear war cannot be won and must never be fought."


title: Liz White (actress)

text: Elizabeth White (born 11 August 1979) is an English actress, known for her roles as Annie Cartwright in the BBC series "Life on Mars" and Emma Keane in the Channel 4 school-based drama series "Ackley Bridge".


title: Liz White (actress)

text: White's other prominent TV roles were in series 1 of the ITV drama "The Fixer", playing Jess Mercer, the sister of John Mercer. She also played Shannon in "The Empresses' New Clothes", an episode of "Fairy Tales", which were the BBC's modern takes on classic children's stories. In April 2011, she appeared in the BBC adaptation "The Crimson Petal and the White".


title: Liz White (actress)

text: She featured in the music video for Bush's final single "Inflatable", and starred in the Hammer Films 2012 adaptation of "The Woman in Black" as the eponymous woman. In July 2014, White starred as Melissa in episodes 1 and 2 of the original audio drama 'Osiris' by Everybodyelse Productions, and in 2014 as Lizzie Mottershead in BBC One's "Our Zoo", a drama series about the man who created Chester Zoo and the effect it had on his family.


title: Liz White (actress)

text: On stage, she starred in the lead role of Heavenly Critchfield in Tennessee Williams' "Spring Storm" at the National Theatre in London in 2010, transferred from The Royal & Derngate Northampton production where it premiered in 2009. In 2011, she appeared in "A Woman Killed with Kindness" by Thomas Heywood at the Lyttelton at the National Theatre in 2011, where she appeared in 2013 again in a double role in Simon Stephens' play "Port".


title: Liz White (actress)

text: In October 2014, she appeared as Chrysothemis in "Electra" by Sophocles opposite Kristin Scott Thomas at the Old Vic Theatre in London, which also starred Peter Wight who played her father-in-law in the BBC series "Our Zoo".


title: Liz White (actress)

text: In 2017, it was announced that White would appear in a revival of Jim Cartwright's play "Road" at the Royal Court Theatre Later that year, she began appearing in the Channel 4 drama series "Ackley Bridge" as Emma Keane, a role she portrayed until 2019.


title: Liz White (actress)

text: In 2019, White portrayed Joy Davidman at the Chichester Festival Theatre's production of Shadowlands, along with National Youth Theatre actors Hugh Bonneville and Andrew Havill.


title: Yamina

text: Yamina or Yemina (; ) is an Israeli political alliance of right-wing parties that originally included the New Right and the Union of Right-Wing Parties (a union of The Jewish Home and Tkuma). The current incarnation of the alliance includes only the New Right, as The Jewish Home left the alliance on 14 July 2020, and the Religious Zionist Party left on 20 January 2021.


title: Yamina

text: The list was created ahead of the September 2019 Israeli legislative election, in which Yamina secured seven seats in the Knesset. The alliance was expected to split on 6 October, with the New Right as its own faction, while Tkuma and the Jewish Home will stay together, though the alliance continued to negotiate as a single bloc in the aftermath of the election. The meeting on 6 October was postponed, with some citing disagreements on whether Yamina should split, while others referred to it as a "technical" matter. The alliance did split on 10 October 2019, and re-formed on 15 January 2020 in the run-up to the 2020 Israeli legislative election.


title: Yamina

text: On 21 July 2019, after not making it past the electoral threshold in the April 2019 Israeli legislative election, New Right leader Naftali Bennett decided to give leadership of the party to Ayelet Shaked. In her opening leadership speech, Shaked declared that she will seek to unite with the Union of Right-Wing Parties (URWP) and other right-wing parties.


title: Yamina

text: The following day, negotiations with the URWP began. The negotiations initially stalled, as URWP leader Rafi Peretz was unwilling to concede leadership of the list to Shaked, and disagreements arose over how many spots each of the three involved parties would receive on the list. Another subject that arose in the negotiations was whether the radical former URWP member Otzma Yehudit should be included in the new joint list.


title: Yamina

text: Sara Netanyahu (the wife of the former prime minister) was recorded speaking with Rafi Peretz' wife, Michal Peretz, in an attempt to convince Peretz to retain his number one slot on the list; she was unsuccessful. It was also revealed that Benjamin Netanyahu was involved (despite his denial). The URWP and the New Right agreed to a joint run on 29 July 2019, with the New Right's Ayelet Shaked leading the joint list. As part of the agreement, the alliance declared that they would negotiate together to establish a right-wing government under Benjamin Netanyahu.


title: Yamina

text: On 22 April 2020, it was reported that Bennett was now "considering all options" for Yamina's political future, including departing from Netanyahu's government, which had just agreed to form a joint government with leader of the opposition Blue and White party Benny Gantz, and joining the opposition. Bennett was reported to be unhappy with the new coalition government's decision to hold back on the issue of judicial reform.


title: Yamina

text: In May 2020, Yamina announced that it would go to opposition. The day before, Peretz, the leader of The Jewish Home, had split from the party, and would be named as the Minister of Jerusalem in the thirty-fifth government of Israel. On 17 May 2020, Bennett met with Gantz, who also succeeded him as Defence Minister, and declared that Yamina was now a "head held high" member of the opposition.


title: Yamina

text: Tkuma, which rebranded as the Religious Zionist Party on 7 January 2021, split from Yamina on 20 January. On 9 May 2021, it was reported that Bennett and Yesh Atid leader Yair Lapid had made major headway in the coalition talks for forming a new Israeli government. On 30 May 2021, Bennett announced in a televised address that Yamina would join a unity government with Yair Lapid after all but one Yamina MK agreed to back this decision. A poll at the time found that 61% of Yamina voters would not vote for the party due to it being part of the unity government.


title: Yamina

text: Yamina announced on 27 July 2022 that it had allied with Derekh Eretz as the Zionist Spirit alliance to contest the 2022 Israeli legislative election. Yamina left the alliance on 11 September 2022, at the insistence of The Jewish Home, which had asked on 9 September that Shaked split from Derekh Eretz as a prerequisite for a joint run between itself and Shaked.


title: Yamina

text: Party members of The Jewish Home (including Hagit Moshe and Yossi Brodny) had ratified an agreement on a joint run between Yamina and itself two days later. The joint run was expected to be announced on 12 September, though it was not held that day due to disagreements within The Jewish Home on the details. The announcement was made the next day and the joint run was approved by the central committee of The Jewish Home on 14 September.


title: Yamina

text: Alongside these united principles, each party retains its own independent platform. Thus, the New Right represents the more "liberal" Religious and Secular right, The Jewish Home represents "mainstream" Religious Zionism, while Tkuma represents the more hawkish and Chardal Religious Zionists.


title: Allen Payne

text: Allen Payne (born Allen Roberts on July 7, 1968) is an American actor best known for his role as Jason Alexander in the 1994 drama film "Jason's Lyric", as well as his portrayal of C.J. Payne on the family sitcom "Tyler Perry's House of Payne" (2006–present). Payne is also known for his portrayal of Lance Rodman on NBC's "The Cosby Show" during its final two seasons. On film, Payne also played Gerald "Gee Money" Wells in the 1991 film "New Jack City", and Detective Justice in the 1995 film "Vampire in Brooklyn".


title: Allen Payne

text: Payne was born Allen Roberts in the Harlem area of New York City, the eldest son of Allen Roberts and Barbara Reeves. He attended Pennsauken High School in Pennsauken Township, New Jersey.


title: Allen Payne

text: Payne's first television role was in a 1990 episode of "The Cosby Show". Over the span of two seasons, he portrayed Charmaine's boyfriend, Lance Rodman. Payne subsequently appeared in episodes of "The Fresh Prince Of Bel-Air" and "Malcolm & Eddie".


title: Allen Payne

text: Payne has appeared in many films. He played "Dead Mike" in the Nelson George-produced and George and Chris Rock-written hip-hop parody "CB4". He also appeared in "New Jack City", "Jason's Lyric", "Vampire in Brooklyn", "Double Platinum", and "The Perfect Storm". Beginning in 2006, he starred as C.J. Payne on "Tyler Perry's House of Payne". He also appeared in a Stacy Lattisaw video "I'm Not The Same Girl".


title: Allen Payne

text: In 2022, he also stars and reprised his role as "Gee Money" in the stage adaptation of "New Jack City: Live on Stage", produced by playwright Je'Caryous Johnson.


title: Real analysis

text: In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability.


title: Real analysis

text: Real analysis is distinguished from complex analysis, which deals with the study of complex numbers and their functions.


title: Real analysis

text: The theorems of real analysis rely on the properties of the real number system, which must be established. The real number system consists of an uncountable set (formula_1), together with two binary operations denoted and , and an order denoted . The operations make the real numbers a field, and, along with the order, an ordered field. The real number system is the unique "complete ordered field", in the sense that any other complete ordered field is isomorphic to it. Intuitively, completeness means that there are no 'gaps' in the real numbers. This property distinguishes the real numbers from other ordered fields (e.g., the rational numbers formula_2) and is critical to the proof of several key properties of functions of the real numbers. The completeness of the reals is often conveniently expressed as the "least upper bound property" (see below).


title: Real analysis

text: The real numbers have various lattice-theoretic properties that are absent in the complex numbers. Also, the real numbers form an ordered field, in which sums and products of positive numbers are also positive. Moreover, the ordering of the real numbers is total, and the real numbers have the least upper bound property: "Every nonempty subset of formula_1 that has an upper bound has a least upper bound that is also a real number." These order-theoretic properties lead to a number of fundamental results in real analysis, such as the monotone convergence theorem, the intermediate value theorem and the mean value theorem.


title: Real analysis

text: However, while the results in real analysis are stated for real numbers, many of these results can be generalized to other mathematical objects. In particular, many ideas in functional analysis and operator theory generalize properties of the real numbers – such generalizations include the theories of Riesz spaces and positive operators. Also, mathematicians consider real and imaginary parts of complex sequences, or by pointwise evaluation of operator sequences.


title: Real analysis

text: Many of the theorems of real analysis are consequences of the topological properties of the real number line. The order properties of the real numbers described above are closely related to these topological properties. As a topological space, the real numbers has a "standard topology", which is the order topology induced by order formula_4. Alternatively, by defining the "metric" or "distance function" formula_5 using the absolute value function as the real numbers become the prototypical example of a metric space. The topology induced by metric formula_6 turns out to be identical to the standard topology induced by order formula_4. Theorems like the intermediate value theorem that are essentially topological in nature can often be proved in the more general setting of metric or topological spaces rather than in formula_1 only. Often, such proofs tend to be shorter or simpler compared to classical proofs that apply direct methods.


title: Real analysis

text: A sequence is a function whose domain is a countable, totally ordered set. The domain is usually taken to be the natural numbers, although it is occasionally convenient to also consider bidirectional sequences indexed by the set of all integers, including negative indices.


title: Real analysis

text: Of interest in real analysis, a real-valued sequence, here indexed by the natural numbers, is a map formula_9. Each formula_10 is referred to as a term (or, less commonly, an element) of the sequence. A sequence is rarely denoted explicitly as a function; instead, by convention, it is almost always notated as if it were an ordered ∞-tuple, with individual terms or a general term enclosed in parentheses:


title: Real analysis

text: A sequence that tends to a limit (i.e., formula_12 exists) is said to be convergent; otherwise it is divergent. ("See the section on limits and convergence for details.") A real-valued sequence formula_13 is bounded if there exists formula_14 such that formula_15 for all formula_16. A real-valued sequence formula_13 is monotonically increasing or decreasing if


title: Real analysis

text: holds, respectively. If either holds, the sequence is said to be monotonic. The monotonicity is strict if the chained inequalities still hold with formula_20 or formula_21 replaced by < or >.


title: Real analysis

text: Given a sequence formula_13, another sequence formula_23 is a subsequence of formula_13 if formula_25 for all positive integers formula_26 and formula_27 is a strictly increasing sequence of natural numbers.


title: Real analysis

text: Roughly speaking, a limit is the value that a function or a sequence "approaches" as the input or index approaches some value. (This value can include the symbols formula_28 when addressing the behavior of a function or sequence as the variable increases or decreases without bound.) The idea of a limit is fundamental to calculus (and mathematical analysis in general) and its formal definition is used in turn to define notions like continuity, derivatives, and integrals. (In fact, the study of limiting behavior has been used as a characteristic that distinguishes calculus and mathematical analysis from other branches of mathematics.)


title: Real analysis

text: The concept of limit was informally introduced for functions by Newton and Leibniz, at the end of the 17th century, for building infinitesimal calculus. For sequences, the concept was introduced by Cauchy, and made rigorous, at the end of the 19th century by Bolzano and Weierstrass, who gave the modern ε-δ definition, which follows.


title: Real analysis

text: Definition. Let formula_29 be a real-valued function defined on We say that formula_30 tends to formula_31 as formula_32 approaches formula_33, or that the limit of formula_30 as formula_32 approaches formula_33 is formula_31 if, for any formula_38, there exists formula_39 such that for all formula_40, formula_41 implies that formula_42. We write this symbolically as


title: Real analysis

text: Intuitively, this definition can be thought of in the following way: We say that formula_45 as formula_46, when, given any positive number formula_47, no matter how small, we can always find a formula_48, such that we can guarantee that formula_30 and formula_31 are less than formula_47 apart, as long as formula_32 (in the domain of formula_29) is a real number that is less than formula_48 away from formula_33 but distinct from formula_33. The purpose of the last stipulation, which corresponds to the condition formula_57 in the definition, is to ensure that formula_58 does not imply anything about the value of formula_59 itself. Actually, formula_33 does not even need to be in the domain of formula_29 in order for formula_62 to exist.


title: Real analysis

text: In a slightly different but related context, the concept of a limit applies to the behavior of a sequence formula_13 when formula_64 becomes large.


title: Real analysis

text: Definition. Let formula_13 be a real-valued sequence. We say that formula_13 converges to formula_67 if, for any formula_68, there exists a natural number formula_69 such that formula_70 implies that formula_71. We write this symbolically as


title: Real analysis

text: Generalizing to a real-valued function of a real variable, a slight modification of this definition (replacement of sequence formula_13 and term formula_77 by function formula_29 and value formula_30 and natural numbers formula_69 and formula_64 by real numbers formula_82 and formula_32, respectively) yields the definition of the limit of formula_30 as formula_32 increases without bound, notated formula_86. Reversing the inequality formula_87 to formula_88 gives the corresponding definition of the limit of formula_30 as formula_32 "decreases" "without bound",


title: Real analysis

text: Sometimes, it is useful to conclude that a sequence converges, even though the value to which it converges is unknown or irrelevant. In these cases, the concept of a Cauchy sequence is useful.


title: Real analysis

text: Definition. Let formula_13 be a real-valued sequence. We say that formula_13 is a Cauchy sequence if, for any formula_68, there exists a natural number formula_69 such that formula_95 implies that formula_96.


title: Real analysis

text: It can be shown that a real-valued sequence is Cauchy if and only if it is convergent. This property of the real numbers is expressed by saying that the real numbers endowed with the standard metric, formula_97, is a complete metric space. In a general metric space, however, a Cauchy sequence need not converge.


title: Real analysis

text: In addition, for real-valued sequences that are monotonic, it can be shown that the sequence is bounded if and only if it is convergent.


title: Real analysis

text: In addition to sequences of numbers, one may also speak of "sequences of functions" "on" formula_98, that is, infinite, ordered families of functions formula_99, denoted formula_100, and their convergence properties. However, in the case of sequences of functions, there are two kinds of convergence, known as "pointwise convergence" and "uniform convergence", that need to be distinguished.


title: Real analysis

text: Roughly speaking, pointwise convergence of functions formula_101 to a limiting function formula_102, denoted formula_103, simply means that given any formula_40, formula_105 as formula_106. In contrast, uniform convergence is a stronger type of convergence, in the sense that a uniformly convergent sequence of functions also converges pointwise, but not conversely. Uniform convergence requires members of the family of functions, formula_101, to fall within some error formula_68 of formula_29 for "every value of formula_40", whenever formula_70, for some integer formula_69. For a family of functions to uniformly converge, sometimes denoted formula_113, such a value of formula_69 must exist for any formula_38 given, no matter how small. Intuitively, we can visualize this situation by imagining that, for a large enough formula_69, the functions formula_117 are all confined within a 'tube' of width formula_118 about formula_29 (that is, between formula_120 and formula_121) "for every value in their domain" formula_122.


title: Real analysis

text: The distinction between pointwise and uniform convergence is important when exchanging the order of two limiting operations (e.g., taking a limit, a derivative, or integral) is desired: in order for the exchange to be well-behaved, many theorems of real analysis call for uniform convergence. For example, a sequence of continuous functions (see below) is guaranteed to converge to a continuous limiting function if the convergence is uniform, while the limiting function may not be continuous if convergence is only pointwise. Karl Weierstrass is generally credited for clearly defining the concept of uniform convergence and fully investigating its implications.


title: Real analysis

text: Compactness is a concept from general topology that plays an important role in many of the theorems of real analysis. The property of compactness is a generalization of the notion of a set being "closed" and "bounded". (In the context of real analysis, these notions are equivalent: a set in Euclidean space is compact if and only if it is closed and bounded.) Briefly, a closed set contains all of its boundary points, while a set is bounded if there exists a real number such that the distance between any two points of the set is less than that number. In formula_1, sets that are closed and bounded, and therefore compact, include the empty set, any finite number of points, closed intervals, and their finite unions. However, this list is not exhaustive; for instance, the set formula_124 is a compact set; the Cantor ternary set formula_125 is another example of a compact set. On the other hand, the set formula_126 is not compact because it is bounded but not closed, as the boundary point 0 is not a member of the set. The set formula_127 is also not compact because it is closed but not bounded.


title: Real analysis

text: This definition also holds for Euclidean space of any finite dimension, formula_129, but it is not valid for metric spaces in general. The equivalence of the definition with the definition of compactness based on subcovers, given later in this section, is known as the Heine-Borel theorem.


title: Real analysis

text: A more general definition that applies to all metric spaces uses the notion of a subsequence (see above).


title: Real analysis

text: Definition. A set formula_122 in a metric space is compact if every sequence in formula_122 has a convergent subsequence.


title: Real analysis

text: This particular property is known as "subsequential compactness". In formula_1, a set is subsequentially compact if and only if it is closed and bounded, making this definition equivalent to the one given above. Subsequential compactness is equivalent to the definition of compactness based on subcovers for metric spaces, but not for topological spaces in general.


title: Real analysis

text: The most general definition of compactness relies on the notion of "open covers" and "subcovers", which is applicable to topological spaces (and thus to metric spaces and formula_1 as special cases). In brief, a collection of open sets formula_134 is said to be an "open cover" of set formula_135 if the union of these sets is a superset of formula_135. This open cover is said to have a "finite subcover" if a finite subcollection of the formula_134 could be found that also covers formula_135.


title: Real analysis

text: Definition. A set formula_135 in a topological space is compact if every open cover of formula_135 has a finite subcover.


title: Real analysis

text: Compact sets are well-behaved with respect to properties like convergence and continuity. For instance, any Cauchy sequence in a compact metric space is convergent. As another example, the image of a compact metric space under a continuous map is also compact.


title: Real analysis

text: A function from the set of real numbers to the real numbers can be represented by a graph in the Cartesian plane; such a function is continuous if, roughly speaking, the graph is a single unbroken curve with no "holes" or "jumps".


title: Real analysis

text: There are several ways to make this intuition mathematically rigorous. Several definitions of varying levels of generality can be given. In cases where two or more definitions are applicable, they are readily shown to be equivalent to one another, so the most convenient definition can be used to determine whether a given function is continuous or not. In the first definition given below, formula_141 is a function defined on a non-degenerate interval formula_142 of the set of real numbers as its domain. Some possibilities include formula_143, the whole set of real numbers, an open interval formula_144 or a closed interval formula_145 Here, formula_67 and formula_147 are distinct real numbers, and we exclude the case of formula_142 being empty or consisting of only one point, in particular.


title: Real analysis

text: Definition. If formula_149 is a non-degenerate interval, we say that formula_150 is continuous at formula_151 if formula_152. We say that formula_29 is a continuous map if formula_29 is continuous at every formula_151.


title: Real analysis

text: In contrast to the requirements for formula_29 to have a limit at a point formula_157, which do not constrain the behavior of formula_29 at formula_157 itself, the following two conditions, in addition to the existence of formula_160, must also hold in order for formula_29 to be continuous at formula_157: (i) formula_29 must be defined at formula_157, i.e., formula_157 is in the domain of formula_29; "and" (ii) formula_167 as formula_168. The definition above actually applies to any domain formula_122 that does not contain an isolated point, or equivalently, formula_122 where every formula_171 is a limit point of formula_122. A more general definition applying to formula_173 with a general domain formula_174 is the following:


title: Real analysis

text: Definition. If formula_135 is an arbitrary subset of formula_1, we say that formula_173 is continuous at formula_178 if, for any formula_38, there exists formula_39 such that for all formula_181, formula_182 implies that formula_183. We say that formula_29 is a continuous map if formula_29 is continuous at every formula_178.


title: Real analysis

text: A consequence of this definition is that formula_29 is "trivially continuous at any isolated point" formula_178. This somewhat unintuitive treatment of isolated points is necessary to ensure that our definition of continuity for functions on the real line is consistent with the most general definition of continuity for maps between topological spaces (which includes metric spaces and formula_1 in particular as special cases). This definition, which extends beyond the scope of our discussion of real analysis, is given below for completeness.


title: Real analysis

text: Definition. If formula_135 and formula_191 are topological spaces, we say that formula_192 is continuous at formula_178 if formula_194 is a neighborhood of formula_157 in formula_135 for every neighborhood formula_197 of formula_198 in formula_191. We say that formula_29 is a continuous map if formula_201 is open in formula_135 for every formula_203 open in formula_191.


title: Real analysis

text: Definition. If formula_135 is a subset of the real numbers, we say a function formula_173 is uniformly continuous on formula_135 if, for any formula_68, there exists a formula_39 such that for all formula_213, formula_214 implies that formula_215.


title: Real analysis

text: Explicitly, when a function is uniformly continuous on formula_135, the choice of formula_48 needed to fulfill the definition must work for "all of" formula_135 for a given formula_47. In contrast, when a function is continuous at every point formula_178 (or said to be continuous on formula_135), the choice of formula_48 may depend on both formula_47 "and" formula_157. In contrast to simple continuity, uniform continuity is a property of a function that only makes sense with a specified domain; to speak of uniform continuity at a single point formula_157 is meaningless.


title: Real analysis

text: On a compact set, it is easily shown that all continuous functions are uniformly continuous. If formula_122 is a bounded noncompact subset of formula_1, then there exists formula_102 that is continuous but not uniformly continuous. As a simple example, consider formula_229 defined by formula_230. By choosing points close to 0, we can always make formula_231 for any single choice of formula_39, for a given formula_68.


title: Real analysis

text: Definition. Let formula_234 be an interval on the real line. A function formula_235 is said to be absolutely continuous on formula_142 if for every positive number formula_47, there is a positive number formula_48 such that whenever a finite sequence of pairwise disjoint sub-intervals formula_239 of formula_142 satisfies


title: Real analysis

text: Absolutely continuous functions are continuous: consider the case "n" = 1 in this definition. The collection of all absolutely continuous functions on "I" is denoted AC("I"). Absolute continuity is a fundamental concept in the Lebesgue theory of integration, allowing the formulation of a generalized version of the fundamental theorem of calculus that applies to the Lebesgue integral.


title: Real analysis

text: The notion of the "derivative" of a function or "differentiability" originates from the concept of approximating a function near a given point using the "best" linear approximation. This approximation, if it exists, is unique and is given by the line that is tangent to the function at the given point formula_67, and the slope of the line is the derivative of the function at formula_67.


title: Real analysis

text: exists. This limit is known as the derivative of formula_29 at formula_67, and the function formula_250, possibly defined on only a subset of formula_1, is the derivative (or derivative function) of formula_29. If the derivative exists everywhere, the function is said to be differentiable.


title: Real analysis

text: As a simple consequence of the definition, formula_29 is continuous at formula_67 if it is differentiable there. Differentiability is therefore a stronger regularity condition (condition describing the "smoothness" of a function) than continuity, and it is possible for a function to be continuous on the entire real line but not differentiable anywhere (see Weierstrass's nowhere differentiable continuous function). It is possible to discuss the existence of higher-order derivatives as well, by finding the derivative of a derivative function, and so on.


title: Real analysis

text: One can classify functions by their differentiability class. The class formula_255 (sometimes formula_256 to indicate the interval of applicability) consists of all continuous functions. The class formula_257 consists of all differentiable functions whose derivative is continuous; such functions are called continuously differentiable. Thus, a formula_257 function is exactly a function whose derivative exists and is of class formula_255. In general, the classes "formula_260" can be defined recursively by declaring formula_255 to be the set of all continuous functions and declaring "formula_260" for any positive integer formula_26 to be the set of all differentiable functions whose derivative is in formula_264. In particular, "formula_260" is contained in formula_264 for every formula_26, and there are examples to show that this containment is strict. Class formula_268 is the intersection of the sets "formula_260" as "formula_26" varies over the non-negative integers, and the members of this class are known as the smooth functions. Class formula_271 consists of all analytic functions, and is strictly contained in formula_268 (see bump function for a smooth function that is not analytic).


title: Real analysis

text: A series formalizes the imprecise notion of taking the sum of an endless sequence of numbers. The idea that taking the sum of an "infinite" number of terms can lead to a finite result was counterintuitive to the ancient Greeks and led to the formulation of a number of paradoxes by Zeno and other philosophers. The modern notion of assigning a value to a series avoids dealing with the ill-defined notion of adding an "infinite" number of terms. Instead, the finite sum of the first formula_64 terms of the sequence, known as a partial sum, is considered, and the concept of a limit is applied to the sequence of partial sums as formula_64 grows without bound. The series is assigned the value of this limit, if it exists.


title: Real analysis

text: Given an (infinite) sequence formula_13, we can define an associated series as the formal mathematical object sometimes simply written as formula_276. The partial sums of a series formula_276 are the numbers formula_278. A series formula_276 is said to be convergent if the sequence consisting of its partial sums, formula_280, is convergent; otherwise it is divergent. The sum of a convergent series is defined as the number


title: Real analysis

text: The word "sum" is used here in a metaphorical sense as a shorthand for taking the limit of a sequence of partial sums and should not be interpreted as simply "adding" an infinite number of terms. For instance, in contrast to the behavior of finite sums, rearranging the terms of an infinite series may result in convergence to a different number (see the article on the "Riemann rearrangement theorem" for further discussion).


title: Real analysis

text: An example of a convergent series is a geometric series which forms the basis of one of Zeno's famous paradoxes:


title: Real analysis

text: A series formula_276 is said to converge absolutely if formula_285 is convergent. A convergent series formula_276 for which formula_285 diverges is said to converge non-absolutely. It is easily shown that absolute convergence of a series implies its convergence. On the other hand, an example of a series that converges non-absolutely is


title: Real analysis

text: The Taylor series of a real or complex-valued function "ƒ"("x") that is infinitely differentiable at a real or complex number "a" is the power series


title: Real analysis

text: where "n"! denotes the factorial of "n" and "ƒ"("a") denotes the "n"th derivative of "ƒ" evaluated at the point "a". The derivative of order zero "ƒ" is defined to be "ƒ" itself and and 0! are both defined to be 1. In the case that , the series is also called a Maclaurin series.


title: Real analysis

text: A Taylor series of "f" about point "a" may diverge, converge at only the point "a", converge for all "x" such that formula_291 (the largest such "R" for which convergence is guaranteed is called the "radius of convergence"), or converge on the entire real line. Even a converging Taylor series may converge to a value different from the value of the function at that point. If the Taylor series at a point has a nonzero radius of convergence, and sums to the function in the disc of convergence, then the function is analytic. The analytic functions have many fundamental properties. In particular, an analytic function of a real variable extends naturally to a function of a complex variable. It is in this way that the exponential function, the logarithm, the trigonometric functions and their inverses are extended to functions of a complex variable.


title: Real analysis

text: Fourier series decomposes periodic functions or periodic signals into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or complex exponentials). The study of Fourier series typically occurs and is handled within the branch mathematics > mathematical analysis > Fourier analysis.


title: Real analysis

text: Integration is a formalization of the problem of finding the area bound by a curve and the related problems of determining the length of a curve or volume enclosed by a surface. The basic strategy to solving problems of this type was known to the ancient Greeks and Chinese, and was known as the "method of exhaustion". Generally speaking, the desired area is bounded from above and below, respectively, by increasingly accurate circumscribing and inscribing polygonal approximations whose exact areas can be computed. By considering approximations consisting of a larger and larger ("infinite") number of smaller and smaller ("infinitesimal") pieces, the area bound by the curve can be deduced, as the upper and lower bounds defined by the approximations converge around a common value.


title: Real analysis

text: The spirit of this basic strategy can easily be seen in the definition of the Riemann integral, in which the integral is said to exist if upper and lower Riemann (or Darboux) sums converge to a common value as thinner and thinner rectangular slices ("refinements") are considered. Though the machinery used to define it is much more elaborate compared to the Riemann integral, the Lebesgue integral was defined with similar basic ideas in mind. Compared to the Riemann integral, the more sophisticated Lebesgue integral allows area (or length, volume, etc.; termed a "measure" in general) to be defined and computed for much more complicated and irregular subsets of Euclidean space, although there still exist "non-measurable" subsets for which an area cannot be assigned.


title: Real analysis

text: The Riemann integral is defined in terms of Riemann sums of functions with respect to tagged partitions of an interval. Let formula_292 be a closed interval of the real line; then a tagged partition formula_293 of formula_292 is a finite sequence


title: Real analysis

text: This partitions the interval formula_292 into formula_64 sub-intervals formula_298 indexed by formula_299, each of which is "tagged" with a distinguished point formula_300. For a function formula_29 bounded on formula_292, we define the Riemann sum of formula_29 with respect to tagged partition formula_293 as


title: Real analysis

text: where formula_306 is the width of sub-interval formula_307. Thus, each term of the sum is the area of a rectangle with height equal to the function value at the distinguished point of the given sub-interval, and width the same as the sub-interval width. The mesh of such a tagged partition is the width of the largest sub-interval formed by the partition, formula_308. We say that the Riemann integral of formula_29 on formula_292 is formula_311 if for any formula_38 there exists formula_39 such that, for any tagged partition formula_293 with mesh formula_315, we have


title: Real analysis

text: This is sometimes denoted formula_317. When the chosen tags give the maximum (respectively, minimum) value of each interval, the Riemann sum is known as the upper (respectively, lower) Darboux sum. A function is Darboux integrable if the upper and lower Darboux sums can be made to be arbitrarily close to each other for a sufficiently small mesh. Although this definition gives the Darboux integral the appearance of being a special case of the Riemann integral, they are, in fact, equivalent, in the sense that a function is Darboux integrable if and only if it is Riemann integrable, and the values of the integrals are equal. In fact, calculus and real analysis textbooks often conflate the two, introducing the definition of the Darboux integral as that of the Riemann integral, due to the slightly easier to apply definition of the former.


title: Real analysis

text: The fundamental theorem of calculus asserts that integration and differentiation are inverse operations in a certain sense.


title: Real analysis

text: Lebesgue integration is a mathematical construction that extends the integral to a larger class of functions; it also extends the domains on which these functions can be defined. The concept of a measure, an abstraction of length, area, or volume, is central to Lebesgue integral probability theory.


title: Real analysis

text: Distributions (or generalized functions) are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative.


title: Real analysis

text: Real analysis is an area of analysis that studies concepts such as sequences and their limits, continuity, differentiation, integration and sequences of functions. By definition, real analysis focuses on the real numbers, often including positive and negative infinity to form the extended real line. Real analysis is closely related to complex analysis, which studies broadly the same properties of complex numbers. In complex analysis, it is natural to define differentiation via holomorphic functions, which have a number of useful properties, such as repeated differentiability, expressibility as power series, and satisfying the Cauchy integral formula.


title: Real analysis

text: In real analysis, it is usually more natural to consider differentiable, smooth, or harmonic functions, which are more widely applicable, but may lack some more powerful properties of holomorphic functions. However, results such as the fundamental theorem of algebra are simpler when expressed in terms of complex numbers.


title: Real analysis

text: Techniques from the theory of analytic functions of a complex variable are often used in real analysis – such as evaluation of real integrals by residue calculus.


title: Real analysis

text: Important results include the Bolzano–Weierstrass and Heine–Borel theorems, the intermediate value theorem and mean value theorem, Taylor's theorem, the fundamental theorem of calculus, the Arzelà-Ascoli theorem, the Stone-Weierstrass theorem, Fatou's lemma, and the monotone convergence and dominated convergence theorems.


title: Real analysis

text: Various ideas from real analysis can be generalized from the real line to broader or more abstract contexts. These generalizations link real analysis to other disciplines and subdisciplines. For instance, generalization of ideas like continuous functions and compactness from real analysis to metric spaces and topological spaces connects real analysis to the field of general topology, while generalization of finite-dimensional Euclidean spaces to infinite-dimensional analogs led to the concepts of Banach spaces and Hilbert spaces and, more generally to functional analysis. Georg Cantor's investigation of sets and sequence of real numbers, mappings between them, and the foundational issues of real analysis gave birth to naive set theory. The study of issues of convergence for sequences of functions eventually gave rise to Fourier analysis as a subdiscipline of mathematical analysis. Investigation of the consequences of generalizing differentiability from functions of a real variable to ones of a complex variable gave rise to the concept of holomorphic functions and the inception of complex analysis as another distinct subdiscipline of analysis. On the other hand, the generalization of integration from the Riemann sense to that of Lebesgue led to the formulation of the concept of abstract measure spaces, a fundamental concept in measure theory. Finally, the generalization of integration from the real line to curves and surfaces in higher dimensional space brought about the study of vector calculus, whose further generalization and formalization played an important role in the evolution of the concepts of differential forms and smooth (differentiable) manifolds in differential geometry and other closely related areas of geometry and topology.


title: Ferdowsi

text: Abul-Qâsem Ferdowsi Tusi (; 940 – 1019/1025 CE), also Firdawsi or Ferdowsi (), was a Persian poet and the author of "Shahnameh" ("Book of Kings"), which is one of the world's longest epic poems created by a single poet, and the greatest epic of Persian-speaking countries. Ferdowsi is celebrated as one of the most influential figures of Persian literature and one of the greatest in the history of literature.


title: Ferdowsi

text: Except for his kunya ( – ) and his laqab ( – "Ferdowsī", meaning 'paradisic'), nothing is known with any certainty about his full name. From an early period on, he has been referred to by different additional names and titles, the most common one being / ("philosopher"). Based on this, his full name is given in Persian sources as / . Due to the non-standardized transliteration from Persian into English, different spellings of his name are used in English works, including "Firdawsi", "Firdusi", "Firdosi", "Firdausi", etc. The "Encyclopaedia of Islam" uses the spelling "Firdawsī", based on the standardized transliteration method of the German Oriental Society. The "Encyclopædia Iranica", which uses a modified version of the same method (with a stronger emphasis on Persian intonations), gives the spelling "Ferdowsī". In both cases, the "-ow" and "-aw" are to be pronounced as a diphthong ("[aʊ̯]"), reflecting the original Arabic and the early New Persian pronunciation of the name. The modern Tajik transliteration of his name in Cyrillic script is .


title: Ferdowsi

text: Ferdowsi was born into a family of Iranian landowners ("dehqans") in 940 in the village of Paj, near the city of Tus, in the Khorasan region of the Samanid Empire, which is located in the present-day Razavi Khorasan Province of northeastern Iran. Little is known about Ferdowsi's early life. The poet had a wife, who was probably literate and came from the same "dehqan" class. He had a son, who died at the age of 37, and was mourned by the poet in an elegy which he inserted into the "Shahnameh".


title: Ferdowsi

text: Ferdowsi belonged to the class of "dehqans". These were landowning Iranian aristocrats who had flourished under the Sassanid dynasty (the last pre-Islamic dynasty to rule Iran) and whose power, though diminished, had survived into the Islamic era which followed the Islamic conquests of the 7thcentury. The "dehqans" were attached to the pre-Islamic literary heritage, as their status was associated with it (so much so that "dehqan" is sometimes used as a synonym for "Iranian" in the "Shahnameh"). Thus they saw it as their task to preserve the pre-Islamic cultural traditions, including tales of legendary kings.


title: Ferdowsi

text: The Islamic conquests of the 7th century brought gradual linguistic and cultural changes to the Iranian Plateau. By the late 9th century, as the power of the caliphate had weakened, several local dynasties emerged in Greater Iran. Ferdowsi grew up in Tus, a city under the control of one of these dynasties, the Samanids, who claimed descent from the Sassanid general Bahram Chobin (whose story Ferdowsi recounts in one of the later sections of the "Shahnameh"). The Samanid bureaucracy used the New Persian language, which had been used to bring Islam to the Eastern regions of the Iranian world and supplanted local languages, and commissioned translations of Pahlavi texts into New Persian. Abu Mansur Muhammad, a "dehqan" and governor of Tus, had ordered his minister Abu Mansur Mamari to invite several local scholars to compile a prose "Shahnameh" ("Book of Kings"), which was completed in 1010. Although it no longer survives, Ferdowsi used it as one of the sources of his epic. Samanid rulers were patrons of such important Persian poets as Rudaki and Daqiqi, and Ferdowsi followed in the footsteps of these writers.


title: Ferdowsi

text: Details about Ferdowsi's education are lacking. Judging by the "Shahnameh", there is no evidence he knew either Arabic or Pahlavi.


title: Ferdowsi

text: It is possible that Ferdowsi wrote some early poems which have not survived. He began work on the "Shahnameh" around 977, intending it as a continuation of the work of his fellow poet Daqiqi, who had been assassinated by his slave. Like Daqiqi, Ferdowsi employed the prose "Shahnameh" of ʿAbd-al-Razzāq as a source. He received generous patronage from the Samanid prince Mansur and completed the first version of the "Shahnameh" in 994. When the Turkic Ghaznavids overthrew the Samanids in the late 990s, Ferdowsi continued to work on the poem, rewriting sections to praise the Ghaznavid Sultan Mahmud. Mahmud's attitude to Ferdowsi and how well he rewarded the poet are matters which have long been subject to dispute and have formed the basis of legends about the poet and his patron (see below). The Turkic Mahmud may have been less interested in tales from Iranian history than the Samanids. The later sections of the "Shahnameh" have passages which reveal Ferdowsi's fluctuating moods: in some he complains about old age, poverty, illness and the death of his son; in others, he appears happier. Ferdowsi finally completed his epic on 8 March 1010. Virtually nothing is known with any certainty about the last decade of his life.


title: Ferdowsi

text: Ferdowsi was buried in his own garden, burial in the cemetery of Tus having been forbidden by a local cleric. A Ghaznavid governor of Khorasan constructed a mausoleum over the grave and it became a revered site. The tomb, which had fallen into decay, was rebuilt between 1928 and 1934 by the Society for the National Heritage of Iran on the orders of Reza Shah, and has now become the equivalent of a national shrine.


title: Ferdowsi

text: According to legend, Sultan Mahmud of Ghazni offered Ferdowsi a gold piece for every couplet of the "Shahnameh" he wrote. The poet agreed to receive the money as a lump sum when he had completed the epic. He planned to use it to rebuild the dykes in his native Tus. After thirty years of work, Ferdowsi finished his masterpiece. The sultan prepared to give him 60,000 gold pieces, one for every couplet, as agreed. However, the courtier whom Mahmud had entrusted with the money despised Ferdowsi, regarding him as a heretic, and he replaced the gold coins with silver. Ferdowsi was in the bath house when he received the reward. Finding it was silver and not gold, he gave the money away to the bathkeeper, a refreshment seller, and the slave who had carried the coins. When the courtier told the sultan about Ferdowsi's behaviour, he was furious and threatened to execute him. Ferdowsi fled to Khorasan, having first written a satire on Mahmud, and spent most of the remainder of his life in exile. Mahmud eventually learned the truth about the courtier's deception and had him either banished or executed. By this time, the aged Ferdowsi had returned to Tus. The sultan sent him a new gift of 60,000 gold pieces, but just as the caravan bearing the money entered the gates of Tus, a funeral procession exited the gates on the opposite side: the poet had died from a heart attack.


title: Ferdowsi

text: Ferdowsi's "Shahnameh" is the most popular and influential national epic in Iran and other Persian-speaking nations. The "Shahnameh" is the only surviving work by Ferdowsi regarded as indisputably genuine.


title: Ferdowsi

text: He may have written poems earlier in his life but they no longer exist. A narrative poem, "Yūsof o Zolaykā" (Joseph and Zuleika), was once attributed to him, but scholarly consensus now rejects the idea it is his.


title: Ferdowsi

text: There has also been speculation about the satire Ferdowsi allegedly wrote about Mahmud of Ghazni after the sultan failed to reward him sufficiently. Nezami Aruzi, Ferdowsi's early biographer, claimed that all but six lines had been destroyed by a well-wisher who had paid Ferdowsi a thousand dirhams for the poem. Introductions to some manuscripts of the "Shahnameh" include verses purporting to be the satire. Some scholars have viewed them as fabricated; others are more inclined to believe in their authenticity.


title: Ferdowsi

text: Ferdowsi is one of the undisputed giants of Persian literature. After Ferdowsi's "Shahnameh", a number of other works similar in nature surfaced over the centuries within the cultural sphere of the Persian language. Without exception, all such works were based in style and method on Ferdowsi's "Shahnameh", but none of them could quite achieve the same degree of fame and popularity as Ferdowsi's masterpiece.


title: Ferdowsi

text: Ferdowsi has a unique place in Persian history because of the strides he made in reviving and regenerating the Persian language and cultural traditions. His works are cited as a crucial component in the persistence of the Persian language, as those works allowed much of the tongue to remain codified and intact. In this respect, Ferdowsi surpasses Nizami, Khayyám, Asadi Tusi and other seminal Persian literary figures in his impact on Persian culture and language. Many modern Iranians see him as the father of the modern Persian language.


title: Ferdowsi

text: Ferdowsi in fact was a motivation behind many future Persian figures. One such notable figure was Rezā Shāh Pahlavi, who established an Academy of Persian Language and Literature, in order to attempt to remove Arabic and French words from the Persian language, replacing them with suitable Persian alternatives. In 1934, Rezā Shāh set up a ceremony in Mashhad, Khorasan, celebrating a thousand years of Persian literature since the time of Ferdowsi, titled "Ferdowsi Millennial Celebration", inviting notable European as well as Iranian scholars. Ferdowsi University of Mashhad is a university established in 1949 that also takes its name from Ferdowsi.


title: Ferdowsi

text: The library at Wadham College, Oxford University was named the Ferdowsi Library, and contains a specialised Persian section for scholars.


title: Armpit fetishism

text: Armpit fetishism (also known as maschalagnia) is a type of partialism in which a person is sexually attracted to armpits, which may lead to axillism, or armpit intercourse (sexual activity with one or both armpits).


title: Armpit fetishism

text: The natural body smell is a powerful force in sexual attraction, and can be focused by the strong pungent odor of the armpit: Alex Comfort considered that for a woman to shave her armpits was “simply ignorant vandalism”, obliterating a powerful sexual tool, and praised the French for greater sexual awareness than American deodorant culture in this regard.


title: Armpit fetishism

text: A woman's armpits, armpit hair, and secretions can be seen as essential components of their femininity, whether this is positively or negatively valued. Havelock Ellis found evidence that (in a non-sexual context) smelling one's own armpit could act as a temporary energy boost.


title: Armpit fetishism

text: Certain pheromones found in armpit sweat, namely androstadienone is shown to improve mood when smelled or licked according to a 2013 study.


title: Armpit fetishism

text: Those who have a mild fetish for armpits often enjoy licking, kissing, tasting, tickling and smelling their partner's armpits during sexual foreplay, perhaps asking partners not to shower or wash their armpits nor wear deodorant for a period of hours or even days.


title: Armpit fetishism

text: The symbolic equation of armpit and vagina may underpin the fetish, as also the odor. Sigmund Freud however saw such fetishism as becoming problematic only when such preparatory acts substituted totally for intercourse as a final goal.


title: Armpit fetishism

text: Stressing the importance in axillism of the (unlubricated) friction being confined to the penile shaft, Alex Comfort saw armpit intercourse as "Not an outstandingly rewarding trick but worth trying if you like the idea".


title: Armpit fetishism

text: Problems may, however, arise in a relationship when penis to armpit contact (axillism) becomes an exclusive sexual necessity for the armpit fetishist – something which can produce long-term sexual desire disorder in a couple.


title: Sundae

text: A sundae () is an ice cream dessert of American origin that typically consists of one or more scoops of ice cream topped with sauce or syrup and in some cases other toppings such as: sprinkles, whipped cream, marshmallows, peanuts, maraschino cherries, or other fruits (e.g. bananas and pineapple in a banana split).


title: Sundae

text: Among the many stories about the invention of the sundae, a frequent theme is that the ice cream sundae was a variation of the popular ice cream soda. According to an account published by the Evanston Public Library (Illinois), the sale of soda was prohibited on Sundays in Illinois because they were considered too "frilly".


title: Sundae

text: Other origin stories for the sundae focus on the novelty or inventiveness of the treat or the name of the originator and make no mention of legal pressures.


title: Sundae

text: The ice cream sundae soon became the weekend semi-official soda fountain confection at the beginning of the 1900s and quickly gained popularity. "The Ice Cream Trade Journal" for 1909 listed, along with plain, or French sundae, such unique varieties as Robin Hood sundae, Cocoa Caramel sundae, Black Hawk sundae, Angel Cake sundae, Cherry Dip sundae, Cinnamon Peak sundae, Opera sundae, Fleur D'Orange sundae, Knickerbocker sundae, Tally-Ho Sundae, Bismarck and George Washington sundaes, to name a few.


title: Sundae

text: Various localities have claimed to be the birthplace of the ice cream sundae, including Plainfield, Illinois; New Orleans, Louisiana; Cleveland, Ohio and New York City. According to What's Cooking America, the biggest rivalry (referred to as the "Sundae War") to claim the invention of the ice cream sundae is between Two Rivers, Wisconsin and Ithaca, New York.