title: Soviet Empire

text: The historical relationship between Russia (the dominant republic in the Soviet Union) and these Eastern European countries helps explain their longing to eradicate the remnants of Soviet culture. Poland and the Baltic states epitomize the Soviet attempt to build uniform cultures and political systems. According to Dag Noren, Russia was seeking to constitute and reinforce a buffer zone between itself and Western Europe so as to protect itself from potential future attacks from hostile Western European countries. The Soviet Union had lost 26 to 27 million lives over the course the Second World War. To prevent a recurrence of such costly warfare, Soviet leaders believed that they needed to establish a hierarchy of political and economic dependence between neighboring states and the USSR.


title: Soviet Empire

text: During the Brezhnev era, the policy of "Developed Socialism" declared the Soviet Union to be the most complete socialist country—other countries were "socialist", but the USSR was ""developed" socialist"—explaining its dominant role and hegemony over the other socialist countries. This and the interventionist Brezhnev Doctrine, permitting the invasion of other socialist countries, led to characterisation of the USSR as an empire.


title: Soviet Empire

text: Soviet influence in the "socialist-leaning countries" was mainly political and ideological rather than economically exploitative: the Soviet Union pumped enormous amounts of "international assistance" into them in order to secure influence, ultimately to the detriment of its own economy. The Soviet Union sought a group of countries which would rally to its cause in the event of an attack from Western countries, and support it in the context of the Cold War. After the dissolution of the Soviet Union, the Russian Federation declared itself the successor state, and recognized $103 billion of Soviet foreign debt while also claiming $140 billion of Soviet assets abroad.


title: Soviet Empire

text: Economic expansion did, however, play a significant role in Soviet motivation to spread influence in its satellite territories. These new territories would ensure an increase in the global wealth which the Soviet Union would have a grasp on.


title: Soviet Empire

text: Soviet officials from the Russian Soviet Federative Socialist Republic intertwined this economic opportunity with a potential for migration. In fact, they saw in these Eastern European countries the potential of a great workforce. They offered a welcome to them upon the only condition that they work hard and achieve social success. This ideology was shaped on the model of the meritocratic, 19th-century American foreign policy.


title: Soviet Empire

text: Scholars discussing Soviet empire have discussed it as a formal empire or informal empire. In a more formal interpretation of "Soviet empire", this meant absolutism, resembling Lenin's description of the tsarist empire as a "prison of the peoples" except that this "prison of the peoples" had been actualized during Stalin's regime after Lenin's death.


title: Soviet Empire

text: Another view, especially of the non-Stalinist eras, sees the Soviet empire as constituting an "informal empire" over nominally sovereign states in the Warsaw Pact due to Soviet pressure and military presence. The Soviet informal empire depended on subsidies from Moscow. The informal empire in the wider Warsaw Pact also included linkages between Communist Parties. Some historians consider a more multinational-oriented Soviet Union emphasizing its socialist initiatives, such as Ian Bremmer, who describes a "matryoshka-nationalism" where a pan-Soviet nationalism included other nationalisms. Eric Hobsbawn argued that the Soviet Union had effectively designed nations by drawing borders. Dmitri Trenin wrote that by 1980, the Soviet Union had formed both a formal and informal empire.


title: Soviet Empire

text: The informal empire would have included Soviet economic investments, military occupation, and covert action in Soviet-aligned countries. The studies of informal empire have included Soviet influence on East Germany and 1930s Xinjiang. From the 1919 Karakhan Manifesto to 1927, diplomats of the Soviet Union would promise to revoke concessions in China, but the Soviets secretly kept tsarist concessions such as the Chinese Eastern Railway, as well as consulates, barracks, and churches. After the Sino-Soviet conflict (1929), the Soviet Union regained the Russian Empire's concession of the Chinese Eastern Railway and was held until its return in 1952.


title: Soviet Empire

text: Alexander Wendt suggested that by the time of Stalin's Socialism in one country alignment, socialist internationalism "evolved into an ideology of control rather than revolution under the rubric of socialist internationalism" internally within the Soviet Union. By the start of the Cold War it evolved into a "coded power language" that was once again international, but applied to the Soviet informal empire. At times the USSR signaled toleration of policies of satellite states indirectly, by declaring them consistent or inconsistent with socialist ideology, essentially recreating a hegemonic role. Wendt argued that a "hegemonic ideology" could continue to motivate actions after the original incentives were removed, and argued this explains the "zeal of East German Politburo members who chose not to defend themselves against trumped-up charges during the 1950s purges."


title: Soviet Empire

text: Analyzing the dissolution of the Soviet Union, Koslowski and Kratochwil argued that a postwar Soviet "formal empire" represented by the Warsaw Pact, with Soviet military role and control over of member states' foreign relations, had evolved into an informal suzerainty or "Ottomanization" from the late 1970s to 1989. With Gorbachev's relinquishing of the Brezhnev Doctrine in 1989, the informal empire reduced in pressure to a more conventional sphere of influence, resembling Finlandization but applied to the erstwhile East Bloc states, until the Soviet fall in 1991. By contrast "Austrianization" would have been a realist model of great power politics by which the Soviets would have hypothetically relied on Western guarantees to keep an artificial Soviet sphere of influence. The speed of reform in the 1989 to 1991 period made both a repeat of Finlandization and Austrianization impossible for the Soviet Union.


title: Soviet Empire

text: These countries were the closest allies of the Soviet Union and were also members of the Comecon, a Soviet-led economic community founded in 1949. The members of the Warsaw Pact, sometimes called the Eastern Bloc, were widely viewed as Soviet satellite states. These countries were occupied (or formerly occupied) by the Red Army, and their politics, military, foreign and domestic policies were dominated by the Soviet Union. The Warsaw Pact included the following states:


title: Soviet Empire

text: In addition to the Soviet Union in the United Nations Security Council, the Soviet Union had two of its union republics in the United Nations General Assembly:


title: Soviet Empire

text: These countries were Marxist-Leninist states who were allied with the Soviet Union, but were not part of the Warsaw Pact.


title: Soviet Empire

text: Some countries in the Third World had pro-Soviet governments during the Cold War. In the political terminology of the Soviet Union, these were "countries moving along the socialist road of development" as opposed to the more advanced "countries of developed socialism" which were mostly located in Eastern Europe, but that also included Cuba and Vietnam. They received some aid, either military or economic, from the Soviet Union and were influenced by it to varying degrees. Sometimes, their support for the Soviet Union eventually stopped for various reasons and in some cases the pro-Soviet government lost power while in other cases the same government remained in power, but ultimately ended its alliance with the Soviet Union.


title: Soviet Empire

text: Some communist states were opposed to the Soviet Union and criticized many of its policies. Although they may have had many similarities to the USSR on domestic issues, they were not Soviet allies in international politics. Relations between them and the Soviet Union were often tense, sometimes even to the point of armed conflict.


title: Soviet Empire

text: The position of Finland was complex. During World War II, the Soviet Union invaded Finland in the Winter War, which ended with the 1940 Moscow Peace Treaty. Finland would re-enter the Second World War when they invaded the Soviet Union alongside Germany in late June 1941. The war ended in Soviet victory, but Finland retained most of its territory and its market economy, trading on the Western markets and ultimately joining the Western currency system.


title: Soviet Empire

text: Nevertheless, although Finland was considered neutral, the Finno-Soviet Treaty of 1948 significantly limited Finnish freedom of operation in foreign policy. It required Finland to defend the Soviet Union from attacks through its territory, which in practice prevented Finland from joining NATO, and effectively gave the Soviet Union a veto in Finnish foreign policy. Thus, the Soviet Union could exercise "imperial" hegemonic power even towards a neutral state. Under the Paasikivi–Kekkonen doctrine, Finland sought to maintain friendly relations with the Soviet Union, and extensive bilateral trade developed. In the West, this led to fears of the spread of "Finlandization", where Western allies would no longer reliably support the United States and NATO.


title: Assassination of Park Chung-hee

text: Park Chung-hee, the third President of South Korea, was assassinated on October 26, 1979, during a dinner at the Korean Central Intelligence Agency (KCIA) safehouse inside the Blue House presidential compound in Jongno District, Seoul, South Korea. Kim Jae-gyu, the director of the KCIA and the president's security chief, was responsible for the assassination. Park was shot in the chest and the head, and died almost immediately. Four bodyguards and a presidential chauffeur were also killed. The incident is often referred to as "10.26" or the "10.26 incident" in South Korea.


title: Assassination of Park Chung-hee

text: There is a great deal of controversy surrounding Kim's motives, as it remains uncertain whether the act was part of a planned coup d'état or was merely impulsive.


title: Assassination of Park Chung-hee

text: By the time of his assassination, Park had exercised dictatorial power over South Korea for nearly 18 years.


title: Assassination of Park Chung-hee

text: The Korean Central Intelligence Agency (KCIA) was created in 1961 to coordinate both international and domestic intelligence activities, including those of the military. Almost immediately following its creation, the KCIA was used to suppress any domestic opposition to Park's regime: wiretapping, arresting, and torturing without court order. The KCIA was heavily involved in many behind-the-scenes political maneuvers aimed at weakening the opposition parties through bribing, blackmailing, threatening, or arresting opposing lawmakers. Nevertheless, President Park nearly lost the 1971 presidential election to Kim Dae-jung, despite spending ten percent of the national budget on his election campaign. Park therefore established the Yushin Constitution in 1972 to ensure his perpetual dictatorship. The new constitution replaced direct voting in presidential elections with an indirect voting system involving delegates; allotted one third of the National Assembly seats to the president; repealed presidential term limits; and gave the president the authority to suspend the constitution and issue emergency decrees, appoint all judges, and dismiss the National Assembly. When opposition to the Yushin Constitution arose, Park issued a number of emergency decrees, the first of which made any act of opposition or denial of the Yushin Constitution punishable by imprisonment for up to 15 years.


title: Assassination of Park Chung-hee

text: Despite this, opposition towards Park's rule persisted, and in the 1978 South Korean legislative election, despite Park's Democratic Republican Party (DRP) maintaining a majority, the New Democratic Party (NDP) won the popular vote by a narrow margin, further emboldening them. In September 1979, the courts nullified Kim Young-sam's chairmanship of the NDP and the DRP expelled Kim from the National Assembly in a secret session on October 5, which led all 66 NDP lawmakers to submit their resignations to the National Assembly in protest. The Carter administration in the U.S. recalled its ambassador from Seoul in protest as well. On October 16, when it became known that the government was planning to accept the resignations selectively, democracy protests broke out in Kim's hometown of Busan, the second largest city in South Korea, resulting in arson attacks on 30 police stations over several days. The demonstrations, the largest since the days of President Syngman Rhee, spread to nearby Masan and other cities on October 19, with students and citizens calling for repeal of the Yushin Constitution. The KCIA director, Kim Jae-gyu, went to Busan to investigate the situation and found that the demonstrations were not riots by some college students, but more like a "popular uprising joined by regular citizens" to resist the regime. He warned Park that the uprisings would spread to five other large cities, including Seoul. Park said that he himself would give direct orders to the security forces to fire upon demonstrators if the situation got worse.


title: Assassination of Park Chung-hee

text: While Park faced an increasing opposition to his dictatorship outside Blue House, another kind of conflict was intensifying inside Blue House, between Kim Jae-gyu, who was appointed KCIA Director in December 1976, and Chief Bodyguard Cha Ji-chul, who was appointed to his position in 1974 after Park's wife Yuk Young-soo was killed in an assassination by Mun Se-gwang, an ethnic Korean from Japan.


title: Assassination of Park Chung-hee

text: The rivalry stemmed largely from Cha's increasing encroachment onto KCIA turf and Cha's belittlement of Kim in public. Almost universally disliked yet feared, Cha served Park in close proximity and became his favorite and most trusted advisor. Cha appropriated tanks, helicopters and troops from the Republic of Korea Army, so that the presidential security apparatus essentially had a division under Cha's direct command.


title: Assassination of Park Chung-hee

text: The rivalry between Cha and Kim, whose KCIA was until then the most feared government apparatus, was heightened further by a series of political crises in late 1979, as the two rivals clashed over how to deal with growing opposition to the regime. In the NDP's election of its chairman in 1979, KCIA backed Yi Chul-seung to prevent the election of hardliner Kim Young Sam, but Cha interfered in KCIA's political sabotage with its own behind-scene maneuverings. When Kim Young Sam was elected as the NDP chairman, Cha laid the blame on the KCIA, which infuriated Director Kim.


title: Assassination of Park Chung-hee

text: Later, when Kim Young Sam called on the U.S. to stop supporting Park's regime, in an interview with "The New York Times" reporter Henry Stokes, Cha pushed for Kim's expulsion from the National Assembly, which Director Kim feared to be a disastrous development, (as it turned out to be true when it led to uprisings in Busan and Masan). Cha easily bested his opponent as his hardline approach was favored by Park, and he blamed worsening developments on Director Kim's weak leadership of the KCIA at every opportunity. As Cha came to control the scheduling of Park's meetings and briefings and thus access to the president, KCIA briefings, which were usually the first business in the morning, were pushed back to afternoons. By October, there were widespread rumors that Kim would soon be replaced as KCIA director.


title: Assassination of Park Chung-hee

text: On the day of the assassination, Park and his entourage attended ribbon-cutting ceremonies for a dam in Sapgyo and a KBS TV transmitting station in Dangjin. Director Kim was expected to accompany him since the TV station was under KCIA jurisdiction, but after Cha blocked him from riding in the same helicopter as Park, Director Kim angrily excused himself from the trip.


title: Assassination of Park Chung-hee

text: After the trip, according to KCIA Chief Agent Park Seon-ho, one of the assassination conspirators, Park instructed the KCIA to prepare for one of his numerous banquets, which were held, on average, ten times per month. The banquet was held at a KCIA safehouse inside the Blue House presidential compound.


title: Assassination of Park Chung-hee

text: The banquet was to be attended by Park, Director Kim, Cha, Chief Secretary Kim Gye-won, and two young women – rising singer Sim Soo-bong and a college student named Shin Jae-soon. 15 minutes after Director Kim was notified of the banquet, he called Army Chief of Staff Jeong Seung-hwa, arranging for him to dine with KCIA Deputy Director Kim Jeong-seop in a nearby KCIA building in the same compound.


title: Assassination of Park Chung-hee

text: Just before the dinner, Director Kim told Chief Secretary Kim Gye-won that he would get rid of Cha. It is not clear whether Kim Gye-won misheard, misunderstood, or ignored Kim's words.


title: Assassination of Park Chung-hee

text: During the dinner, volatile political issues, including demonstrations in Busan and the opposition leader Kim Young Sam, were discussed, with Park and Cha taking a hardline, Director Kim calling for moderate measures, while Chief Secretary Kim Gye-won was trying to steer the topic of the discussion to small talk.


title: Assassination of Park Chung-hee

text: Park rebuked Director Kim for not being repressive enough in dealing with protesters and Kim Young Sam, whom Park wanted to have arrested. Each time discussion drifted to other subjects, Cha continued to bring up the inability of KCIA to end the crisis and suggested that demonstrators and opposition lawmakers should be "mowed down with tanks".


title: Assassination of Park Chung-hee

text: The rebukes from Park, and especially Cha, riled Kim, who left the dining room to meet with his closest subordinate, former Marine colonel and KCIA Chief Agent Park Seon-ho, and Army colonel and Director Kim's secretary Park Heung-ju (no relations to the president). Kim said to them: "Chief of Staff and Deputy Director are here as well. Today is the day."


title: Assassination of Park Chung-hee

text: Kim reentered the meeting room with a semi-automatic Walther PPK pistol and opened fire, shooting Cha in the arm and Park in the right chest. The PPK jammed as he attempted to kill Cha, who fled to a bathroom adjacent to the dining room. Kim left the room and came back with a Smith & Wesson Model 36 revolver belonging to his subordinate Park Seon-ho. He killed Cha with a shot to the abdomen before speaking to Park and shooting him in the head execution-style.


title: Assassination of Park Chung-hee

text: Upon hearing the initial shots, Park Seon-ho held two bodyguards in the waiting room at gunpoint and ordered them to put their hands up. He hoped to prevent further bloodshed, especially since he was a friend of one of the bodyguards, but when the other bodyguard attempted to reach for a gun, Park shot them both dead. At the same time, Park Heung-ju and two other KCIA agents stormed the kitchen area and killed the remaining bodyguard.


title: Assassination of Park Chung-hee

text: In all, six people were killed: Park, Cha and three presidential bodyguards in the safe house, as well as a presidential chauffeur outside.


title: Assassination of Park Chung-hee

text: After killing Park, Director Kim asked Chief Secretary Kim to secure the safe house and ran to the nearby KCIA building, where Army Chief of Staff Jeong Seung-hwa was waiting. Jeong had heard the shootings and was discussing them with KCIA Deputy Director Kim Jeong-seop when Director Kim came in to tell them that an emergency situation had arisen.


title: Assassination of Park Chung-hee

text: Later, in a car with Jeong Seung-hwa, Kim notified Jeong that Park had died, but without explaining how. Kim hoped that Jeong and Chief Secretary Kim would support him in the coup, as both had been appointed to their positions on his recommendation and Chief Secretary Kim was especially close to Jeong. The car initially headed to KCIA Headquarters, in Namsan district, but eventually went to army headquarters, in Yongsan district, since the army would have to be involved in declaring emergency martial law.


title: Assassination of Park Chung-hee

text: Many historians believe that Kim made a critical mistake in not going to KCIA headquarters, where he would be in control; however, his failure to gain Jeong's support sealed the fate of the conspirators.


title: Assassination of Park Chung-hee

text: Meanwhile, Chief Secretary Kim took Park's body to the Army hospital and ordered doctors to save him at all costs (without revealing Park's identity). He then went to Prime Minister Choi Kyu-hah to reveal what happened that night.


title: Assassination of Park Chung-hee

text: When Chief of Staff Jeong learned of what happened from Chief Secretary Kim, he ordered Major General Chun Doo-hwan, commander of Security Command, to take Director Kim into custody and investigate the incident.


title: Assassination of Park Chung-hee

text: Director Kim was arrested after he was lured to a secluded area outside army headquarters on the pretext of meeting with Jeong. Eventually, everyone involved in the assassination was arrested, tortured and later executed. In the process, Chun Doo-hwan emerged as a new political force by investigating and subordinating KCIA under his Security Command, and Jeong Seung-hwa became the chief martial law administrator. Later, when Chun Doo-hwan seized power in the Coup d'état of December Twelfth 1979, he had Jeong Seung-hwa and Chief Secretary Kim arrested on suspicion of conspiring with Director Kim.


title: Assassination of Park Chung-hee

text: Kim Jae-kgyu's motive in killing his long-time benefactor President Park has been controversial and the subject of much discussion. There are many theories on Kim's true motive of killing Park. The following are just some of these theories.


title: Assassination of Park Chung-hee

text: One theory is that Kim assassinated Park out of jealousy toward Cha, when he was losing his status and power as No. 2 in Park's regime.


title: Assassination of Park Chung-hee

text: Park Heung-ju, Kim Jae-gyu's secretary and former aide-de-camp of Kim, was executed by firing squad on March 6, 1980: he was executed first because he was on active military service at the time of the assassination.


title: Assassination of Park Chung-hee

text: Seo Young-jun, a safehouse security agent, was released after serving 17 years of a sentence of life imprisonment.


title: Assassination of Park Chung-hee

text: Except for Park Heung-ju and Park Seon-ho, the co-conspirators followed Kim Jae-gyu's orders without knowing whom they were shooting and why.


title: Fenn treasure

text: The Fenn Treasure was a cache of gold and jewels that Forrest Fenn, an art dealer and author from Santa Fe, New Mexico, hid in the Rocky Mountains of the United States. It was found approximately a decade later in 2020 in Wyoming by an anonymous treasure hunter later revealed to be former journalist and medical student Jack Stuef. In attempting to honor what he perceives to be Fenn's wishes after his death in September 2020, he has refused to reveal the location of the treasure. An auction of items from the treasure chest in December of 2022 resulted in $1.3 million in sales.


title: Fenn treasure

text: Forrest Fenn (August 22, 1930 – September 7, 2020) was a pilot in the United States Air Force, obtaining the rank of Major. He was awarded the Silver Star for his service in the Vietnam War where he flew 328 combat missions in 365 days. He retired from the Air Force and ran the Arrowsmith-Fenn Gallery with his partner Rex Arrowsmith, which became the Fenn Galleries which he operated with his wife, Peggy. The gallery was located in Santa Fe, New Mexico, and sold a variety of Native American artifacts, paintings, bronze sculptures, and other art, including forged copies of works by Modigliani, Monet, Degas, and other artists. The gallery reportedly grossed $6 million a year.


title: Fenn treasure

text: In 1988, Fenn was diagnosed with cancer and given a prognosis that it was likely terminal. This inspired him to hide a treasure chest in an outdoor location with the purpose of creating a public search for it. He considered using the location as his final resting place as well. He recovered from the illness and in 2010 self-published "The Thrill of the Chase: A Memoir," a collection of short stories from his life. He described a treasure chest that he said contained gold nuggets, rare coins, jewelry, and gemstones. He went on to write that he hid the chest "in the mountains somewhere north of Santa Fe". Fenn said that the stories in the book included hints to the chest's location and that the poem found in the chapter "Gold and More" contained nine clues that would lead a searcher to the chest. Fenn's book and story prompted a treasure hunt in the Rocky Mountains of New Mexico, Colorado, Wyoming, and Montana. The value of the chest was estimated to be as high as $2 million, depending on the appraisal of the items. In December of 2022, after the treasure had been found, an auction of items from the treasure chest resulted in $1.3 million in sales. Fenn claimed to make no money on the sale of the self-published books out of concern for being labeled a fraud by critics.


title: Fenn treasure

text: Before the treasure hunt, Fenn came into conflict with authorities over federal antiquities law during Operation Cerberus Action. Federal Bureau of Investigation (FBI) agents raided his home in 2009 as part of an investigation into artifact looting in the Four Corners area. Items in his possession reportedly included pieces of chain mail from the Pecos National Historical Park, human hair, a feathered talisman, and a bison skull, some of which were confiscated by federal authorities; no charges were filed. Two people targeted in the case committed suicide, and Fenn blamed the FBI for their deaths.


title: Fenn treasure

text: Five people died while searching for the treasure. This led the chief of the New Mexico State Police, Pete Kassetas, to publicly implore Fenn to end the treasure hunt, stating "He's putting lives at risk."


title: Fenn treasure

text: A number of notable controversies surrounded the treasure hunt. Several searchers were cited or arrested for committing legal infractions in the course of their pursuits.


title: Fenn treasure

text: The treasure chest features a bronze construction with a wood liner and locking front clasp. According to Fenn, it weighs about and its dimensions are . The chest features scenes and reliefs with knights scaling walls on ladders and maidens above throwing flowers down upon them. This style of work appears to be references to the "Le Roman de la Rose" poem about the pursuit of love and scaling the "Castle of Love" which gained popularity around the same time the chest was made. Because of the popularity of the treasure hunt, artists have made modern recreations based on Fenn's chest.


title: Fenn treasure

text: On June 6, 2020, Fenn posted on the searcher blog "Thrill of the Chase" that the treasure had been found: "It was under a canopy of stars in the lush, forested vegetation of the Rocky Mountains and had not moved from the spot where I hid it more than 10 years ago. I do not know the person who found it, but the poem in my book led him to the precise spot. I congratulate the thousands of people who participated in the search and hope they will continue to be drawn by the promise of other discoveries. So the search is over. Look for more information and photos in the coming days."


title: Fenn treasure

text: This was subsequently confirmed by Fenn, who further disclosed in a news article that the finder was a male from the eastern United States who had sent him a photograph. The identity of the finder, the photograph, and the location of the treasure were not revealed. On June 16, Fenn released additional photos on the "Thrill of the Chase" blog site including of himself examining the contents of the chest and one of it sitting in weathered condition implicitly on or near the site where it was found. On July 22 Fenn stated on the "Thrill of the Chase" blog site that the treasure's finder had authorized him to disclose, in the interest of closure for many of its searchers, that it had been hidden in Wyoming.


title: Fenn treasure

text: In December 2020, Jack Stuef, a medical student from Michigan, revealed that he found Fenn's treasure chest and decided to disclose his identity by going public in an interview with "Outside". Due to safety reasons he preferred to stay anonymous but a lawsuit was expected to reveal his identity.


title: Fenn treasure

text: Stuef revealed that two small items indicated in pre-find publicity were not present in the chest, a small gold frog on a necklace and a Spanish emerald ring found at San Lazaro. When Stuef notified Forrest about the missing items, Forrest located the frog within his collection and presented it to Stuef. However, Forrest was not able to find the missing emerald ring.


title: Fenn treasure

text: In July 2021, a French treasure hunter named Bruno Raphoz filed a $10 million lawsuit against Fenn's estate in the United States District Court for the District of New Mexico. According to the complaint, Raphoz had determined that the treasure was hidden in southwestern Colorado, informed Fenn of his solution, and began making preparations to retrieve it. However, his plans were delayed by the COVID-19 pandemic, and Fenn announced soon afterward that the treasure had been found in Wyoming. Raphoz contended that Fenn took advantage of the delay to move the chest from Colorado to Wyoming, noting that its exact final location has not been specified by Stuef or any of Fenn's relatives.


title: NBA All-Defensive Team

text: The NBA All-Defensive Team is an annual National Basketball Association (NBA) honor given since the 1968–69 NBA season to the best defensive players during the regular season. The All-Defensive Team is generally composed of ten players in two five-man lineups, a first and a second team. Voting is conducted by a panel of 123 writers and broadcasters. Prior to the 2013–14 NBA season, voting was performed by the NBA head coaches, who were restricted from voting for players on their own team. The players each receive two points for each first team vote and one point for each second team vote. The top five players with the highest point total make the first team, with the next five making the second team. In the case of a tie at the fifth position of either team, the roster is expanded. If the first team consists of six players due to a tie, the second team will still consist of five players with the potential for more expansion in the event of additional ties. Ties have occurred several times, most recently in 2013 when Tyson Chandler and Joakim Noah tied in votes received.


title: NBA All-Defensive Team

text: Tim Duncan holds the record for the most total selections to the All-Defensive Team with 15. Kevin Garnett and Kobe Bryant follow with 12 total honors each, and Kareem Abdul-Jabbar has 11 total selections. Michael Jordan, Gary Payton, Garnett and Bryant share the record for most NBA All-Defensive first team selections with nine. Scottie Pippen, Bobby Jones, and Duncan made the first team eight times each. Walt Frazier, Dennis Rodman and Chris Paul made the All-Defensive first team seven times.


title: NBA All-Defensive Team

text: When the coaches were responsible for voting, there were occasionally inconsistencies between the All-Defensive Team and the NBA Defensive Player of the Year Award, which has been voted on by the media. On four occasions, the Defensive Player of the Year winner was not voted to the All-Defensive first team in the same year. Player of the Year winners Alvin Robertson (1986), Dikembe Mutombo (1995), Tyson Chandler (2012) and Marc Gasol (2013) were instead named to the second team.


title: Bunsen burner

text: A Bunsen burner, named after Robert Bunsen, is a kind of ambient air gas burner used as laboratory equipment; it produces a single open gas flame, and is used for heating, sterilization, and combustion.


title: Bunsen burner

text: The gas can be natural gas (which is mainly methane) or a liquefied petroleum gas, such as propane, butane, or a mixture. Combustion temperature achieved depends in part on the adiabatic flame temperature of the chosen fuel mixture.


title: Bunsen burner

text: In 1852, the University of Heidelberg hired Bunsen and promised him a new laboratory building. The city of Heidelberg had begun to install coal-gas street lighting, and so the university laid gas lines to the new laboratory.


title: Bunsen burner

text: The designers of the building intended to use the gas not just for illumination, but also in burners for laboratory operations. For any burner lamp, it was desirable to maximize the temperature and minimize luminosity. However, existing laboratory burner lamps left much to be desired not just in terms of the heat of the flame, but also regarding economy and simplicity.


title: Bunsen burner

text: While the building was still under construction in late 1854, Bunsen suggested certain design principles to the university's mechanic, Peter Desaga, and asked him to construct a prototype. Similar principles had been used in an earlier burner design by Michael Faraday, as well as in a device patented in 1856 by the gas engineer R. W. Elsner. The Bunsen/Desaga design succeeded in generating a hot, sootless, non-luminous flame by mixing the gas with air in a controlled fashion before combustion. Desaga created adjustable slits for air at the bottom of the cylindrical burner, with the flame igniting at the top. By the time the building opened early in 1855, Desaga had made 50 burners for Bunsen's students. Two years later Bunsen published a description, and many of his colleagues soon adopted the design. Bunsen burners are now used in laboratories all around the world.


title: Bunsen burner

text: The device in use today safely burns a continuous stream of a flammable gas such as natural gas (which is principally methane) or a liquefied petroleum gas such as propane, butane, or a mixture of both.


title: Bunsen burner

text: The hose barb is connected to a gas nozzle on the laboratory bench with rubber tubing. Most laboratory benches are equipped with multiple gas nozzles connected to a central gas source, as well as vacuum, nitrogen, and steam nozzles. The gas then flows up through the base through a small hole at the bottom of the barrel and is directed upward. There are open slots in the side of the tube bottom to admit air into the stream using the Venturi effect, and the gas burns at the top of the tube once ignited by a flame or spark. The most common methods of lighting the burner are using a match or a spark lighter.


title: Bunsen burner

text: The amount of air mixed with the gas stream affects the completeness of the combustion reaction. Less air yields an incomplete and thus cooler reaction, while a gas stream well mixed with air provides oxygen in a stoichiometric amount and thus a complete and hotter reaction. The air flow can be controlled by opening or closing the slot openings at the base of the barrel, similar in function to the choke in a carburettor.


title: Bunsen burner

text: If the collar at the bottom of the tube is adjusted so more air can mix with the gas before combustion, the flame will burn hotter, appearing blue as a result. If the holes are closed, the gas will only mix with ambient air at the point of combustion, that is, only after it has exited the tube at the top. This reduced mixing produces an incomplete reaction, producing a cooler but brighter yellow, which is often called the "safety flame" or "luminous flame". The yellow flame is luminous due to small soot particles in the flame, which are heated to incandescence. The yellow flame is considered "dirty" because it leaves a layer of carbon on whatever it is heating. When the burner is regulated to produce a hot, blue flame, it can be nearly invisible against some backgrounds. The hottest part of the flame is the tip of the inner flame, while the coolest is the whole inner flame. Increasing the amount of fuel gas flow through the tube by opening the needle valve will increase the size of the flame. However, unless the airflow is adjusted as well, the flame temperature will decrease because an increased amount of gas is now mixed with the same amount of air, starving the flame of oxygen.


title: Bunsen burner

text: Generally, the burner is placed underneath a laboratory tripod, which supports a beaker or other container. The burner will often be placed on a suitable heatproof mat to protect the laboratory bench surface.


title: Bunsen burner

text: A Bunsen burner is also used in microbiology laboratories to sterilise pieces of equipment and to produce an updraft that forces airborne contaminants away from the working area.


title: Bunsen burner

text: Other burners based on the same principle exist. The most important alternatives to the Bunsen burner are:


title: Kim Mu-yeol

text: Kim Mu-yeol (born May 22, 1982) is a South Korean actor. Following a successful career in musical theatre, Kim was first cast in minor parts on film and television. But after getting good reviews in his supporting roles in "The Scam" (2009) and "War of the Arrows" (2011), Kim landed his first major role in Jung Ji-woo's critically acclaimed film "A Muse" (2012), followed by a leading role in the independent film "All Bark No Bite".


title: Kim Mu-yeol

text: Kim Mu-yeol debuted as a musical theatre actor, and among the roles he's played on stage are child murderers Richard/Nathan in "Thrill Me" and gambler Sky Masterson in "Guys and Dolls". He won Best Actor at the 2009 Korea Musical Awards for his portrayal of Melchior in "Spring Awakening", a rock musical which dealt with such taboo subjects as teenage pregnancy, sexual and physical abuse, and homosexuality.


title: Kim Mu-yeol

text: While acting on stage, Kim was cast in minor roles on television and film, and in 2009 he gained notice with a supporting role as a bond broker who is the brains behind "The Scam". Period action epic "War of the Arrows" became one of the biggest hits of 2011 and further raised his profile. In 2012, Kim rose to stardom after the release of the provocative and psychologically rich "A Muse", in which he played a conflicted novelist.


title: Kim Mu-yeol

text: Kim returned to acting upon his military discharge in 2014. He starred in "Northern Limit Line" in 2015, a naval thriller about the Second Battle of Yeonpyeong.


title: Kim Mu-yeol

text: In June 2012, Kim came under growing public criticism over allegations he dodged his compulsory military service. In a report released by the Korean Board of Audit and Inspection (BAI), Kim was deemed fit to serve in active duty as a level two recruit after a March 2001 physical examination. However, throughout 2007 to 2009, Kim was granted postponement on the grounds that he was taking civil service examinations or had been admitted to a work training facility, neither of which took place. During this time he reportedly earned approximately from films, musicals, and television work. In December 2009, he received his final notice for enlistment, having used up the 730 days allowed for postponement. He submitted a request to change his military status in January 2010 because of a knee injury, which was rejected. Finally, a valid exemption was granted on the grounds that he was a "low-income individual" and the sole provider for his family. BAI's contention was that Kim's income is substantially higher than the standard for disqualification due to poverty; thus, the Military Manpower Administration was negligent in their duties by granting the exemption.


title: Kim Mu-yeol

text: Kim’s agency Prain TPC defended him, stating that Kim had been supporting his family by working as a security guard, construction worker, and at a mobile phone factory since his late teens. When his father collapsed from a cerebral hemorrhage and was diagnosed with cancer in 2008, the treatments incurred a lot of debt for the family. Their worsening financial condition caused them to become totally dependent on Kim, resulting in his said filing for an exemption in 2010.


title: Kim Mu-yeol

text: Given the publicity, a reinvestigation into the case was launched and Kim was asked by the production company to leave the film "11 A.M." (he was replaced by Choi Daniel).


title: Kim Mu-yeol

text: On October 4, 2012, Kim released a statement that though there was no wrongdoing on his part, he had decided to voluntarily enter the army "to recover his honor damaged by the rumors."


title: Kim Mu-yeol

text: In January 2013, Kim starred in military musical "The Promise". It was co-produced by the Ministry of National Defense and Korea Musical Theatre Association, to commemorate the 60th anniversary of the signing of the armistice. It ran from January 9 to 20 at the National Theater of Korea, with a cast composed of actors Ji Hyun-woo and Jung Tae-woo, as well as singers Leeteuk of Super Junior, Yoon Hak of Supernova, and Lee Hyun of 8Eight. The musical centered around a group of soldiers who keep a promise made to each other during the 6.25 war. When the "entertainment soldiers" unit was disbanded in August 2013, Kim was reassigned to a frontline combat unit of the 12th Infantry Division headquartered in Inje County, Gangwon Province.


title: Kim Mu-yeol

text: In February 2014, Kim underwent surgery to treat a cartilage injury in his left knee, and afterwards received rehabilitation treatment for nearly two months at a military hospital near Seoul. Criticism was raised regarding his lengthy sick leave, but the defense ministry refused to provide detailed information regarding Kim's health condition, arguing that it was an infringement on his privacy.


title: Kim Mu-yeol

text: After a romantic tweet that Kim meant to be a private message to Yoon Seung-ah was accidentally posted on the actor’s Twitter page, their agencies confirmed in February 2012 that the two were dating. Kim and Yoon married on April 4, 2015.


title: Rich Communication Services

text: Rich Communication Services (RCS) is a communication protocol between mobile telephone carriers and between phone and carrier, aiming at replacing SMS messages with a text-message system that is richer, provides phonebook polling (for service discovery), and can transmit in-call multimedia. It is part of the broader IP Multimedia Subsystem. Google added support for end-to-end encryption for one-on-one conversations in their own extension.


title: Rich Communication Services

text: In early 2020, it was estimated that RCS was available from 88 operators in 59 countries with approximately 390 million users per month.


title: Rich Communication Services

text: The Rich Communication Suite industry initiative<ref name="http://www.rtve.es/noticias/20120612/joyn-servicio-mensajeria-instantanea-limitado-operadoras-moviles/534852.shtml"></ref>


title: Rich Communication Services

text: was formed by a group of industry promoters in 2007. In February 2008 the GSM Association officially became the project home of RCS and an RCS steering committee was established by the organisation.


title: Rich Communication Services

text: The steering committee specified the definition, testing, and integration of the services in the application suite known as RCS. Three years later, the RCS project released a new specification – RCS-e (e = 'enhanced'), which included various iterations of the original RCS specifications. The GSMA program is now called Rich Communication Services.


title: Rich Communication Services

text: The GSMA published the Universal Profile in November 2016. The Universal Profile is a single GSMA specification for advanced communications. Carriers that deploy the Universal Profile guarantee interconnection with other carriers. 47 mobile network operators, 11 manufacturers, and 2 OS providers (Google and Microsoft) have announced their support. Google's Jibe Cloud platform is an implementation of the RCS Universal Profile, designed to help carriers launch RCS quickly and scale easily.


title: Rich Communication Services

text: Samsung is the major device original equipment manufacturer (OEM) to support RCS. Samsung RCS capable devices have been commercially launched in Europe since 2012 and in the United States since 2015.


title: Rich Communication Services

text: Google supports RCS on Android devices with its Android SMS app Messages. In April 2018, it was reported that Google would be transferring the team that was working on its Google Allo messaging service to work on a wider RCS implementation. In June 2019, Google announced that it would begin to deploy RCS on an opt-in basis via the Messages app (branded as "chat features"), with service compliant with the Universal Profile and hosted by Google rather than the user's carrier. The rollout of this functionality began in France and the United Kingdom. In response to concerns over the lack of end-to-end encryption in RCS, Google stated that it would only retain message data in transit until it is delivered to the recipient. In November 2020, Google later announced that it would begin to roll out end-to-end encryption for one-on-one conversations between Messages users, beginning with the beta version of the app. In December 2020, Samsung updated its Samsung Experience messages app to also allow users to opt into Chat.


title: Rich Communication Services

text: In October 2019, the four major U.S. carriers announced an agreement to form the "Cross-Carrier Messaging Initiative" to jointly implement RCS using a newly developed app. This service will be compatible with the Universal Profile. However, both T-Mobile and AT&T later signed deals with Google to replace their messaging app with Google's own Messages app.


title: Rich Communication Services

text: In September 2022, Apple Inc. CEO Tim Cook said the company has no plans to support RCS on its devices or any interoperability with iMessage.


title: Rich Communication Services

text: RCS combines different services defined by 3GPP and Open Mobile Alliance (OMA) with an enhanced phonebook. Another phone's capabilities and presence information can be discovered and displayed by a mobile phone.


title: Rich Communication Services

text: RCS reuses 3GPP specified IMS core system as the underlying service platform taking care of issues such as authentication, authorization, registration, charging and routing.


title: Rich Communication Services

text: The GSMA defined a series of specific implementations of the RCS specifications. The RCS specifications often define a number of options for implementing individual communications features, resulting in challenges in delivering interoperable services between carriers. The RCS specifications aim to define a more specific implementation that promotes standardization and simplify interconnection between carriers.


title: Rich Communication Services

text: The GSMA's Universal Profile is a single set of features for product development and operator deployment of RCS.


title: Rich Communication Services

text: RCS Business Messaging (RBM) is the B2C (A2P in telecoms terminology) version of RCS. This is supposed to be an answer to third-party messaging apps (or OTTs) absorbing mobile operators' messaging traffic and associated revenues. While RCS is designed to win back Person-to-Person (P2P) traffic, RBM is intended to retain and grow this A2P traffic. RCS offers "rich" features similar to those of messaging apps, but delivered (in theory) via the preloaded SMS messaging app - for example Google Messages or Samsung Messages. By making these features available in a B2C setting, RBM is expected to attract marketing and customer service spend from enterprises, thanks to improved customer engagement and interactive features that facilitate new use cases. This was the primary reason for the development of RCS by the GSMA.


title: Rich Communication Services

text: RBM includes features not available to ordinary users, including predefined quick-reply suggestions, rich cards, carousels, and branding. This last feature is intended to increase consumer confidence and reduce fraud through the implementation of a verified sender system. These additional features are only available with the use of a messaging-as-a-platform (MaaP) server integrated with the operator's network. The MaaP controls the verified sender details, unlocking RBM features, while also segregating P2P and A2P RCS messages, aiding monetisation of the latter (SMS currently suffers from grey routes, where A2P messages are sent over P2P connections, which are cheaper or often free).


title: Rich Communication Services

text: According to GSMA PR in 2012, Rich Communication Services (RCS) carriers from around the globe supporting the RCS standard included AT&T, Bell Mobility, Bharti Airtel, Deutsche Telekom, Jio, KPN, KT Corporation, LG U+, Orange, Orascom Telecom, Rogers Communications, SFR, SK Telecom, Telecom Italia, Telefónica, Telia Company, Telus, Verizon and Vodafone.


title: Rich Communication Services

text: Universal Profile is currently backed by "a large and growing ecosystem" (68 supporters in 2019). Universal Profile support is optional in 4G, but mandatory in 5G networks and devices.


title: Rich Communication Services

text: Like SMS, RCS requires national and international interconnects to enable roaming. As with SMS, this will be accomplished with hubbing - where third-party providers complete agreements with individual operators to interwork their systems. Each subsequent operator that connects to a hub is therefore connected automatically to all other connected operators. This eliminates the need to each operator to connect to all the others to which they may need to send messages. RCS hubs are provided by stakeholders with a vested interest in increasing RCS use. These include traditional SMS hub providers (e.g. Global Message Services and Sinch), software and hardware vendors (e.g. Interop Technologies, Mavenir, and ZTE), and also Google via its Jibe Cloud platform.


title: Rich Communication Services

text: The RCS interop and testing (IOT) accreditation process was started by the GSMA in order to improve the quality of testing, increase transparency, drive scale, minimize complexity and accelerate time-to-market (TTM) of joyn services. Companies need to undertake the IOT process from the GSMA to apply for a license to use the service mark joyn.


title: Rich Communication Services

text: "Accredited" means that the device, client or network has undertaken a series of test cases (150 to 300) in a specific set of conditions, provided test results and traces that have been analysed by the GSMA RCS IOT team and any IOT issues arising resolved with the submitter.


title: Rich Communication Services

text: "Accreditation Ready" is the designation awarded to a hosted RCS service that has undertaken the same series of test cases as the mobile network operator, provided test results and traces that have been analysed by the GSMA RCS IOT team and any IoT issues arising resolved with the submitter.


title: Rich Communication Services

text: Amnesty International researcher Joe Westby criticized RCS for not allowing end-to-end encryption, because it is treated as a service of carriers and thus subject to lawful interception.


title: Rich Communication Services

text: "The Verge" criticized the inconsistent support of RCS in the United States, with carriers not supporting RCS in all markets, not certifying service on all phones, or not yet supporting the Universal Profile. Concerns were shown over Google's decision to run its own RCS service due to the possibility of antitrust scrutiny, but it was acknowledged that Google had to do so in order to bypass the carriers' inconsistent support of RCS, as it wanted to have a service more comparable to Apple's iMessage service available on Android.


title: Rich Communication Services

text: "Ars Technica" also criticized Google's move to launch a direct-to-consumer RCS service, considering it a contradiction of RCS being native to the carrier to provide features reminiscent of messaging apps, counting it as being among various past and unsuccessful attempts by Google to develop an in-house messaging service (including Google Talk, Google+ Messenger, Hangouts, and Allo), and noting limitations: such as its dependencies on phone numbers as the identity (whereas email-based accounts are telco-agnostic), not being capable of being readily synchronized between multiple devices, and the aforementioned lack of end-to-end encryption. In June 2021 Google introduced end-to-end encryption in Google Messages, an app supporting RCS. Encryption is supported only if two users are on Messages in a 1:1 chat (not group chat), both with RCS turned on.


title: Nucleobase

text: Nucleobases, also known as "nitrogenous bases" or often simply "bases", are nitrogen-containing biological compounds that form nucleosides, which, in turn, are components of nucleotides, with all of these monomers constituting the basic building blocks of nucleic acids. The ability of nucleobases to form base pairs and to stack one upon another leads directly to long-chain helical structures such as ribonucleic acid (RNA) and deoxyribonucleic acid (DNA). Five nucleobases—adenine (A), cytosine (C), guanine (G), thymine (T), and uracil (U)—are called "primary" or "canonical". They function as the fundamental units of the genetic code, with the bases A, G, C, and T being found in DNA while A, G, C, and U are found in RNA. Thymine and uracil are distinguished by merely the presence or absence of a methyl group on the fifth carbon (C5) of these heterocyclic six-membered rings.


title: Nucleobase

text: In addition, some viruses have aminoadenine (Z) instead of adenine. It differs in having an extra amine group, creating a more stable bond to thymine.


title: Nucleobase

text: Adenine and guanine have a fused-ring skeletal structure derived of purine, hence they are called purine bases. The purine nitrogenous bases are characterized by their single amino group (–), at the C6 carbon in adenine and C2 in guanine. Similarly, the simple-ring structure of cytosine, uracil, and thymine is derived of pyrimidine, so those three bases are called the pyrimidine bases. Each of the base pairs in a typical double-helix DNA comprises a purine and a pyrimidine: either an A paired with a T or a C paired with a G. These purine-pyrimidine pairs, which are called "base complements", connect the two strands of the helix and are often compared to the rungs of a ladder. The pairing of purines and pyrimidines may result, in part, from dimensional constraints, as this combination enables a geometry of constant width for the DNA spiral helix. The A–T and C–G pairings are based on double or triple hydrogen bonds between the amine and carbonyl groups on the complementary bases.


title: Nucleobase

text: Nucleobases such as adenine, guanine, xanthine, hypoxanthine, purine, 2,6-diaminopurine, and 6,8-diaminopurine may have formed in outer space as well as on earth.


title: Nucleobase

text: The origin of the term "base" reflects these compounds' chemical properties in acid–base reactions, but those properties are not especially important for understanding most of the biological functions of nucleobases.


title: Nucleobase

text: At the sides of nucleic acid structure, phosphate molecules successively connect the two sugar-rings of two adjacent nucleotide monomers, thereby creating a long chain biomolecule. These chain-joins of phosphates with sugars (ribose or deoxyribose) create the "backbone" strands for a single- or double helix biomolecule. In the double helix of DNA, the two strands are oriented chemically in opposite directions, which permits base pairing by providing complementarity between the two bases, and which is essential for replication of or transcription of the encoded information found in DNA.


title: Nucleobase

text: DNA and RNA also contain other (non-primary) bases that have been modified after the nucleic acid chain has been formed. In DNA, the most common modified base is 5-methylcytosine (mC). In RNA, there are many modified bases, including those contained in the nucleosides pseudouridine (Ψ), dihydrouridine (D), inosine (I), and 7-methylguanosine (mG).


title: Nucleobase

text: Hypoxanthine and xanthine are two of the many bases created through mutagen presence, both of them through deamination (replacement of the amine-group with a carbonyl-group). Hypoxanthine is produced from adenine, xanthine from guanine, and uracil results from deamination of cytosine.


title: Nucleobase

text: The most common applications are used as fluorescent probes, either directly or indirectly, such as aminoallyl nucleotide, which are used to label cRNA or cDNA in microarrays. Several groups are working on alternative "extra" base pairs to extend the genetic code, such as isoguanine and isocytosine or the fluorescent 2-amino-6-(2-thienyl)purine and pyrrole-2-carbaldehyde.


title: Nucleobase

text: In medicine, several nucleoside analogues are used as anticancer and antiviral agents. The viral polymerase incorporates these compounds with non-canonical bases. These compounds are activated in the cells by being converted into nucleotides; they are administered as nucleosides as charged nucleotides cannot easily cross cell membranes. At least one set of new base pairs has been announced as of May 2014.


title: Nucleobase

text: In order to understand how life arose knowledge is required of chemical pathways that permit formation of the key building blocks of life under plausible prebiotic conditions. According to the RNA world hypothesis free-floating ribonucleotides were present in the primitive soup. These were the fundamental molecules that combined in series to form RNA. Molecules as complex as RNA must have arisen from small molecules whose reactivity was governed by physico-chemical processes. RNA is composed of purine and pyrimidine nucleotides, both of which are necessary for reliable information transfer, and thus Darwinian evolution. Nam et al. demonstrated the direct condensation of nucleobases with ribose to give ribonucleosides in aqueous microdroplets, a key step leading to RNA formation. Similar results were obtained by Becker et al.


title: Oyster sauce

text: Oyster sauce describes a number of sauces made by cooking oysters. The most common in modern use is a viscous dark brown condiment made from oyster extracts, sugar, salt and water thickened with corn starch. Some versions may be darkened with caramel, though high-quality oyster sauce is naturally dark. It is commonly used in Chinese, Thai, Malay, Vietnamese, and Khmer cuisine.


title: Oyster sauce

text: Oyster sauce production began in China no later than the mid-1870s. Oysters were boiled in three iron basins for half an hour then removed for drying on rattan either by sun or over a moderate fire. The water from the basins was reduced in a fourth basin to "a blackish sauce". Sea-water, salt and/or soy could be added.


title: Oyster sauce

text: Today, many shortcuts have been made to create a similar flavor more quickly and at reduced cost. Oyster sauces today are usually made with a base of sugar and salt and thickened with corn starch. Oyster extracts or essences are then used to give flavor to the base sauce. Other ingredients, such as soy sauce and monosodium glutamate, may also be added to deepen the flavor and add color. The quality of the oyster sauce will greatly affect the flavor.


title: Oyster sauce

text: Oyster sauce is made manually in the traditional method. Some oyster sauce manufacturers have improved the process to mass-produce oyster sauce with automation. The oyster extracts are mixed with sugar, corn starch, and the like, with the weighing and mixing processes powered by an automatic electronic system before uniform blending on the automatic production line. The mixed ingredients are cooked in a sealed automatic production system at high temperature by a computerized system. The cooked sauce is transferred to the filling system through sealed pipelines, and reaches the market shelves only after multiple rounds of inspection.


title: Oyster sauce

text: Oyster sauce adds a savory flavor to many meat and vegetable dishes. The sauce is a staple for much Chinese family-style cooking. It is commonly used in noodle stir-fries, such as chow mein. It is also found in popular Chinese-American dishes such as beef with stir-fried vegetables. Oyster sauce can also be used as a topping for some dishes.


title: Oyster sauce

text: Since its early stage of development, oyster sauce has been widely popular with Cantonese chefs as a traditional umami rich condiment.


title: Oyster sauce

text: Applications are no longer restricted to Cantonese cuisine. Be it the well-balanced Shandong cuisine, the spicy hot Sichuanese cuisine, or the seafood and red stewing-dominated Jiangsu and Zhejiang cuisine, oyster sauce enhances flavor. It brings out the umami flavor.


title: Oyster sauce

text: Dishes that may use oyster sauce include Crab in oyster sauce, Kai-lan, Buddha's delight, Hainanese chicken rice, Cashew chicken, Lo mein, Cha siu baau, Har gow, Kai yat sai, Wonton noodles, and Daikon cake.


title: Oyster sauce

text: While oyster sauce and fish sauce are both briny and may have related histories, they are different products. Fish sauce is watery, clear, and salty, whereas oyster sauce is made by reducing oyster extracts and therefore sweeter with a hint of salt and not as strong an aroma as fish sauce.


title: Oyster sauce

text: "True" oyster sauce of good quality should be made by condensing oyster extracts, the white broth produced by boiling oysters in water. This opaque broth, similar to the color of clam juice found in supermarkets, is then reduced until a desired viscosity has been reached and the liquid has caramelized to a brown color. No other additives, not even salt, should be added to the sauce, since the oysters should provide all the savory flavor. However, this method is prohibitively expensive.


title: Oyster sauce

text: Many modern oyster sauces are thickened with cornstarch, flavored with oyster essence or extract and darkened with caramel.


title: Oyster sauce

text: Vegetarian oyster sauce prepared from mushrooms, often oyster mushrooms or shiitake mushrooms, is also popular and generally lower in price. It may contain more taste enhancers if less mushroom extract is used to reduce costs.


title: Oyster sauce

text: Most of the oyster sauces available on the market contain added monosodium glutamate (MSG). In recent years MSG-free varieties can also be found.


title: Oyster sauce

text: In 19th century French and English cooking, "oyster sauce" referred to a variant of sauce blanche flavored with oysters, using a base of milk and melted butter rather than purely reducing the oysters by cooking. The white sauce version was moistened with cream, whereas in brown oyster sauce, the cream was replaced with gravy. Common recipes using the sauce included "Steak and oyster sauce", documented as early as 1806, and "Cod and oyster sauce". This sauce was still being eaten in Australia in the 1970s.


title: Oyster sauce

text: In 2001, the United Kingdom Food Standards Agency found in tests of various oyster sauces and soy sauces that 22% of samples contained a chemical called 3-MCPD (3-monochloropropane-1,2-diol) at levels considerably higher than those deemed safe by the European Union. About two thirds of these samples also contained a second chemical, called 1,3-DCP (1,3-dichloropropanol), which experts advise should not be present at any levels in food. Both chemicals have the potential to cause cancer, and the Agency recommended that the affected products be withdrawn from shelves and avoided.


title: Oyster sauce

text: The joint Australia New Zealand Food Authority (ANZFA) said it had taken emergency action to amend its food standards code to set a limit for 3-MCPD in soy sauce of 0.02 milligrams per kilogram, in line with European Commission standards that came into force in the EU in April 2002.


title: Lists of Metro-Goldwyn-Mayer films

text: This is a list of feature films originally released and/or distributed by Metro-Goldwyn-Mayer (to include MGM/UA Entertainment Co., MGM/UA Communications Co., MGM–Pathe Communications Co. and MGM/UA Distribution Co.).


title: Lists of Metro-Goldwyn-Mayer films

text: This list does not include films from United Artists before it merged with MGM (except for co-productions), nor does it include other studios that MGM acquired (such as Orion Pictures, The Samuel Goldwyn Company, Cannon Films).


title: Lists of Metro-Goldwyn-Mayer films

text: The pre-May 1986 Metro-Goldwyn-Mayer catalogue is owned by Warner Bros. Discovery through the Turner Entertainment Co.


title: Itō Hirobumi

text: A London-educated samurai of the Chōshū Domain and a central figure in the Meiji Restoration, Itō Hirobumi chaired the bureau which drafted the Constitution for the newly formed Empire of Japan. Looking to the West for inspiration, Itō rejected the United States Constitution as too liberal and the Spanish Restoration as too despotic. Instead, he drew on British and German models, particularly the Prussian Constitution of 1850. Dissatisfied with Christianity's pervasiveness in European legal precedent, he replaced such religious references with those rooted in the more traditionally Japanese concept of a "kokutai" or "national polity" which hence became the constitutional justification for imperial authority.


title: Itō Hirobumi

text: During the 1880s, Itō emerged as the most powerful figure in the Meiji government. By 1885, he became the first Prime Minister of Japan, a position he went on to hold four times (thereby making his tenure one of the longest in Japanese history). Even out of office as the nation's head of government, he continued to wield enormous influence over Japan's policies as a permanent imperial adviser, or , and the President of the Emperor's Privy Council. A staunch monarchist, Itō favored a large, all-powerful bureaucracy which answered solely to the Emperor and opposed the formation of political parties. His third term as Prime Minister was ended in 1898 by the opposition's consolidation into the Kenseitō party, prompting him to found the Rikken Seiyūkai party to counter its rise. In 1901, he resigned his fourth and final ministry upon tiring of party politics.


title: Itō Hirobumi

text: On the world stage, Itō presided over an ambitious foreign policy. He strengthened diplomatic ties with the Western powers including Germany, the United States and especially the United Kingdom. In Asia, he oversaw the First Sino-Japanese War and negotiated the surrender of China's ruling Qing dynasty on terms aggressively favourable to Japan, including the annexation of Taiwan and the release of Korea from the Chinese Imperial tribute system. While expanding his country's claims in Asia, Itō sought to avoid conflict with the Russian Empire through the policy of "Man-Kan kōkan" – the proposed surrender of Manchuria to Russia's sphere of influence in exchange for recognition of Japanese hegemony in Korea. However, in a diplomatic visit to Saint Petersburg in November 1901, Itō found Russian authorities completely unreceptive to such terms. Consequently, Japan's incumbent Prime Minister, Katsura Tarō, elected to abandon the pursuit of "Man-Kan kōkan", which resulted in an escalation of tensions culminating in the Russo-Japanese War.


title: Itō Hirobumi

text: After Japanese forces emerged victorious over Russia, the ensuing Japan–Korea Treaty of 1905 made Itō the first Japanese Resident-General of Korea. Despite initially supporting the sovereignty of the indigenous Joseon monarchy, he ultimately consented to the total annexation of Korea in response to pressure from the increasingly powerful Imperial Army. Shortly thereafter, he resigned as Resident-General in 1909 and assumed office once again as President of the Imperial Privy Council. Four months later, Itō was assassinated by Korean-independence activist and nationalist An Jung-geun in Manchuria. The annexation process was formalised by another treaty the following year after Ito's death. Through his daughter Ikuko, Itō was the father-in-law of politician, intellectual and author Suematsu Kenchō.


title: Itō Hirobumi

text: Hayashi Risuke () was born on October 16, 1841, in Tsukari, Kumage, Suō Province (present-day Hikari, Yamaguchi Prefecture), the eldest son of farmer Hayashi Jūzō and his wife Kotoko. After his father went bankrupt and left for Hagi, Yamaguchi in 1846, he went to live at his mother's parental home. In 1849, Jūzō invited the family to Hagi and the family reunited. There Risuke entered Kubo Gorō Saemon's school. Because the family was poor, when Risuke was 12, Jūzō was adopted by samurai servant Mizui Buhē. In 1854, Mizui Buhē was adopted by samurai foot soldier ("ashigaru") Itō Yaemon from Aihata, Saba. Mizui Buhē was renamed Itō Naoemon, Jūzō took the name Itō Jūzō, and Hayashi Risuke was renamed Itō Shunsuke at first, then Itō Hirobumi. These adoptions allowed both Hirobumi and his father Jūzō to rise to the samurai class and become "ashigaru". Jūzō was the biological son of Hayashi Sukezaemon (林助左衛門), a 5th generation descendant of Hayashi Nobuyoshi (林信吉) who was a member of the Hayashi clan of Owari (尾張林氏).


title: Itō Hirobumi

text: He was a student of Yoshida Shōin at the Shōka Sonjuku and later joined the "Sonnō jōi" movement ("to revere the Emperor and expel the barbarians"), together with Katsura Kogorō. Active in the movement, he took part in an incendiary attack of the British legation on 31 January 1863 led by Takasugi Shinsaku, and in the company of Yamao Yōzō attacked and mortally wounded the head of the Wagakukōdansho institute on 2 February 1863, believing a false report that the institute was looking into ways of toppling the Emperor. Itō was chosen as one of the Chōshū Five who studied at University College London in 1863, and the experience in Great Britain eventually convinced him Japan needed to adopt Western ways.


title: Itō Hirobumi

text: In 1864, Itō returned to Japan with fellow student Inoue Kaoru to attempt to warn Chōshū Domain against going to war with the foreign powers (the Bombardment of Shimonoseki) over the right of passage through the Straits of Shimonoseki. At that time, he met Ernest Satow for the first time, later a lifelong friend.


title: Itō Hirobumi

text: After the Meiji Restoration of 1868, Itō was appointed governor of Hyōgo Prefecture, junior councilor for Foreign Affairs, and sent to the United States in 1870 to study Western currency systems. Returning to Japan in 1871, he established Japan's taxation system. With the advice of Edmund Morel, a chief engineer of the railway department, Ito endeavored to found the Public Works together with Yamao Yozo. Later that year, he was sent on the Iwakura Mission around the world as vice-envoy extraordinary, during which he won the confidence of Ōkubo Toshimichi, one of the leaders of the Meiji government.


title: Itō Hirobumi

text: In 1873, Itō was made a full councilor, Minister of Public Works, and in 1875 chairman of the first Assembly of Prefectural Governors. He participated in the Osaka Conference of 1875. After Ōkubo's assassination, he took over the post of Home Minister and secured a central position in the Meiji government. By 1881, he successfully pushed for the resignation of Ōkuma Shigenobu, thereby allowing him to emerge as the "de facto" leader of the Meiji government.


title: Itō Hirobumi

text: Itō went to Europe in 1882 to study the constitutions of those countries, spending nearly 18 months away from Japan. While working on a constitution for Japan, he also wrote the first Imperial Household Law and established the Japanese peerage system ("kazoku") in 1884.


title: Itō Hirobumi

text: In 1885, he negotiated the Convention of Tientsin with Li Hongzhang, normalizing Japan's diplomatic relations with Qing-dynasty China. In the same year, In 1885, Itō established a cabinet system of government based on European ideas, replacing the Daijō-kan as the nation's main policy-making organization.


title: Itō Hirobumi

text: On 22 December 1885, Itō became the first prime minister of Japan. On 30 April 1888, Itō resigned as prime minister, but headed the new Privy Council to maintain power behind-the-scenes. In 1889, he also became the first "genrō". The Meiji Constitution was promulgated in February 1889. He had added to it the references to the "kokutai" or "national polity" as the justification of the emperor's authority through his divine descent and the unbroken line of emperors, and the unique relationship between subject and sovereign. This stemmed from his rejection of some European notions as unfit for Japan, as they stemmed from European constitutional practice and Christianity.


title: Itō Hirobumi

text: He remained a powerful force while Kuroda Kiyotaka and Yamagata Aritomo, his political nemeses, were prime ministers.


title: Itō Hirobumi

text: During Itō's second term as prime minister (8 August 1892 – 31 August 1896), he supported the First Sino-Japanese War and negotiated the Treaty of Shimonoseki in March 1895 with his ailing foreign minister Mutsu Munemitsu. In the Anglo-Japanese Treaty of Commerce and Navigation of 1894, he succeeded in removing some of the onerous unequal treaty clauses that had plagued Japanese foreign relations since the start of the Meiji period.


title: Itō Hirobumi

text: During Itō's third term as prime minister (12 January – 30 June 1898), he was forced to contend with the rise of political parties. Both the Liberal Party and the "Shimpotō" opposed his proposed new land taxes, and in retaliation, Itō dissolved the Diet and called for new elections. As a result, both parties merged into the "Kenseitō", won a majority of the seats, and forced Itō to resign. This lesson taught Itō the need for a pro-government political party, so he organized the "Rikken Seiyūkai" (Constitutional Association of Political Friendship) in 1900. Itō's womanizing was a popular theme in editorial cartoons and in parodies by contemporary comedians, and was used by his political enemies in their campaign against him.


title: Itō Hirobumi

text: Itō returned to office as prime minister for a fourth term from 19 October 1900, to 10 May 1901, this time facing political opposition from the House of Peers. Weary of political back-stabbing, he resigned in 1901, but remained as head of the Privy Council as the premiership alternated between Saionji Kinmochi and Katsura Tarō.


title: Itō Hirobumi

text: Toward the end of August 1901, Itō announced his intention of visiting the United States to recuperate. This turned into a long journey in the course of which he visited the major cities of the United States and Europe. He set off from Yokohama on 18 September, traveled through the U.S. to New York City, and received an honorary doctorate (LL.D.) from Yale University in late October.) He then sailed to Boulogne, reaching Paris on 4 November. On 25 November, he reached Saint Petersburg, having been asked by the new prime minister, Katsura Tarō, to sound out the Russians, entirely unofficially, on their intentions in the Far East. Japan hoped to achieve what it called "Man-Kan kōkan", the exchange of a free hand for Russia in Manchuria for a free hand for Japan in Korea, but Russia, feeling greatly superior to Japan and unwilling to give up the use of Korean ports for its navy, was in no mood to compromise. Foreign minister Vladimir Lamsdorf "thought that time was on the side of his country because of the [Trans-Siberian] railway and there was no need to make concessions to the Japanese". Itō left empty-handed for Berlin (where he received honors from Kaiser Wilhelm), Brussels, and London. Meanwhile, Katsura had decided that "Man-Kan kōkan" was no longer desirable for Japan, which should not renounce activity in Manchuria. In Britain, Ito met with Lord Lansdowne, which helped lay the groundwork for the Anglo-Japanese Alliance announced early the following year. The failure of his mission to Russia was "one of the most important events in the run-up to the Russo-Japanese War".


title: Itō Hirobumi

text: While Prime Minister, Ito invited Professor George Trumbull Ladd of Yale University to serve as a diplomatic adviser to promote mutual understanding between Japan and the United States. Lectures delivered by Ladd in Japan revolutionized its educational methods; he was the first foreigner to receive the Third Class honor (conferred by the Emperor in 1899) and the Second Class honor (in 1907) in the Orders of the Rising Sun. He later wrote a book on his personal experiences in Korea and with Resident-General Itō. When Ladd died, half his ashes were buried in a Buddhist temple in Tokyo and a monument was erected to him.


title: Itō Hirobumi

text: In November 1905, following the Russo-Japanese War, the Japan–Korea Treaty of 1905 was made between the Empire of Japan and the Empire of Korea, making Korea a Japanese protectorate. After the treaty had been signed, Itō became the first Resident-General of Korea on 21 December 1905. In 1907, he urged Emperor Gojong to abdicate in favor of his son Sunjong and secured the Japan–Korea Treaty of 1907, thereby giving Japan authority to dictate Korea's internal affairs.


title: Itō Hirobumi

text: While Itō was firmly against Korea falling into China or Russia's sphere of influence, he also opposed its annexation, advocating instead that the territory should be treated as a "protectorate". When the cabinet voted in favor of annexing Korea, he proposed that the process be delayed in the hopes that the decision could eventually be reversed. However, Itō ultimately changed his mind


title: Itō Hirobumi

text: and approved plans to have the region annexed on 10 April 1909. Despite changing his position, he was forced to resign on 14 June 1909 by the Imperial Japanese Army (one of the foremost advocates for Korea's annexation). His assassination is believed to have accelerated the path to the Japan–Korea Annexation Treaty.


title: Itō Hirobumi

text: Itō arrived at the Harbin railway station on 26 October 1909 for a meeting with Vladimir Kokovtsov, a Russian representative in Manchuria. There An Jung-geun, a Korean nationalist and independence activist, fired six shots, three of which hit Itō in the chest. He died shortly thereafter. His body was returned to Japan on the Imperial Japanese Navy cruiser , and he was accorded a state funeral. An Jung-geun later listed "15 reasons why Itō should be killed" at his trial.


title: Itō Hirobumi

text: A portrait of Itō Hirobumi was on the obverse of the Series C 1,000 yen note from 1963 until a new series was issued in 1984. Itō's former house in Shinagawa, Tokyo has been transported to the site of his childhood home in Yamaguchi prefecture. It is now preserved as a museum near the Shōin Jinja in Hagi. The publishing company Hakubunkan takes its name from "Hakubun", an alternate pronunciation of Itō's given name.


title: Itō Hirobumi

text: The Annals of Sunjong record that Gojong held a positive view of Itō's governorship. In an entry for 28 October 1909, almost three years after being forced to abdicate his throne, the former emperor praised Itō, who had died two days earlier, for his efforts to develop Japanese civilization in Korea. However, the integrity of Joseon dated after the Japan–Korea Treaty of 1905 is considered dubious by Korean scholars due to the influence exerted over record-keeping by the Japanese.


title: Itō Hirobumi

text: Itō has been portrayed several times in Korean cinema. His assassination was the subject of North Korea's "An Jung-gun Shoots Ito Hirobumi" in 1979 and South Korea's "Thomas Ahn Joong Keun" in 2004; both films made his assassin An Jung-geun the protagonist. The 1973 South Korean film "" is a biopic of Itō's adopted Korean daughter Bae Jeong-ja (1870–1950).


title: Itō Hirobumi

text: Itō argued the Pan-Asian view that if East Asians did not co-operate closely with one another, Japan, Korea and China would all fall victim to Western imperialism. Initially, Gojong and the Joseon government shared that belief and agreed to collaborate with the Japanese military. Korean intellectuals had predicted that the victor of the Russo-Japanese War would assume hegemony over their peninsula, and as an Asian power, Japan enjoyed greater public support in Korea than Russia. However, policies such as land confiscation and the drafting of forced labor turned popular opinion against the Japanese, a trend exacerbated by the arrest or execution of those who resisted. Ironically, An Jung-geun was also a proponent of what was later called Pan-Asianism. He believed in a union of the three East Asian nations to repel Western imperialism and restore peace in the region.


title: Itō Hirobumi

text: On October 26, 1932, the Japanese unveiled in Seoul the Hakubun-ji Buddhist Temple dedicated to Prince Ito. Full official name "Prince Ito Memorial Temple (伊藤公爵祈念寺院)". Situated in then Susumu Tadashidan Park on the north slope of Namsan, which after liberation became Jangchungdan Park 장충단 공원. From October 1945, the main hall served as student home, ca. 1960 replaced by a guest house of the Park Chung-Hee administration, then reconstructed and again a student guest house. In 1979 it was incorporated into the grounds of the Shilla Hotel then opened. Several other parts of the temple are still at the site.


title: Rounding

text: Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression with .


title: Rounding

text: Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as but is known to be accurate only to within a few hundred units is usually better stated as "about ".


title: Rounding

text: On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representation with a fixed number of significant digits. In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless.


title: Rounding

text: Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as "the table-maker's dilemma".


title: Rounding

text: Rounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals.


title: Rounding

text: A wavy equals sign (≈: "approximately equal to") is sometimes used to indicate rounding of exact numbers, e.g., 9.98 ≈ 10. This sign was introduced by Alfred George Greenhill in 1892.


title: Rounding

text: Because it is not usually possible for a method to satisfy all ideal characteristics, many different rounding methods exist.


title: Rounding

text: As a general rule, rounding is idempotent; i.e., once a number has been rounded, rounding it again will not change its value. Rounding functions are also monotonic; i.e., . In the general case of a discrete range, they are piecewise constant functions.


title: Rounding

text: The most basic form of rounding is to replace an arbitrary number by an integer. All the following rounding modes are concrete implementations of an abstract single-argument "round()" procedure. These are true functions (with the exception of those that use randomness).


title: Rounding

text: These four methods are called directed rounding, as the displacements from the original number to the rounded value are all directed toward or away from the same limiting value (0, +∞, or −∞). Directed rounding is used in interval arithmetic and is often required in financial calculations.


title: Rounding

text: If is positive, round-down is the same as round-toward-zero, and round-up is the same as round-away-from-zero. If is negative, round-down is the same as round-away-from-zero, and round-up is the same as round-toward-zero. In any case, if is an integer, is just .


title: Rounding

text: Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result. A famous instance involved a new index set up by the Vancouver Stock Exchange in 1982. It was initially set at 1000.000 (three decimal places of accuracy), and after 22 months had fallen to about 520 — whereas stock prices had generally increased in the period. The problem was caused by the index being recalculated thousands of times daily, and always being rounded down to 3 decimal places, in such a way that the rounding errors accumulated. Recalculating with better rounding gave an index value of 1098.892 at the end of the same period.


title: Rounding

text: Rounding a number to the nearest integer requires some tie-breaking rule for those cases when is exactly half-way between two integers — that is, when the fraction part of is exactly 0.5.


title: Rounding

text: If it were not for the 0.5 fractional parts, the round-off errors introduced by the round to nearest method would be symmetric: for every fraction that gets rounded down (such as 0.268), there is a complementary fraction (namely, 0.732) that gets rounded up by the same amount.


title: Rounding

text: When rounding a large set of fixed-point numbers with uniformly distributed fractional parts, the rounding errors by all values, with the omission of those having 0.5 fractional part, would statistically compensate each other. This means that the expected (average) value of the rounded numbers is equal to the expected value of the original numbers when numbers with fractional part 0.5 from the set are removed.


title: Rounding

text: In practice, floating-point numbers are typically used, which have even more computational nuances because they are not equally spaced.


title: Rounding

text: The following tie-breaking rule, called round half up (or round half toward positive infinity), is widely used in many disciplines. That is, half-way values of are always rounded up.


title: Rounding

text: However, some programming languages (such as Java, Python) define their "half up" as "round half away from zero" here.


title: Rounding

text: This method only requires checking one digit to determine rounding direction in two's complement and similar representations.


title: Rounding

text: One may also use round half down (or round half toward negative infinity) as opposed to the more common "round half up".


title: Rounding

text: However, some programming languages (such as Java, Python) define their "half down" as "round half toward zero" here.


title: Rounding

text: One may also round half toward zero (or round half away from infinity) as opposed to the conventional "round half away from zero".


title: Rounding

text: This method treats positive and negative values symmetrically, and therefore is free of overall positive/negative bias if the original numbers are positive or negative with equal probability. It does, however, still have bias toward zero.


title: Rounding

text: The other tie-breaking method commonly taught and used is the round half away from zero (or round half toward infinity), namely:


title: Rounding

text: This can be more efficient on binary computers because only the first omitted bit needs to be considered to determine if it rounds up (on a 1) or down (on a 0). This is one method used when rounding to significant figures due to its simplicity.


title: Rounding

text: This method, also known as commercial rounding, treats positive and negative values symmetrically, and therefore is free of overall positive/negative bias if the original numbers are positive or negative with equal probability. It does, however, still have bias away from zero.


title: Rounding

text: It is often used for currency conversions and price roundings (when the amount is first converted into the smallest significant subdivision of the currency, such as cents of a euro) as it is easy to explain by just considering the first fractional digit, independently of supplementary precision digits or sign of the amount (for strict equivalence between the paying and recipient of the amount).


title: Rounding

text: A tie-breaking rule without positive/negative bias "and" without bias toward/away from zero is round half to even. By this convention, if the fractional part of is 0.5, then is the even integer nearest to . Thus, for example, +23.5 becomes +24, as does +24.5; however, −23.5 becomes −24, as does −24.5. This function minimizes the expected error when summing over rounded figures, even when the inputs are mostly positive or mostly negative, provided they are neither mostly even nor mostly odd.


title: Rounding

text: This variant of the round-to-nearest method is also called convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, odd–even rounding, or bankers' rounding.


title: Rounding

text: This is the default rounding mode used in IEEE 754 operations for results in binary floating-point formats, and used when rounding to significant figures.


title: Rounding

text: By eliminating bias, repeated addition or subtraction of independent numbers, as in a one-dimensional random walk, will give a rounded result with an error that tends to grow in proportion to the square root of the number of operations rather than linearly.


title: Rounding

text: However, this rule distorts the distribution by increasing the probability of evens relative to odds. Typically this is less important than the biases that are eliminated by this method.


title: Rounding

text: A similar tie-breaking rule to round half to even is round half to odd. In this approach, if the fractional part of is 0.5, then is the odd integer nearest to . Thus, for example, +23.5 becomes +23, as does +22.5; while −23.5 becomes −23, as does −22.5.


title: Rounding

text: This method is also free from positive/negative bias and bias toward/away from zero, provided the numbers to be rounded are neither mostly even nor mostly odd. It also shares the round half to even property of distorting the original distribution, as it increases the probability of odds relative to evens.


title: Rounding

text: This variant is almost never used in computations, except in situations where one wants to avoid increasing the scale of floating-point numbers, which have a limited exponent range. With "round half to even", a non-infinite number would round to infinity, and a small value would round to a normal non-zero value. Effectively, this mode prefers preserving the existing scale of tie numbers, avoiding out-of-range results when possible for numeral systems of even radix (such as binary and decimal).


title: Rounding

text: This rounding mode (RPSP in this chapter) is used to avoid getting wrong result with double (including multiple) rounding. With this rounding mode, one can avoid wrong result after double rounding, if all roundings except the final one are done using RPSP, and only final rounding uses the externally requested mode.


title: Rounding

text: With decimal arithmetic, if there is a choice between numbers with the smallest significant digit 0 or 1, 4 or 5, 5 or 6, 9 or 0, then the digit different from 0 or 5 shall be selected; otherwise, choice is arbitrary. IBM defines that, in the latter case, a digit with the smaller magnitude shall be selected. RPSP can be applied with the step between two consequent roundings as small as a single digit (for example, rounding to 1/10 can be applied after rounding to 1/100).


title: Rounding

text: In the example from "Double rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9.


title: Rounding

text: With binary arithmetic, the rounding is made as "round to odd" (not to be mixed with "round half to odd".) For example, when rounding to 1/4:


title: Rounding

text: For correct results, RPSP shall be applied with the step of at least 2 binary digits, otherwise, wrong result may appear. For example,


title: Rounding

text: If the step is 2 bits or more, RPSP gives 3.25 which, in turn, round-half-to-even to integer results in 3.


title: Rounding

text: One method, more obscure than most, is to alternate direction when rounding a number with 0.5 fractional part. All others are rounded to the closest integer.


title: Rounding

text: If occurrences of 0.5 fractional parts occur significantly more than a restart of the occurrence "counting", then it is effectively bias free. With guaranteed zero bias, it is useful if the numbers are to be summed or averaged.


title: Rounding

text: Like round-half-to-even and round-half-to-odd, this rule is essentially free of overall bias, but it is also fair among even and odd values. An advantage over alternate tie-breaking is that the last direction of rounding on the 0.5 fractional part does not have to be "remembered".


title: Rounding

text: Rounding as follows to one of the closest integer toward negative infinity and the closest integer toward positive infinity, with a probability dependent on the proximity is called stochastic rounding and will give an unbiased result on average.


title: Rounding

text: Stochastic rounding can be accurate in a way that a rounding function can never be. For example, suppose one started with 0 and added 0.3 to that one hundred times while rounding the running total between every addition. The result would be 0 with regular rounding, but with stochastic rounding, the expected result would be 30, which is the same value obtained without rounding. This can be useful in machine learning where the training may use low precision arithmetic iteratively. Stochastic rounding is also a way to achieve 1-dimensional dithering.


title: Rounding

text: The most common type of rounding is to round to an integer; or, more generally, to an integer multiple of some increment — such as rounding to whole tenths of seconds, hundredths of a dollar, to whole multiples of 1/2 or 1/8 inch, to whole dozens or thousands, etc.


title: Rounding

text: In general, rounding a number to a multiple of some specified positive value entails the following steps:


title: Rounding

text: For example, rounding  = 2.1784 dollars to whole cents (i.e., to a multiple of 0.01) entails computing 2.1784 / 0.01 = 217.84, then rounding that to 218, and finally computing 218 × 0.01 = 2.18.


title: Rounding

text: When rounding to a predetermined number of significant digits, the increment depends on the magnitude of the number to be rounded (or of the rounded result).


title: Rounding

text: The increment is normally a finite fraction in whatever numeral system is used to represent the numbers. For display to humans, that usually means the decimal numeral system (that is, is an integer times a power of 10, like 1/1000 or 25/100). For intermediate values stored in digital computers, it often means the binary numeral system ( is an integer times a power of 2).


title: Rounding

text: The abstract single-argument "round()" function that returns an integer from an arbitrary real value has at least a dozen distinct concrete definitions presented in the rounding to integer section. The abstract two-argument "roundToMultiple()" function is formally defined here, but in many cases it is used with the implicit value  = 1 for the increment and then reduces to the equivalent abstract single-argument function, with also the same dozen distinct concrete definitions.


title: Rounding

text: Rounding to a specified "power" is very different from rounding to a specified "multiple"; for example, it is common in computing to need to round a number to a whole power of 2. The steps, in general, to round a positive number to a power of some positive number other than 1, are:


title: Rounding

text: This type of rounding, which is also named rounding to a logarithmic scale, is a variant of rounding to a specified power. Rounding on a logarithmic scale is accomplished by taking the log of the amount and doing normal rounding to the nearest value on the log scale.


title: Rounding

text: For example, resistors are supplied with preferred numbers on a logarithmic scale. In particular, for resistors with a 10% accuracy, they are supplied with nominal values 100, 120, 150, 180, 220, etc. rounded to multiples of 10 (E12 series). If a calculation indicates a resistor of 165 ohms is required then log(150) = 2.176, log(165) = 2.217 and log(180) = 2.255. The logarithm of 165 is closer to the logarithm of 180 therefore a 180 ohm resistor would be the first choice if there are no other considerations.


title: Rounding

text: Whether a value rounds to or depends upon whether the squared value is greater than or less than the product . The value 165 rounds to 180 in the resistors example because is greater than .


title: Rounding

text: In floating-point arithmetic, rounding aims to turn a given value into a value with a specified number of digits. In other words, should be a multiple of a number that depends on the magnitude of . The number is a power of the base (usually 2 or 10) of the floating-point representation.


title: Rounding

text: Apart from this detail, all the variants of rounding discussed above apply to the rounding of floating-point numbers as well. The algorithm for such rounding is presented in the Scaled rounding section above, but with a constant scaling factor  = 1, and an integer base  > 1.