Crew.

Mattingly had originally been assigned to the prime crew of Apollo 13, but was exposed to rubella through Duke, at that time on the back-up crew for Apollo 13, who had caught it from one of his children. He never contracted the illness, but was nevertheless removed from the crew and replaced by his backup, Jack Swigert, three days before the launch. Young, a captain in the United States Navy, had flown on three spaceflights prior to Apollo 16: Gemini 3, Gemini 10 and Apollo 10, which orbited the Moon. One of 19 astronauts selected by NASA in April 1966, Duke had never flown in space before Apollo 16. He served on the support crew of Apollo 10 and was a capsule communicator (CAPCOM) for Apollo 11.

Backup crew.

Although not officially announced, the original backup crew consisted of Fred W. Haise (CDR), William R. Pogue (CMP) and Gerald P. Carr (LMP), who were targeted for the prime crew assignment on Apollo 19. However, after the cancellations

Mission insignia.

The insignia of Apollo 16 is dominated by a rendering of an American eagle and a red, white and blue shield, representing the people of the United States, over a gray background representing the

Planning and training.

Landing site selection.

Apollo 16 was the second of the Apollo type J missions, featuring the use of the Lunar Roving Vehicle, increased scientific capability, and lunar surface stays of three days. As Apollo 16 was the penultimate mission in the Apollo program and there was no new hardware or procedures to test on the lunar surface, the last two missions (the other being Apollo 17) presented opportunities for astronauts to clear up some uncertainties in understanding the Moon's properties. Although previous Apollo expeditions, including Apollo 14 and Apollo 15, obtained samples of pre-mare lunar material, before lava began to upwell from the Moon's interior and flood

Training.

In preparing for their mission, in addition to the usual Apollo spacecraft training, Young and Duke, along with backup commander Fred Haise, underwent an extensive geological training program that included several field trips to introduce them to concepts and techniques they would use in analyzing features and collecting samples on the lunar surface. During these trips, they visited and provided scientific descriptions of geologic features they were likely to encounter. In July 1971, they visited Sudbury, Ontario, Canada for geology training exercises, the first time U.S. astronauts did so. Geologists chose the area because of a wide

Mission highlights.

Launch and outbound trip.

The launch of Apollo 16 was delayed one month from March 17 to April 16. This was the first launch delay in the Apollo program due to a technical problem. During the delay, the space suits, a spacecraft separation mechanism and batteries in the lunar module (LM) were modified and tested. There were concerns that the explosive mechanism designed to separate the docking ring from the command module (CM) would not create enough pressure to completely sever the ring. This, along with a dexterity issue in Young's space suit and fluctuations in the capacity of the lunar module batteries, required investigation and trouble-shooting. In January 1972, three months before the planned April launch date, a fuel tank in the command module was accidentally damaged during a routine test. The rocket was returned to the Vertical Assembly Building (VAB) and the fuel tank replaced, and the rocket returned to the launch pad in February in time for the scheduled launch.  The official mission countdown began on Monday, April 10, 1972, at 8:30 AM, six days before the launch. At this point the SaturnV rocket's three stages were powered up and drinking

Lunar surface.

The crew continued preparing for lunar module activation and undocking shortly after waking up to begin flight day five. The boom that extended the mass spectrometer out from the CSM's scientific instruments bay was stuck, semi-deployed. It was decided that Young and Duke would visually inspect the boom after undocking from the CSM in the LM. They entered the LM for activation and checkout of the spacecraft's systems. Despite entering the LM 40 minutes ahead of schedule, they completed preparations only 10 minutes early due to numerous delays in the process. With the preparations finished, they undocked in the LM "Orion" from Mattingly in the CSM "Casper" 96 hours, 13 minutes, 31 seconds into the mission. For the rest of the two crafts' passes over the near side of the Moon, Mattingly prepared to shift "Casper" to a circular orbit while Young and Duke prepared "Orion" for the descent to the lunar surface. At this point, during tests of the CSM's steerable rocket engine in preparation for the burn to modify the craft's orbit, a malfunction occurred in the engine's backup system. According to mission rules, "Orion" would have then re-docked with "Casper", in case Mission Control decided to abort the landing and use the lunar module's engines for the return trip to Earth. After several hours of analysis, however, mission controllers determined that the malfunction could be worked around and Young and Duke could proceed with the landing. As a result of this, powered descent to the lunar surface began about six hours behind schedule. Because of the delay, Young and Duke began their descent to the surface at an altitude higher than that of any previous mission, at. At an altitude of about, Young was able to view the landing site in its entirety. Throttle-down of the LM's landing engine occurred on time and the spacecraft tilted forward to its landing orientation

Return to Earth.

Eight minutes before departing the lunar surface, CAPCOM James Irwin notified Young and Duke from Mission Control that they were go for liftoff. Two minutes before launch, they activated the "Master Arm" switch and then the "Abort Stage" button, after which they awaited ignition of "Orion"s ascent stage engine. When the ascent stage ignited, small explosive charges severed the ascent stage from the descent stage and cables connecting the two were severed by a guillotine-like mechanism. Six minutes after liftoff, at a speed of about, Young and Duke reached lunar orbit. Young and Duke successfully rendezvoused and re-docked with Mattingly in the CSM. To minimize the transfer of lunar dust from the LM cabin into the CSM, Young and

Particles and Fields Subsatellite PFS-2.

The Apollo 16 Particles and Fields Subsatellite (PFS-2) was a small satellite released into lunar orbit from the service module. Its principal objective was to measure charged particles and magnetic fields all around the Moon as the Moon orbited Earth, similar to its sister spacecraft, PFS-1, released eight months earlier by Apollo 15. "The low orbits of both subsatellites were to be

Spacecraft locations.

The aircraft carrier USS "Ticonderoga" delivered the Apollo 16 command module to the North Island Naval Air Station, near San Diego, California, on Friday, May 5, 1972. On Monday, May 8, 1972, ground service equipment being used to empty the residual toxic reaction control system fuel in the command module tanks exploded in a Naval Air Station hangar. Forty-six people were sent to the hospital for 24 to 48 hours' observation, most suffering from inhalation of toxic fumes. Most seriously injured was a technician who suffered a fractured kneecap when the GSE cart overturned on him. A hole was blown in the hangar roof 250 feet above; about 40 windows in the hangar were shattered. The command module suffered a three-inch gash in one panel.  The Apollo 16 command module "Casper" is on display at the U.S. Space & Rocket Center in Huntsville, Alabama. The lunar module ascent stage separated 24 April 1972 but a loss of attitude control rendered it out of control. It orbited the Moon for about a year. Its impact site remains unknown. The S-IVB was deliberately crashed into the Moon. However, due to a communication failure before impact the exact location was unknown until January 2016, when it was discovered within Mare Insularum by the Lunar Reconnaissance Orbiter, approximately southwest of Copernicus Crater.  Duke donated some flown items, including a lunar map, to Kennesaw State University in Kennesaw, Georgia. He left two items on the Moon, both of which he photographed. The most famous is a plastic-encased photo portrait of his family (NASA Photo AS16-117-18841). The reverse of the photo is signed by Duke's family and bears this message: "This is the family of Astronaut Duke from Planet Earth. Landed on the Moon, April 1972." The other item was a commemorative medal issued by the United States Air Force, which was celebrating its 25th anniversary in 1972. He took two medals, leaving one on the Moon and donating the other to the Wright-Patterson Air Force Base museum.  In 2006, shortly after Hurricane Ernesto affected Bath, North Carolina, eleven-year-old Kevin Schanze discovered a piece of metal debris on the ground near his beach home. Schanze and a friend discovered a "stamp" on the flat metal sheet, which upon further inspection turned out to be a faded copy of the Apollo 16 mission insignia. NASA later confirmed the object to be a piece of the first stage of the SaturnV that had launched Apollo 16 into space. In July 2011, after returning the piece of debris at NASA's request, 16-year-old Schanze was given an all-access tour of the Kennedy Space Center and VIP seating for the launch of STS-135, the final mission of the Space Shuttle program.

Apollo 16 was the tenth crewed mission in the United States Apollo space program, the fifth and penultimate to land on the Moon, and the second to land in the lunar highlands. The second of Apollo's "J missions," it was crewed by Commander John Young, Lunar Module Pilot Charles Duke and Command Module Pilot Ken Mattingly. Launched from the Kennedy Space Center in Florida at 12:54 PM EST on April 16, 1972, the mission lasted 11 days, 1hour, and 51 minutes, and concluded at 2:45 p.m. EST on April 27.

阿波罗16号(英语:Apollo 16)是阿波罗计划中的第十次载人航天任务,也是人类历史上第五次成功登月的任务。


Taxonomy and phylogeny.

The gerenuk was first described by Victor Brooke in 1879 on the basis of three male specimens procured on "the mainland of Africa, north of the island of Zanzibar". Brooke used the scientific name "Gazella walleri", on the request of Gerald Waller (who provided the specimens) to name it after his deceased brother. The type locality was later corrected by John Kirk, who originally obtained the specimens on the "coast near the River Juba in southern Somaliland" before giving them to Waller. In 1886, Franz Friedrich Kohl proposed a new genus for the gerenuk, "Litocranius". The common name derives from the Somali name for the animal ("gáránúug"); the first recorded use of the name dates back to 1895. It is also known as the "giraffe gazelle" due to its similarity to the giraffe.  Two subspecies have been proposed, but these are considered to be independent species by some authors.  In 1997 Colin Groves proposed that "Litocranius" is a sister taxon of the similarly long-necked dibatag ("Ammodorcas clarkei"), but withdrew from this in 2000. A 1999 phylogenetic study based on cytochrome b and cytochrome c oxidase subunit III analysis showed that the tribe Antilopini, to which the gerenuk belongs, is monophyletic. In 2013, Eva Verena Bärmann and colleagues (of the University of Cambridge) revised the phylogeny of tribe on the basis of nuclear and mitochondrial gene analysis. The cladogram prepared by them (given below) showed that the springbok ("Antidorcas marsupialis") forms a clade with the gerenuk; this clade is sister to the saiga ("Saiga tatarica", tribe Saigini) and the genera "Antilope" (blackbuck), "Eudorcas", "Gazella" and "Nanger" (of Antilopini).

Description.

The gerenuk is a notably tall, slender antelope that resembles gazelles. It is characterised by its long, slender neck and limbs, the flat, wedge-like head and the large, round eyes. Males are nearly tall, and the shorter females ; the head-and-body length is typically between. Males weigh between ; females are lighter, weighing. The species is sexually dimorphic. The tail, that ends in a black tuft, measures.  Two types of colouration are clearly visible on the smooth coat: the reddish brown dorsal parts (the back or the "saddle"), and the lighter flanks, fawn to buff. The underbelly and insides of the legs are cream in colour. The eyes and the mouth are surrounded by white fur. Females have a dark patch on the crown. The horns, present only on males, are lyre-like ("S"-shaped). Curving backward then slightly forward, these measure.  The gerenuk resembles the dibatag, with which it is sympatric in eastern and central Somalia and southeastern Ethiopia. Both are brachyodonts and share several facial and cranial features, along with a two-tone colouration of the coat and strong thick horns (only in males). However, there are also some features distinguishing it from the gerenuk, including major morphological differences in horns, horn cores, tail, postorbital area and basioccipital processes. The gerenuk has a longer, heavier neck and a shorter tail. A finer point of difference is the absence of an inward-curving lobe in the lower edge of the ear (near its tip) in the gerenuk. The subspecies of the gerenuk are similar in colouration; the southern gerenuk is the smaller of the two.

Ecology and behaviour.

The gerenuk is a diurnal animal (active mainly during the day), though it typically stands or rests in shade during the noon. Foraging and feeding is the major activity throughout the day; females appear to spend longer time in feeding. The gerenuk may expose itself to rain, probably to cool its body. The social structure consists of small herds of two to six members. Herds typically comprise members of a single sex, though female herds additionally have juveniles. Some males lead a solitary life.  Fighting and travel are uncommon, possibly as a strategy to save energy for foraging. Both sexes maintain home ranges large, and might overlap. Those of males are scent-marked with preorbital gland secretions and guarded - hence these may be termed territories. The sedentary tendency of the antelope appears to increase with age.

Diet.

Primarily a browser, the gerenuk feed on foliage of bushes as well as trees, shoots, herbs, flowers and fruits. It can reach higher branches and twigs better than other gazelles and antelopes by standing erect on its hindlegs and elongating its neck; this helps it reach over above the ground. "Acacia" species are eaten whenever available, while evergreen vegetation forms the diet during droughts. The pointed mouth assists in extracting leaves from thorny vegetation. The gerenuk does not drink water regularly. Major predators of the antelope include Cape hunting dogs, cheetahs, hyenas, lions and leopards.

Reproduction.

Gerenuk reproduce throughout the year. Females reach sexual maturity at around one year, and males reach sexual maturity at 1.5 years, although in the wild they may only be successful after acquiring a territory (perhaps 3.5 years). The gestation period is about seven months. They are born one at a time, weighing about at birth. Offspring were produced through artificial insemination for the first time in 2010 at White Oak Conservation in Yulee, Florida. Four female calves were born, and one of the four was later inseminated successfully by White Oak and SEZARC (South-East Zoo Alliance for Reproduction & Conservation), creating a second generation of calves born from artificial insemination. Gerenuk can live thirteen years or more in captivity, and at least eight years in the wild.

The gerenuk (; ; "Litocranius walleri"), also known as the giraffe gazelle, is a long-necked antelope found in the Horn of Africa and the drier parts of East Africa. The sole member of the genus "Litocranius", the gerenuk was first described by the naturalist Victor Brooke in 1879. It is characterised by its long, slender neck and limbs. The antelope is tall, and weighs between. Two types of colouration are clearly visible on the smooth coat: the reddish brown back or the "saddle", and the lighter flanks, fawn to buff. The horns, present only on males, are lyre-shaped. Curving backward then slightly forward, these measure.

长颈羚(学名"Litocranius walleri")是一种生活在东非的羚羊。牠的名字起源于索马里语的哺乳动物。牠们可以重达52公斤及肩高超过1米。于交配时份,雄性的颈部会明显的肿胀。牠们可以单以后腿站立,并达7呎的高度。只有雄性有着短厚,像竖琴形状,长达17吋的角。牠们的皮在背部是赤红色,两侧颜色较浅,腹部则是白色的。


History.

1916–1934: Deutsches Stadion.

During the 1912 Summer Olympics, the city of Berlin was designated by the International Olympic Committee (IOC) to host the 1916 Summer Olympics. Germany's proposed stadium for this event was to be located in Charlottenburg, in the Grunewald Forest, to the west of Berlin—thus the stadium was also known as "Grunewaldstadion". A horse racing-course already existed there which belonged to the Berliner Rennverein, and even today the old ticket booths survive on Jesse-Owens-Allee. The government of Germany decided not to build in the nearby Grunewald forest, or to renovate buildings that already existed. Because of this desire, they hired the same architect who originally had built the "Rennverein", Otto March.  March decided to bury the stadium in the ground ("Erdstadion", in German). However, the 1916 Olympic Games were cancelled due to World War I. In the 1920s the first buildings of a school, the "Deutsches Sportforum" (German Sport Forum), dedicated to the teaching of professors of physical education and the study of sport science were built northeast of the stadium site. From 1926 to 1929, Otto March's sons (Werner and Walter) were assigned to build an annex for these institutions, though the finalization was delayed until 1936.

1936–1945: Olympiastadion.

In 1931, the International Olympic Committee selected Berlin to host the 11th Summer Olympics. Originally, the German government decided merely to restore the earlier Olympiastadion (Olympic Stadium) of 1916, with Werner March again retained to do this.  When the Nazis came to power in Germany (1933), they decided to use the Olympic Games in 1936 for propaganda purposes. With these plans in mind, Adolf Hitler ordered the construction of a great sports complex in Grunewald named the "Reichssportfeld" with a totally new Olympiastadion. Architect Werner March remained in charge of the project, assisted by his brother Walter.  Construction took place from 1934 to 1936. When the Reichssportfeld was finished, it was. It consisted of (east to west): the Olympiastadion, the Maifeld (Mayfield, capacity of 50,000) and the Waldbühne amphitheater (capacity of 25,000), in addition to various places, buildings and facilities for different sports (such as football, swimming, equestrian events, and field hockey) in the northern part.  Werner March built the new Olympiastadion on the foundation of the original Deutsches Stadion, once again with the lower half of the structure recessed 12 metres (39.4 feet) below ground level.  The capacity of the Olympiastadion reached 110,000 spectators. It also possessed a special stand for Adolf Hitler and his political associates. At its end, aligned with the symmetrically-designed layout of the buildings of the Olympischer Platz and toward the Maifeld, was the Marathon Gate with a big receptacle for the Olympic Flame.

Maifeld.

The Maifeld (Mayfield) was created as a huge lawn (11.2 hectares, 28 acres) for gymnastic demonstrations, specifically annual May Day celebrations by the government. The area was surrounded by 19 metres of land elevation (62 ft), even though the Olympiastadion (to the east) was only 17 metres (55 ft) high. The total capacity was 250,000 people, with 60,000 in the large stands that extended at the west end.  Also located there were the Langemarck-Halle (below) and the Bell Tower (rising high). The walls were built with sturdy stone from the area of the Lower Alps, and also feature equine sculptures (work of Josef Wackerle). This consisted of huge halls built under the stands of the Maifeld. Pillars were raised on which hung flags and shields commemorating all the forces that participated in a battle fought in Langemark (West Flanders, Belgium) on 10 November 1914, during the First World War. Since 2006, the ground floor is home to a public exhibit providing historical information on the area of the former Reichssportfeld.  During the 1936 Olympics, the Maifeld was used for polo and equestrian dressage events.  After the Second World War, the occupying forces of the British Army (Berlin Infantry Brigade) annually celebrated the King's or Queen's Official Birthday on the Maifeld and used it for a variety of sporting activities including cricket. Starting in 2012, Maifeld became home to the Berlin Cricket Club.

Bell Tower.

The Bell Tower crowned the western end of the Reichs Sportfield planted amid the tiers of the Maifeld stands. It was 77 metres (247 ft) high. From its peak could be observed the whole city of Berlin. During the games, it was used as observation post by administrators and police officials, doctors and the media. In the tower was the Olympic Bell. On its surface were the Olympic Rings with an eagle, the year 1936, the Brandenburg Gate, the date 1.-16. August and a motto between two swastikas: "I call the youth of the world" and "11. Olympic Games Berlin" – although the games were the 10th (Summer) Olympics, they were the Games of the XI Olympiad.  The Bell Tower was the only part of the Reichssportfeld that was destroyed in the war. The Third Reich used the tower's structure to store archives (such as films). The Soviet troops set its contents on fire, turning the tower into a makeshift chimney. The structure emerged from the fire severely damaged and weakened.  In 1947, the British engineers demolished the tower; however, it was reconstructed accurately in 1962. The Olympic Bell (which had survived the fire and remained in its place in the tower) fell 77 metres and cracked and has been incapable of sounding since then. In 1956, the bell was rescued, only in order to be used as a practice target for shooting with anti-tank ammunition. The damaged old bell survives and serves as a memorial.  The recreation of the tower was carried out from 1960 to 1962, once again by the architect Werner March, following the original blueprints. The present tower became an important tourist destination offering a panorama of Berlin, Spandau, the Havel Valley, Potsdam, Nauen and Hennigsdorf.  The most significant battle around the Olympiastadion was in April 1945 when the Soviet army fought to capture it. This was during the final battle of the Second World War in Europe, with the total invasion of Berlin as the Allies' target. The Olympiastadion survived the war almost untouched; it only suffered the impact of machine gun shots.

1945–1990: West Berlin era.

After the war, the former "Reichssportfeld" became the headquarters of the British military occupation forces. The administration settled in the northeastern buildings designed by the March brothers in the 1920s, which the Third Reich had used for official sport organisations such as the Reich Academy of Physical Training and extended by 1936, adding the "Haus des deutschen Sports" (House of German Sports) and other buildings (which belong since 1994 to the Olympiapark Berlin, a central sporting facility of the City of Berlin). Soon, the British forces renovated war-damaged buildings but also converted interiors to their specific needs (one gymnasium was converted into a dining hall, another into a garage). From 1951 to 2005, the Olympischer Platz had a giant antenna transmitting for all the portable radios in Berlin.  From then until 1994 and their departure, British forces held an annual celebration of the Queen's Official Birthday in the Maifeld with thousands of spectators from Berlin present. During the 1960s, American military and high school football teams introduced hundreds of thousands of Berliners to American football at the stadium in exhibition games.  During those years, Bundesliga football matches were played in the Olympiastadion, with Hertha BSC as local team. In the Maifeld, several competitions of football, rugby and polo were staged too. In the summers, the Waldbühne resumed its classical music concerts, and playing movies. The theatre was also used as an improvised ring for boxing matches.

1990–2004: Reunified Berlin.

In 1998, Berliners debated the destiny of the Olympiastadion in light of the legacy it represented for Germany. Some wanted to tear the stadium down and build a new one from scratch, while others favoured letting it slowly crumble "like the Colosseum in Rome". Finally, it was decided to renovate the Olympiastadion.  FIFA chose it as one of the venues of the 2006 FIFA World Cup. The State of Berlin hired a consortium composed of Walter Bau AG and "DYWIDAG" that won the €45 million franchise. The consortium took charge of the operation of the facilities together with Hertha BSC and the Government of Berlin after the remodelling. On 3 July 2000, the renovation began with a ceremony presided over by the Chancellor Gerhard Schröder, accompanied by Eberhard Diepgen (Mayor of Berlin), Franz Beckenbauer and Prof. Dr. Ignaz Walter.

2004–present: Multi-purpose arena.

The re-inauguration celebrations of the new Olympic Stadium were carried out on 31 July 2004, and 1 August 2004. On that day, Saturday, the party began with performances from Pink, Nena and Daniel Barenboim. It culminated at night with the opening ceremony. On day two, friendly matches were played between different categories of the club Hertha BSC and visiting teams. On 8 September 2004, Brazil played Germany.  In 2011, the venue hosted the World Culture Festival organized by the Art of Living where 70,000 people meditated for peace.  In 2018, the venue hosted the 2018 European Athletics Championships.

Stadium.

Renovation.

With the intention of creating a more intimate atmosphere for football games, the playing field was lowered by. Approximately of sand was excavated. The lower tier of seating in the stadium was demolished and rebuilt at a completely different angle of inclination.  The roof was extended to cover a total of, with 20 roof-supporting columns carrying a weight of of steel. The roof rises over the seats and is made up of transparent panels that allow sunlight to stream in during the day. The western portion (on the Marathon Arch) is open to reveal the Bell Tower to the spectators.  The conservation factor of the Olympiastadion as a historical monument was also considered, especially with respect to the preservation of the natural stone blocks. After criticisms, the colour of the athletics track around the game field was changed from red to blue, reflecting the colours of Hertha BSC.  The renovations used of concrete and of pre-cast reinforced concrete elements. Some of concrete was demolished and removed and of natural stone was refurbished.  The Olympiastadion was equipped with the latest technology in artificial illumination and sound equipment. It has 113 VIP stands, a set of restaurants, and two underground garages (for 630 cars). The total cost of the remodelling and amplification was €242 million.

Capacity.

The new Olympic Stadium has the highest all-seated capacity in Germany. It has a permanent capacity of 74,475 seats. The upper tier has 31 seating rows at an average slope of 23° and houses 36,455 seats, of which 36,032 are regular seats, 290 are seats on the press stand and 133 are seats in skyboxes. The lower tier has 42 seating rows at an average angle of 25,4° and houses 38,020 seats, of which 32,310 are regular seats, 560 are box seats, 563 are lounge seats (expandable to 743), 4,413 are business seats and 174 are wheelchair spaces.  For certain football matches, such as those between Hertha BSC and FC Bayern München, the capacity can be temporarily expanded. This is made by the addition of mobile grandstand over the Marathon Arch. The extended capacity reached 76,197 seats in 2014.  The only stadiums in Germany that have higher total capacities are the Signal Iduna Park in Dortmund and the Allianz Arena in Munich. However, the Signal Iduna Park and the Allianz Arena have both seating and standing areas, and their all-seated capacities are lower than that of the Olympiastadion. The total capacity of the Allianz Arena is also lower than the extended capacity of the Olympiastadion.

Tenant.

The stadium has been used as the home venue for the Bundesliga's Hertha BSC since 1963. In 1963, the Bundesliga was formed, and Hertha BSC participated by direct invitation, leaving its old stadium (the "Plumpe") to use the Olympiastadion. On 24 August, it played the first local match against 1. FC Nürnberg, with the final score 1–1. However, in 1965, the German Football Association found Hertha BSC guilty of bribery and relegated them to the Regional Leagues.  In 1968, Hertha returned to the first division, and to the Olympiastadion, and in 1971 sold "Plumpe". The second half of the 1970s was quite successful for Hertha BSC Berlin. In 1979, it reached the semifinals of the UEFA Cup, but was defeated by Red Star Belgrade. Hertha reached the finals of the German Cup twice (1977 and 1979). In the 1980s, Hertha had a declining role in the Bundesliga, and fell to the Regional Leagues in 1986, although they later recovered reaching the Second Division (1988–1989).  With the demolition of the Berlin Wall in November 1989, a spontaneous feeling of sympathy between Hertha and 1. FC Union Berlin from Eastern Berlin arose, which culminated in a friendly match at the Olympiastadion with 50,000 spectators (27 January 1990). In 1990, Hertha returned to the First Division, although it fell again to the Second Division from 1991 until 1997. Since 1997, the club has improved, climbing up the Bundesliga table and qualifying for the UEFA Champions League, with matches against top European teams like Chelsea and A.C. Milan.

Notable events.

The Olympiastadion held the world record for the attendance of a baseball game during the 1936 Olympics thought to be over 100,000.  Since 1985, the stadium has hosted the finals of both the DFB-Pokal and its companion women's tournament, the Frauen DFB Pokal. However, it did not host the 2010 final of the Frauen DFB Pokal, which was held at Cologne's RheinEnergieStadion as part of an experimental test to host the event in a different city.  The stadium hosted five American Bowls between 1990-1994. The stadium was also home to Berlin Thunder, an American football team in NFL Europa, from 2003 until the league's operator, the U.S. National Football League, closed down the money-losing competition in 2007.  The stadium also hosted The World Culture Festival. 2011 was to celebrate 30 years of service to humanity by Art of Living Foundation.  The stadium also hosts the Internationales Stadionfest, which also served as an IAAF Golden League event until 2010. The future of the event is currently unknown.  The stadium hosted the 2009 World Championships in Athletics where Usain Bolt broke the 100 metres and 200 metres world records.

1936 Summer Olympics.

On 1 August 1936, the Olympics were officially inaugurated by the head of state Adolf Hitler, and the Olympic cauldron was lit by athlete Fritz Schilgen. Four million tickets were sold for all the events of the 1936 Summer Olympics. This was also the first Olympics with television transmission (25 viewing spaces were scattered all over Berlin and Potsdam) and radio transmissions in 28 languages (with 20 radio vans and 300 microphones).  While the Olympic flame had been used for the first time in Amsterdam 1928, in Berlin 1936 a marathon-like tour of the Olympic torch was introduced, from Olympia in Greece, crossing six frontiers with a journey of to Berlin, through Greece, Bulgaria, Yugoslavia, Hungary, Czechoslovakia, Austria and Germany. The original idea of this Olympic torch relay was Carl Diem's, who was a political advisor to Propaganda Minister Joseph Goebbels, specialising in Olympic affairs. The Olympics were the subject of the propaganda film "Olympia" (1938) by Leni Riefenstahl.  Among the sport competitions, one of the most memorable events was the performance of the African-American track and field athlete Jesse Owens, representing the United States of America. Owens won the gold medal in the 100, 200, long jump and 4 x 100 relay. One of the main streets outside the stadium is named Jesse Owens Allee in recognition of his performance. The stadium also hosted the equestrian jumping, football, and handball events.

1974 FIFA World Cup Group A.

Three matches from Group A (West Germany, Chile, East Germany and Australia) were played in the Olympiastadion. The third match, Australia vs Chile, was played in torrential rain. The historic match between the two German teams, however, was played in Hamburg. The hosts, West Germany, won the tournament.

2006 FIFA World Cup.

The following matches were played in Berlin, for the 2006 FIFA World Cup:

2011 FIFA Women's World Cup.

In 2011, the Olympiastadion hosted Germany's opening match in the 2011 FIFA Women's World Cup. It was the only match in the tournament to be contested at the stadium.

2015 UEFA Champions League Final.

In May 2013, the Olympiastadion was chosen as the venue for the 2015 UEFA Champions League Final. FC Barcelona won their fifth title and completed a second treble.

Cultural references.

The stadium was used as a location scene in the cinematic cold-war spy drama "The Quiller Memorandum" (1966).

Transport.

U-Bahn.

The underground train (U-Bahn) U2 takes visitors directly to the station Olympiastadion. It's a short walk from there to the stadium (East Gate entrance: 500m, South Gate entrance: 870m). Average travel time: 14 minutes from Zoologischer Garten, 24 minutes from Potsdamer Platz, 34 minutes from Alexanderplatz.

S-Bahn.

The regional train (S-Bahn) S5 takes visitors directly to the station Olympiastadion. It's a short walk from there to the stadium (South Gate entrance via exit Flatowallee: 200 m, East Gate entrance via exit Trakehner Allee: 250m). Average travel time: 7 minutes from Spandau station, 14 minutes from Zoologischer Garten, 22 minutes from Friedrichstrasse, 26 minutes from Alexanderplatz.

Bus.

With the bus lines M49 and 218 visitors can reach the stop Flatowallee. It's a short walk from there to the stadium. With the bus line 104 visitors can reach the underground station Neu-Westend. From there it is a walk directly to the stadium. Visitors also can take the underground train and exit at the station Olympiastadion.

Olympiastadion () is a sports stadium at Olympiapark Berlin in Berlin, Germany. It was originally built by Werner March for the 1936 Summer Olympics. During the Olympics, the record attendance was thought to be over 100,000. Today the stadium is part of the Olympiapark Berlin.

柏林奥林匹克体育场()是一座位于德国柏林的大型体育场地,建于为举办1936年夏季奥林匹克运动会而建的德意志体育场原址,该场馆与现有建筑物均由玛赫家族设计,前者由奥托·玛赫设计,后者则由其子维纳·玛赫设计。


History.

Negative feedback as a control technique may be seen in the refinements of the water clock introduced by Ktesibios of Alexandria in the 3rd century BCE. Self-regulating mechanisms have existed since antiquity, and were used to maintain a constant level in the reservoirs of water clocks as early as 200 BCE. Negative feedback was implemented in the 17th Century. Cornelius Drebbel had built thermostatically-controlled incubators and ovens in the early 1600s, and centrifugal governors were used to regulate the distance and pressure between millstones in windmills. James Watt patented a form of governor in 1788 to control the speed of his steam engine, and James Clerk Maxwell in 1868 described "component motions" associated with these governors that lead to a decrease in a disturbance or the amplitude of an oscillation.  The term "feedback" was well established by the 1920s, in reference to a means of boosting the gain of an electronic amplifier. Friis and Jensen described this action as "positive feedback" and made passing mention of a contrasting "negative feed-back action" in 1924. Harold Stephen Black came up with the idea of using negative feedback in electronic amplifiers in 1927, submitted a patent application in 1928, and detailed its use in his paper of 1934, where he defined negative feedback as a type of coupling that "reduced" the gain of the amplifier, in the process greatly increasing its stability and bandwidth.  Karl Küpfmüller published papers on a negative-feedback-based automatic gain control system and a feedback system stability criterion in 1928.  Nyquist and Bode built on Black's work to develop a theory of amplifier stability.  Early researchers in the area of cybernetics subsequently generalized the idea of negative feedback to cover any goal-seeking or purposeful behavior.  Cybernetics pioneer Norbert Wiener helped to formalize the concepts of feedback control, defining feedback in general as "the chain of the transmission and return of information", and negative feedback as the case when:  While the view of feedback as any "circularity of action" helped to keep the theory simple and consistent, Ashby pointed out that, while it may clash with definitions that require a "materially evident" connection, "the exact definition of feedback is nowhere important". Ashby pointed out the limitations of the concept of "feedback": To reduce confusion, later authors have suggested alternative terms such as "degenerative", "self-correcting", "balancing", or "discrepancy-reducing" in place of "negative".

Overview.

In many physical and biological systems, qualitatively different influences can oppose each other. For example, in biochemistry, one set of chemicals drives the system in a given direction, whereas another set of chemicals drives it in an opposing direction. If one or both of these opposing influences are non-linear, equilibrium point(s) result.  In biology, this process (in general, biochemical) is often referred to as homeostasis; whereas in mechanics, the more common term is equilibrium.  In engineering, mathematics and the physical, and biological sciences, common terms for the points around which the system gravitates include: attractors, stable states, eigenstates/eigenfunctions, equilibrium points, and setpoints.  In control theory, "negative" refers to the sign of the multiplier in mathematical models for feedback. In delta notation, −Δoutput is added to or mixed into the input. In multivariate systems, vectors help to illustrate how several influences can both partially complement and partially oppose each other.  Some authors, in particular with respect to modelling business systems, use "negative" to refer to the reduction in difference between the desired and actual behavior of a system. In a psychology context, on the other hand, "negative" refers to the valence of the feedback – attractive versus aversive, or praise versus criticism.  In contrast, positive feedback is feedback in which the system responds so as to increase the magnitude of any particular perturbation, resulting in amplification of the original signal instead of stabilization. Any system in which there is positive feedback together with a gain greater than one will result in a runaway situation. Both positive and negative feedback require a feedback loop to operate.  However, negative feedback systems can still be subject to oscillations. This is caused by the slight delays around any loop. Due to these delays the feedback signal of some frequencies can arrive one half cycle later which will have a similar effect to positive feedback and these frequencies can reinforce themselves and grow over time. This problem is often dealt with by attenuating or changing the phase of the problematic frequencies. Unless the system naturally has sufficient damping, many negative feedback systems have low pass filters or dampers fitted.

Some specific implementations.

There are a large number of different examples of negative feedback and some are discussed below.

Error-controlled regulation.

One use of feedback is to make a system (say "T") self-regulating to minimize the effect of a disturbance (say "D"). Using a negative feedback loop, a measurement of some variable (for example, a process variable, say "E") is subtracted from a required value (the'set point') to estimate an operational error in system status, which is then used by a regulator (say "R") to reduce the gap between the measurement and the required value. The regulator modifies the input to the system "T" according to its interpretation of the error in the status of the system. This error may be introduced by a variety of possible disturbances or 'upsets', some slow and some rapid. The regulation in such systems can range from a simple 'on-off' control to a more complex processing of the error signal.  It may be noted that the physical form of the signals in the system may change from point to point. So, for example, a change in weather may cause a disturbance to the "heat" input to a house (as an example of the system "T") that is monitored by a thermometer as a change in "temperature" (as an example of an 'essential variable' "E"), converted by the thermostat (a 'comparator') into an "electrical" error in status compared to the'set point' "S", and subsequently used by the regulator (containing a 'controller' that commands "gas" control valves and an ignitor) ultimately to change the "heat" provided by a furnace (an 'effector') to counter the initial weather-related disturbance in heat input to the house.  Error controlled regulation is typically carried out using a Proportional-Integral-Derivative Controller (PID controller). The regulator signal is derived from a weighted sum of the error signal, integral of the error signal, and derivative of the error signal. The weights of the respective components depend on the application.  Mathematically, the regulator signal is given by: where

Negative feedback amplifier.

The negative feedback amplifier was invented by Harold Stephen Black at Bell Laboratories in 1927, and granted a patent in 1937 (US Patent 2,102,671 "a continuation of application Serial No. 298,155, filed August 8, 1928...").  There are many advantages to feedback in amplifiers. In design, the type of feedback and amount of feedback are carefully selected to weigh and optimize these various benefits.  Advantages of negative voltage feedback in amplifiers are-  Though negative feedback has many advantages, amplifiers with feedback can oscillate. See the article on step response. They may even exhibit instability. Harry Nyquist of Bell Laboratories proposed the Nyquist stability criterion and the Nyquist plot that identify stable feedback systems, including amplifiers and control systems. The figure shows a simplified block diagram of a negative feedback amplifier.  The feedback sets the overall (closed-loop) amplifier gain at a value:  where the approximate value assumes β"A " » 1. This expression shows that a gain greater than one requires β < 1. Because the approximate gain 1/β is independent of the open-loop gain "A", the feedback is said to 'desensitize' the closed-loop gain to variations in "A " (for example, due to manufacturing variations between units, or temperature effects upon components), provided only that the gain "A" is sufficiently large. In this context, the factor (1+β"A") is often called the 'desensitivity factor', and in the broader context of feedback effects that include other matters like electrical impedance and bandwidth, the 'improvement factor'.  If the disturbance "D" is included, the amplifier output becomes:  which shows that the feedback reduces the effect of the disturbance by the 'improvement factor' (1+β "A"). The disturbance "D" might arise from fluctuations in the amplifier output due to noise and nonlinearity (distortion) within this amplifier, or from other noise sources such as power supplies.  The difference signal "I"–β"O" at the amplifier input is sometimes called the "error signal". According to the diagram, the error signal is:  From this expression, it can be seen that a large 'improvement factor' (or a large loop gain β"A") tends to keep this error signal small.  Although the diagram illustrates the principles of the negative feedback amplifier, modeling a real amplifier as a unilateral forward amplification block and a unilateral feedback block has significant limitations. For methods of analysis that do not make these idealizations, see the article Negative feedback amplifier.

Operational amplifier circuits.

The operational amplifier was originally developed as a building block for the construction of analog computers, but is now used almost universally in all kinds of applications including audio equipment and control systems.  Operational amplifier circuits typically employ negative feedback to get a predictable transfer function. Since the open-loop gain of an op-amp is extremely large, a small differential input signal would drive the output of the amplifier to one rail or the other in the absence of negative feedback. A simple example of the use of feedback is the op-amp voltage amplifier shown in the figure.  The idealized model of an operational amplifier assumes that the gain is infinite, the input impedance is infinite, output resistance is zero, and input offset currents and voltages are zero. Such an ideal amplifier draws no current from the resistor divider. Ignoring dynamics (transient effects and propagation delay), the infinite gain of the ideal op-amp means this feedback circuit drives the voltage difference between the two op-amp inputs to zero. Consequently, the voltage gain of the circuit in the diagram, assuming an ideal op amp, is the reciprocal of feedback voltage division ratio β:  A real op-amp has a high but finite gain "A" at low frequencies, decreasing gradually at higher frequencies. In addition, it exhibits a finite input impedance and a non-zero output impedance. Although practical op-amps are not ideal, the model of an ideal op-amp often suffices to understand circuit operation at low enough frequencies. As discussed in the previous section, the feedback circuit stabilizes the closed-loop gain and desensitizes the output to fluctuations generated inside the amplifier itself.

Mechanical engineering.

An example of the use of negative feedback control is the ballcock control of water level (see diagram), or a pressure regulator. In modern engineering, negative feedback loops are found in engine governors, fuel injection systems and carburettors. Similar control mechanisms are used in heating and cooling systems, such as those involving air conditioners, refrigerators, or freezers.

Biology.

Some biological systems exhibit negative feedback such as the baroreflex in blood pressure regulation and erythropoiesis. Many biological processes (e.g., in the human anatomy) use negative feedback. Examples of this are numerous, from the regulating of body temperature, to the regulating of blood glucose levels. The disruption of feedback loops can lead to undesirable results: in the case of blood glucose levels, if negative feedback fails, the glucose levels in the blood may begin to rise dramatically, thus resulting in diabetes.  For hormone secretion regulated by the negative feedback loop: when gland X releases hormone X, this stimulates target cells to release hormone Y. When there is an excess of hormone Y, gland X "senses" this and inhibits its release of hormone X. As shown in the figure, most endocrine hormones are controlled by a physiologic negative feedback inhibition loop, such as the glucocorticoids secreted by the adrenal cortex. The hypothalamus secretes corticotropin-releasing hormone (CRH), which directs the anterior pituitary gland to secrete adrenocorticotropic hormone (ACTH). In turn, ACTH directs the adrenal cortex to secrete glucocorticoids, such as cortisol. Glucocorticoids not only perform their respective functions throughout the body but also negatively affect the release of further stimulating secretions of both the hypothalamus and the pituitary gland, effectively reducing the output of glucocorticoids once a sufficient amount has been released.

Chemistry.

Closed systems containing substances undergoing a reversible chemical reaction can also exhibit negative feedback in accordance with Le Chatelier's principle which shift the chemical equilibrium to the opposite side of the reaction in order to reduce a stress. For example, in the reaction If a mixture of the reactants and products exists at equilibrium in a sealed container and nitrogen gas is added to this system, then the equilibrium will shift toward the product side in response. If the temperature is raised, then the equilibrium will shift toward the reactant side which, because the reverse reaction is endothermic, will partially reduces the temperature.

Self-organization.

Self-organization is the capability of certain systems "of organizing their own behavior or structure". There are many possible factors contributing to this capacity, and most often positive feedback is identified as a possible contributor. However, negative feedback also can play a role.

Economics.

In economics, automatic stabilisers are government programs that are intended to work as negative feedback to dampen fluctuations in real GDP.  Mainstream economics asserts that the market pricing mechanism operates to match supply and demand, because mismatches between them feed back into the decision-making of suppliers and demanders of goods, altering prices and thereby reducing any discrepancy. However Norbert Wiener wrote in 1948:  The notion of economic equilibrium being maintained in this fashion by market forces has also been questioned by numerous heterodox economists such as financier George Soros and leading ecological economist and steady-state theorist Herman Daly, who was with the World Bank in 1988–1994.

Environmental Applications.

A basic and common example of a negative feedback system in the environment is the interaction among cloud cover, plant growth, solar radiation, and planet temperature. As incoming solar radiation increases, planet temperature increases. As the temperature increases, the amount of plant life that can grow increases. This plant life can then make products such as sulfur which produce more cloud cover. An increase in cloud cover leads to higher albedo, or surface reflectivity, of the Earth. As albedo increases, however, the amount of solar radiation decreases. This, in turn, affects the rest of the cycle.  Cloud cover, and in turn planet albedo and temperature, is also influenced by the hydrological cycle. As planet temperature increases, more water vapor is produced, creating more clouds. The clouds then block incoming solar radiation, lowering the temperature of the planet. This interaction produces less water vapor and therefore less cloud cover. The cycle then repeats in a negative feedback loop. In this way, negative feedback loops in the environment have a stabilizing effect.

Negative feedback (or balancing feedback) occurs when some function of the output of a system, process, or mechanism is fed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances.

负回馈(英语:negative feedback),是反馈的一种。是指系统的输出会影响系统的输入,在输出变动时,所造成的影响恰和原来变动的趋势相反;反之,就称为正回馈。另一种说法是系统在一个条件变化时,系统会作出抵抗该变化的行为、变动持续减少。例如人的体温上升时会流汗,流汗会散热使体温下降,就是负反馈的一个例子;在自然界有许多系统有负反馈的特性,其他例子包括勒沙特列原理和楞次定律。


Description.

The male green swordtail grows to a maximum overall length of and the female to. The name ‘swordtail’ is derived from the elongated lower lobe of the male's caudal fin (tailfin). Sexual dimorphism is moderate, with the female being larger than the male, but lacking the ‘sword’. The wild form is olive green in color, with a red or brown lateral stripe and speckles on the dorsal and, sometimes, caudal fins. The male's ‘sword’ is yellow, edged in black below. Captive breeding has produced many color varieties, including black, red, and many patterns thereof, for the aquarium hobby.  The green swordtail prefers swift-flowing, heavily vegetated rivers and streams, but is also found in warm springs and canals. Omnivorous, its diet includes both plants and small crustaceans, insects, and annelid worms.

Invasive species.

"X. hellerii" has become a nuisance pest as an introduced species in a number of countries. It has caused ecological damage because of its ability to rapidly reproduce in high numbers. Feral populations have established themselves in southern Africa, including Natal, Hawaii, Madagascar and eastern Transvaal in South Africa and Otjikoto Lake in Namibia. Significant populations have also established themselves along the east coast of Australia.

Etymology and taxonomy.

The binomial of the green swordtail is made up of its generic name, "Xiphophorus" which means "sword bearer" in Greek, a reference to the extended lower part of the caudal fin which is referred to as the "sword". The specific name honours the collector of the type, the Austrian botanist Karl Bartholomaeus Heller (1824-1880), who discovered this fish while exploring México in 1845-1848. The green swordtail was described from Heller's type by Johann Jakob Heckel in 1848 with the type locality given as Orizaba, Mexico. It is the type species of the genus "Xiphophorus".

Aquarium Fish.

One of the most popular tropical aquarium fish, the green swordtail has been bred into various hybrid forms for the aquarium hobby due to its hardiness and suitability for community tanks.  "X. hellerii" is a common laboratory animal and has been used as a model organism in studies involving female mate preference and male conflict.  It is often designated "X. helleri" (with one ‘i’), but authorities consider this an orthographic error and the spelling with two ‘i’s to be the valid specific epithet. It is named after Karl Bartholomaeus Heller, who collected the type specimen. Due to interbreeding with the southern platyfish or ‘platy’, most swordtails in aquariums are hybrids to some degree.  The males’ elongated caudal fins have been found to significantly affect their chances at mating. The presence of a well-endowed male spurs the maturity of females, while it inhibits the maturity of juvenile males in the vicinity of the well-endowed male.

The green swordtail ("Xiphophorus hellerii") is a species of freshwater/brackish fish in family Poeciliidae of order Cyprinodontiformes. A live-bearer, it is closely related to the southern platyfish or ‘platy’ ("X. maculatus") and can crossbreed with it. It is native to an area of North and Central America stretching from Veracruz, Mexico, to northwestern Honduras.

剑尾鱼(学名:),为辐鳍鱼纲<unk>形目花<unk>科的其中一种,分布于中美洲墨西哥Nantla至洪都拉斯西北部的淡水流域,并引进到许多国家,体长可达14公分,栖息在水流快速、植被生长的溪流或湖泊、池塘,属杂食性,主要以甲壳类、蠕虫、昆虫等为食,人工饲养可投喂饲料,适应能力强,性情温和,不易生病,可以和其他无攻击性的热带鱼混养。但剑尾鱼喜欢跳跃,因此鱼缸要加盖。否则容易跳出导致死亡。雌鱼要比雄鱼体形要大,雄鱼尾部有延长的剑状突出,雌鱼尾部也有剑状突出但与雄鱼相较下较短,有单剑,也有双剑。 红剑鱼是一种人工培育的品种,是剑尾鱼经杂交选育的,通体红色,尾剑一般镶有黑边,十分美丽。


Definitions.

Let be a vector space or an affine space over the real numbers, or, more generally, over some ordered field. This includes Euclidean spaces, which are affine spaces. A subset of is convex if, for all and in, the line segment connecting and is included in. This means that the affine combination belongs to, for all and in, and in the interval. This implies that convexity (the property of being convex) is invariant under affine transformations. This implies also that a convex set in a real or complex topological vector space is path-connected, thus connected.  A set is "" if every point on the line segment connecting and other than the endpoints is inside the interior of.  A set is "absolutely convex" if it is convex and balanced.  The convex subsets of (the set of real numbers) are the intervals and the points of. Some examples of convex subsets of the Euclidean plane are solid regular polygons, solid triangles, and intersections of solid triangles. Some examples of convex subsets of a Euclidean 3-dimensional space are the Archimedean solids and the Platonic solids. The Kepler-Poinsot polyhedra are examples of non-convex sets.

Non-convex set.

A set that is not convex is called a "non-convex set". A polygon that is not a convex polygon is sometimes called a concave polygon, and some sources more generally use the term "concave set" to mean a non-convex set, but most authorities prohibit this usage.  The complement of a convex set, such as the epigraph of a concave function, is sometimes called a "reverse convex set", especially in the context of mathematical optimization.

Properties.

Given points in a convex set, and nonnegative numbers such that, the affine combination belongs to. As the definition of a convex set is the case, this property characterizes convex sets.  Such an affine combination is called a convex combination of.

Intersections and unions.

The collection of convex subsets of a vector space, an affine space, or a Euclidean space has the following properties:

Closed convex sets.

Closed convex sets are convex sets that contain all their limit points. They can be characterised as the intersections of "closed half-spaces" (sets of point in space that lie on and to one side of a hyperplane).  From what has just been said, it is clear that such intersections are convex, and they will also be closed sets. To prove the converse, i.e., every convex set may be represented as such intersection, one needs the supporting hyperplane theorem in the form that for a given closed convex set and point outside it, there is a closed half-space that contains and not. The supporting hyperplane theorem is a special case of the Hahn–Banach theorem of functional analysis.

Convex sets and rectangles.

Let "C" be a convex body in the plane. We can inscribe a rectangle "r" in "C" such that a homothetic copy "R" of "r" is circumscribed about "C". The positive homothety ratio is at most 2 and:

Blaschke-Santaló diagrams.

The set formula_3 of all planar convex bodies can be parameterized in terms of the convex body diameter "D", its inradius "r" (the biggest circle contained in the convex body) and its circumradius "R" (the smallest circle containing the convex body). In fact, this set can be described by the set of inequalities given byformula_4  formula_5  formula_6  formula_7and can be visualized as the image of the function "g" that maps a convex body to the point given by ("r"/"R", "D"/2"R"). The image of this function is known a ("r", "D", "R") Blachke-Santaló diagram.  Alternatively, the set formula_3 can also be parametrized by its width (the smallest distance between any two different parallel support hyperplanes), perimeter and area.

Other properties.

Let "X" be a topological vector space and formula_9 be convex.

Convex hulls and Minkowski sums.

Convex hulls.

Every subset of the vector space is contained within a smallest convex set (called the convex hull of ), namely the intersection of all convex sets containing. The convex-hull operator Conv() has the characteristic properties of a hull operator: The convex-hull operation is needed for the set of convex sets to form a lattice, in which the ""join"" operation is the convex hull of the union of two convex sets The intersection of any collection of convex sets is itself convex, so the convex subsets of a (real or complex) vector space form a complete lattice.

Minkowski addition.

In a real vector-space, the "Minkowski sum" of two (non-empty) sets, and, is defined to be the set formed by the addition of vectors element-wise from the summand-sets More generally, the "Minkowski sum" of a finite family of (non-empty) sets is the set formed by element-wise addition of vectors  For Minkowski addition, the "zero set" containing only the zero vector has special importance: For every non-empty subset S of a vector space in algebraic terminology, is the identity element of Minkowski addition (on the collection of non-empty sets).

Convex hulls of Minkowski sums.

Minkowski addition behaves well with respect to the operation of taking convex hulls, as shown by the following proposition:  Let be subsets of a real vector-space, the convex hull of their Minkowski sum is the Minkowski sum of their convex hulls  This result holds more generally for each finite collection of non-empty sets:  In mathematical terminology, the operations of Minkowski summation and of forming convex hulls are commuting operations.

Minkowski sums of convex sets.

The Minkowski sum of two compact convex sets is compact. The sum of a compact convex set and a closed convex set is closed.  The following famous theorem, proved by Dieudonné in 1966, gives a sufficient condition for the difference of two closed convex subsets to be closed. It uses the concept of a recession cone of a non-empty convex subset "S", defined as: where this set is a convex cone containing formula_23 and satisfying formula_24. Note that if "S" is closed and convex then formula_25 is closed and for all formula_26, formula_27.  Theorem (Dieudonné). Let "A" and "B" be non-empty, closed, and convex subsets of a locally convex topological vector space such that formula_28 is a linear subspace. If "A" or "B" is locally compact then "A" − "B" is closed.

Generalizations and extensions for convexity.

The notion of convexity in the Euclidean space may be generalized by modifying the definition in some or other aspects. The common name "generalized convexity" is used, because the resulting objects retain certain properties of convex sets.

Star-convex (star-shaped) sets.

Let be a set in a real or complex vector space. is star convex (star-shaped) if there exists an in such that the line segment from to any point in is contained in. Hence a non-empty convex set is always star-convex but a star-convex set is not always convex.

Orthogonal convexity.

An example of generalized convexity is orthogonal convexity.  A set in the Euclidean space is called orthogonally convex or ortho-convex, if any segment parallel to any of the coordinate axes connecting two points of lies totally within. It is easy to prove that an intersection of any collection of orthoconvex sets is orthoconvex. Some other properties of convex sets are valid as well.

Non-Euclidean geometry.

The definition of a convex set and a convex hull extends naturally to geometries which are not Euclidean by defining a geodesically convex set to be one that contains the geodesics joining any two points in the set.

Order topology.

Convexity can be extended for a totally ordered set endowed with the order topology.  Let. The subspace is a convex set if for each pair of points in such that, the interval is contained in. That is, is convex if and only if for all in, implies.  A convex set is not connected in general: a counter-example is given by the space, which is both convex and totally disconnected.

Convexity spaces.

The notion of convexity may be generalised to other objects, if certain properties of convexity are selected as axioms.  Given a set, a convexity over is a collection of subsets of satisfying the following axioms:  The elements of are called convex sets and the pair is called a convexity space. For the ordinary convexity, the first two axioms hold, and the third one is trivial.  For an alternative definition of abstract convexity, more suited to discrete geometry, see the "convex geometries" associated with antimatroids.

In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points, it contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersect every line into a single line segment (possibly empty). For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex.

在点集拓扑学与欧几里得空间中,凸集(Convex set)是一个点集合,其中每两点之间的直线点都落在该点集合中。


Early life.

Pelagius was a Visigoth nobleman, the son of Fafila. The "Chronica Albeldensis" says that this Fafila was a "dux" of Gallaecia, who was killed by Wittiza. The "Chronicle of Alfonso III" identifies Pelagius as a grandson of Chindasuinth and says that his father was blinded in Córdoba, at the instigation of Wittiza. Wittiza is also said to have exiled Pelagius from Toledo upon assuming the crown in 702. In the opinion of Roger Collins, this is a late tradition and the account of the "Albeldensis", which locates Pelagius' origins in the north of the peninsula, is more credible. Both chronicles agree, however, that he was a Visigoth who was exiled from Toledo by Wittiza.  According to the later tradition, Munuza, the Berber governor of "Iegione" (either Gijón or León), became attracted to Pelagius' sister and sent word to Tariq ibn Ziyad, who ordered him to capture Pelagius and send him to Córdoba. If Munuza's seat is identified with Gijón, it may be inferred that the Arabs had established their rule in the Asturias and that Pelagius was not the leader of a local resistance to Arab conquest. Pelagius may have come to terms with the Arab elite whereby he was permitted to govern locally in the manner of the previous Visigoths, as is known to have occurred between Arab rulers and Visigothic noblemen elsewhere, as in the case of Theudimer, although most historians consider this unlikely.

Reign.

At some point Pelagius is said to have rebelled, but for what reasons is unknown; such rebellions by local authorities against their superiors formed a common theme in Visigothic Spain. A Muslim army was sent against him under the command of Alkama and the Christian bishop of Seville, Oppa. That Alkama was the general and that there was a bishop of Seville named Oppa among his ranks is generally accepted. A battle was fought near Covadonga ("in monte Auseva" or "in monte Libana") in which Alkama was killed and Oppa captured. Moorish chronicles of the event describe Pelagius and his small force as "thirty wild donkeys", as reported by al-Maqqari in the 17th century. The battle is usually dated to 718 or 719, between the governorships of al-Hurr and as-Sham, though some have dated it as late as 722 and the "Chronica Albeldensia" dates it in the 740s.  After his election as "princeps" (prince, principal leader) of the Asturians by the local magnates in the Visigothic manner, Pelagius made his capital at Cangas de Onís. The "" says about this election: And he [Pelagius], going to his mountainous lands, gathered all those who were going to council and ascended a big mountain named Asseuua. He spread his orders between all the Astures, who gathered in council and elected Pelagius as their "princeps". His kingdom, firstly centred on the eastern Asturias, soon grew. He married his daughter Ermesinda to the future king Alfonso I, son of Pelagius' eastern neighbour, Duke Peter of Cantabria.  Pelagius reigned for eighteen or nineteen years until his death in 737, when he was succeeded by his son Fafila.  He was buried in the church of Santa Eulalia de Abamia, located in the surroundings of the village of Corao, near Cangas de Onís. His remains were transferred by King Alfonso X of Castile to the Holy Cave of Covadonga, as were those of his wife Gaudiosa and his sister. He left, in addition to his son and successor Fafila, a daughter, Ermesinda, who was to become progenitress, along with King Alfonso I of Asturias ("Alfonso the Catholic"), of the later royalty of Asturias.

Historiography.

The chief sources for Pelagius's life and career are two Latin chronicles written in the late ninth century in the kingdom he founded. The first is the "Chronica Albeldensia", written at Albelda towards 881, and preserved in the "Codex Vigilanus," with a continuation to 976. The latter is the "Chronicle of Alfonso III", which was revised in the early tenth century and preserved in two textual traditions that diverge in several key passages: the ', preserved in the "Códice de Roda", and the ', supposedly written by Sebastian, Bishop of Salamanca (910–913). The only likely earlier written sources from which these chroniclers could derive information are regnal lists.

Pelagius (; ; ; ; "c". 685 – 737) was an Iberian Visigoth nobleman who founded the Kingdom of Asturias in 718. Pelagius is credited with initiating the "Reconquista", the Christian reconquest of the Iberian Peninsula from the Moors, and establishing the Asturian monarchy, making him the forefather of all the future Iberian monarchies, including the Kings of Castile, the Kings of León, and the Kings of Portugal.

佩拉约(,,约685年-737年)是西哥德的贵族,他建立了阿斯图里亚斯王国,从718年开始统治直到去世。他在科瓦东加战役的胜利,被视为「收复失地运动」的起点,基督徒从摩尔人手中收复伊比利半岛,从他建立独立的基督教国家对抗摩尔人政权开始,但是并没有强力的证据证明他的目的是复兴过去的西哥德王国或者只是因为任何宗教渴望的刺激。


History.

All through history, the availability of salt has been pivotal to civilization. What is now thought to have been the first city in Europe is Solnitsata, in Bulgaria, which was a salt mine, providing the area now known as the Balkans with salt since 5400 BC. Even the name Solnitsata means "salt works".  While people have used canning and artificial refrigeration to preserve food for the last hundred years or so, salt has been the best-known food preservative, especially for meat, for many thousands of years. A very ancient salt-works operation has been discovered at the Poiana Slatinei archaeological site next to a salt spring in Lunca, Neamț County, Romania. Evidence indicates that Neolithic people of the Precucuteni Culture were boiling the salt-laden spring water through the process of briquetage to extract the salt as far back as 6050 BC. The salt extracted from this operation may have had a direct correlation to the rapid growth of this society's population soon after its initial production began. The harvest of salt from the surface of Xiechi Lake near Yuncheng in Shanxi, China, dates back to at least 6000 BC, making it one of the oldest verifiable saltworks.  There is more salt in animal tissues, such as meat, blood, and milk, than in plant tissues. Nomads who subsist on their flocks and herds do not eat salt with their food, but agriculturalists, feeding mainly on cereals and vegetable matter, need to supplement their diet with salt. With the spread of civilization, salt became one of the world's main trading commodities. It was of high value to the ancient Hebrews, the Greeks, the Romans, the Byzantines, the Hittites and other peoples of antiquity. In the Middle East, salt was used to ceremonially seal an agreement, and the ancient Hebrews made a "covenant of salt" with God and sprinkled salt on their offerings to show their trust in him. An ancient practice in time of war was salting the earth: scattering salt around in a defeated city to prevent plant growth. The Bible tells the story of King Abimelech who was ordered by God to do this at Shechem, and various texts claim that the Roman general Scipio Aemilianus Africanus ploughed over and sowed the city of Carthage with salt after it was defeated in the Third Punic War (146 BC). Salt may have been used for barter in connection with the obsidian trade in Anatolia in the Neolithic Era. Salt was included among funeral offerings found in ancient Egyptian tombs from the third millennium BC, as were salted birds, and salt fish. From about 2800 BC, the Egyptians began exporting salt fish to the Phoenicians in return for Lebanon cedar, glass, and the dye Tyrian purple; the Phoenicians traded Egyptian salted fish and salt from North Africa throughout their Mediterranean trade empire. Herodotus described salt trading routes across Libya back in the 5th century BC. In the early years of the Roman Empire, roads were built for the transportation of salt from the salt imported at Ostia to the capital.  In Africa, salt was used as currency south of the Sahara, and slabs of rock salt were used as coins in Abyssinia. Moorish merchants in the 6th century traded salt for gold, weight for weight. The Tuareg have traditionally maintained routes across the Sahara especially for the transportation of salt by Azalai (salt caravans). The caravans still cross the desert from southern Niger to Bilma, although much of the trade now takes place by truck. Each camel takes two bales of fodder and two of trade goods northwards and returns laden with salt pillars and dates. In Gabon, before the arrival of Europeans, the coast people carried on a remunerative trade with those of the interior by the medium of sea salt. This was gradually displaced by the salt that Europeans brought in sacks, so that the coast natives lost their previous profits; as of the author's writing in 1958, sea salt was still the currency best appreciated in the interior.  Salzburg, Hallstatt, and Hallein lie within of each other on the river Salzach in central Austria in an area with extensive salt deposits. Salzach literally means "salt river" and Salzburg "salt castle", both taking their names from the German word meaning salt and Hallstatt was the site of the world's first salt mine. The town gave its name to the Hallstatt culture that began mining for salt in the area in about 800 BC. Around 400 BC, the townsfolk, who had previously used pickaxes and shovels, began open pan salt making. During the first millennium BC, Celtic communities grew rich trading salt and salted meat to Ancient Greece and Ancient Rome in exchange for wine and other luxuries.  The word "salary" comes from the Latin word for salt. The reason for this is unknown; a persistent modern claim that the Roman Legions were sometimes paid in salt is baseless. The word "salad" literally means "salted", and comes from the ancient Roman practice of salting leaf vegetables..  The commonly used Tamil word for ‘salary’ is ‘sambalam’,In pure Tamil ‘Oodhiyam’ is the word for salary, but it isn’t in use anymore.Interestingly, the etymology of the English word ‘salary’ goes back to the Latin word ‘sal’, meaning ‘salt’. It’s similar for ‘sambalam’ too.Just like Roman soldiers were allowed a ‘salt’ allowance, in Tamil Nadu, rice and salt were given as payment for work. In early Tamil, the word for rice was the ‘samba’ (since Samba was the rice which was used then), and salt was called ‘alam’. So the word for payment became ‘sambalam’ and it soon replaced the word ‘udhiyam’.  Wars have been fought over salt. Venice fought and won a war with Genoa over the product, and it played an important part in the American Revolution. Cities on overland trade routes grew rich by levying duties, and towns like Liverpool flourished on the export of salt extracted from the salt mines of Cheshire. Various governments have at different times imposed salt taxes on their peoples. The voyages of Christopher Columbus are said to have been financed from salt production in southern Spain, and the oppressive salt tax in France was one of the causes of the French Revolution. After being repealed, this tax was reimposed by Napoleon when he became emperor to pay for his foreign wars, and was not finally abolished until 1946. In 1930, Mahatma Gandhi led at least 100,000 people on the "Dandi March" or "Salt Satyagraha", in which protesters made their own salt from the sea thus defying British rule and avoiding paying the salt tax. This civil disobedience inspired millions of common people and elevated the Indian independence movement from an elitist movement to a national struggle.

Chemistry.

Salt is mostly sodium chloride, the ionic compound with the formula NaCl, representing equal proportions of sodium and chlorine. Sea salt and freshly mined salt (much of which is sea salt from prehistoric seas) also contain small amounts of trace elements (which in these small amounts are generally good for plant and animal health ). Mined salt is often refined in the production of table salt; it is dissolved in water, purified via precipitation of other minerals out of solution, and re-evaporated. During this same refining process it is often also iodized. Salt crystals are translucent and cubic in shape; they normally appear white but impurities may give them a blue or purple tinge. The molar mass of salt is 58.443 g/mol, its melting point is 801 °C (1,474 °F) and its boiling point 1,465 °C (2,669 °F). Its density is 2.17 grams per cubic centimetre and it is readily soluble in water. When dissolved in water it separates into Na and Cl ions, and the solubility is 359 grams per litre. From cold solutions, salt crystallises as the dihydrate NaCl·2HO. Solutions of sodium chloride have very different properties from those of pure water; the freezing point is −21.12 °C (−6.02 °F) for 23.31 wt% of salt, and the boiling point of saturated salt solution is around 108.7 °C (227.7 °F).

Edible salt.

Salt is essential to the health of humans and other animals, and it is one of the five basic taste sensations. Salt is used in many cuisines around the world, and it is often found in salt shakers on diners' eating tables for their personal use on food. Salt is also an ingredient in many manufactured foodstuffs. Table salt is a refined salt containing about 97 to 99 percent sodium chloride. Usually, anticaking agents such as sodium aluminosilicate or magnesium carbonate are added to make it free-flowing. Iodized salt, containing potassium iodide, is widely available. Some people put a desiccant, such as a few grains of uncooked rice or a saltine cracker, in their salt shakers to absorb extra moisture and help break up salt clumps that may otherwise form.

Fortified table salt.

Some table salt sold for consumption contains additives which address a variety of health concerns, especially in the developing world. The identities and amounts of additives vary widely from country to country. Iodine is an important micronutrient for humans, and a deficiency of the element can cause lowered production of thyroxine (hypothyroidism) and enlargement of the thyroid gland (endemic goitre) in adults or cretinism in children. Iodized salt has been used to correct these conditions since 1924 and consists of table salt mixed with a minute amount of potassium iodide, sodium iodide or sodium iodate. A small amount of dextrose may also be added to stabilize the iodine. Iodine deficiency affects about two billion people around the world and is the leading preventable cause of mental retardation. Iodized table salt has significantly reduced disorders of iodine deficiency in countries where it is used.  The amount of iodine and the specific iodine compound added to salt varies from country to country. In the United States, the Food and Drug Administration (FDA) recommends [21 CFR 101.9 (c)(8)(iv)] 150 micrograms of iodine per day for both men and women. US iodized salt contains 46–77 ppm (parts per million), whereas in the UK the iodine content of iodized salt is recommended to be 10–22 ppm.  Sodium ferrocyanide, also known as yellow prussiate of soda, is sometimes added to salt as an anticaking agent. The additive is considered safe for human consumption. Such anticaking agents have been added since at least 1911 when magnesium carbonate was first added to salt to make it flow more freely. The safety of sodium ferrocyanide as a food additive was found to be provisionally acceptable by the Committee on Toxicity in 1988. Other anticaking agents sometimes used include tricalcium phosphate, calcium or magnesium carbonates, fatty acid salts (acid salts), magnesium oxide, silicon dioxide, calcium silicate, sodium aluminosilicate and calcium aluminosilicate. Both the European Union and the United States Food and Drug Administration permitted the use of aluminium in the latter two compounds.  In "doubly fortified salt", both iodide and iron salts are added. The latter alleviates iron deficiency anaemia, which interferes with the mental development of an estimated 40% of infants in the developing world. A typical iron source is ferrous fumarate. Another additive, especially important for pregnant women, is folic acid (vitamin B), which gives the table salt a yellow color. Folic acid helps prevent neural tube defects and anaemia, which affect young mothers, especially in developing countries.  A lack of fluorine in the diet is the cause of a greatly increased incidence of dental caries. Fluoride salts can be added to table salt with the goal of reducing tooth decay, especially in countries that have not benefited from fluoridated toothpastes and fluoridated water. The practice is more common in some European countries where water fluoridation is not carried out. In France, 35% of the table salt sold contains added sodium fluoride.

Other kinds.

Unrefined sea salt contains small amounts of magnesium and calcium halides and sulfates, traces of algal products, salt-resistant bacteria and sediment particles. The calcium and magnesium salts confer a faintly bitter overtone, and they make unrefined sea salt hygroscopic (i.e., it gradually absorbs moisture from air if stored uncovered). Algal products contribute a mildly "fishy" or "sea-air" odour, the latter from organobromine compounds. Sediments, the proportion of which varies with the source, give the salt a dull grey appearance. Since taste and aroma compounds are often detectable by humans in minute concentrations, sea salt may have a more complex flavor than pure sodium chloride when sprinkled on top of food. When salt is added during cooking however, these flavors would likely be overwhelmed by those of the food ingredients. The refined salt industry cites scientific studies saying that raw sea and rock salts do not contain enough iodine salts to prevent iodine deficiency diseases.  Himalayan salt is known for its distinct pink hue. It is used in cooking as a substitute for table salt. Is it also used as cookware, in salt lamps and in spas. It is mined from the Salt Range mountains in Pakistan.  Different natural salts have different mineralities depending on their source, giving each one a unique flavour. Fleur de sel, a natural sea salt from the surface of evaporating brine in salt pans, has a unique flavour varying with the region from which it is produced. In traditional Korean cuisine, so-called "bamboo salt" is prepared by roasting salt in a bamboo container plugged with mud at both ends. This product absorbs minerals from the bamboo and the mud, and has been claimed to increase the anticlastogenic and antimutagenic properties of doenjang (a fermented bean paste).  Kosher or kitchen salt has a larger grain size than table salt and is used in cooking. It can be useful for brining, bread or pretzel making and as a scrubbing agent when combined with oil.  Pickling salt is made of ultra-fine grains to speed dissolving to make brine.

Salt in food.

Salt is present in most foods, but in naturally occurring foodstuffs such as meats, vegetables and fruit, it is present in very small quantities. It is often added to processed foods (such as canned foods and especially salted foods, pickled foods, and snack foods or other convenience foods), where it functions as both a preservative and a flavoring. Dairy salt is used in the preparation of butter and cheese products. As a flavoring, salt enhances the taste of other foods by suppressing the bitterness of those foods making them more palatable and relatively sweeter.  Before the advent of electrically powered refrigeration, salting was one of the main methods of food preservation. Thus, herring contains 67 mg sodium per 100 g, while kipper, its preserved form, contains 990 mg. Similarly, pork typically contains 63 mg while bacon contains 1,480 mg, and potatoes contain 7 mg but potato crisps 800 mg per 100 g. Salt is also used in cooking, such as with salt crusts. The main sources of salt in the Western diet, apart from direct use of sodium chloride, are bread and cereal products, meat products and milk and dairy products.  In many East Asian cultures, salt is not traditionally used as a condiment. In its place, condiments such as soy sauce, fish sauce and oyster sauce tend to have a high sodium content and fill a similar role to table salt in western cultures. They are most often used for cooking rather than as table condiments.

Sodium consumption and health.

Table salt is made up of just under 40% sodium by weight, so a 6g serving (1teaspoon) contains about 2,400mg of sodium. Sodium serves a vital purpose in the human body: via its role as an electrolyte, it helps nerves and muscles to function correctly, and it is one factor involved in the osmotic regulation of water content in body organs (fluid balance). Most of the sodium in the Western diet comes from salt. The habitual salt intake in many Western countries is about 10 g per day, and it is higher than that in many countries in Eastern Europe and Asia. The high level of sodium in many processed foods has a major impact on the total amount consumed. In the United States, 75% of the sodium eaten comes from processed and restaurant foods, 11% from cooking and table use and the rest from what is found naturally in foodstuffs.  Because consuming too much sodium increases risk of cardiovascular diseases, health organizations generally recommend that people reduce their dietary intake of salt. High sodium intake is associated with a greater risk of stroke, total cardiovascular disease and kidney disease. A reduction in sodium intake by 1,000 mg per day may reduce cardiovascular disease by about 30 percent. In adults and children with no acute illness, a decrease in the intake of sodium from the typical high levels reduces blood pressure. A low sodium diet results in a greater improvement in blood pressure in people with hypertension.  The World Health Organization recommends that adults should consume less than 2,000 mg of sodium (which is contained in 5g of salt) per day. Guidelines by the United States recommend that people with hypertension, African Americans, and middle-aged and older adults should limit consumption to no more than 1,500 mg of sodium per day and meet the potassium recommendation of 4,700 mg/day with a healthy diet of fruits and vegetables.  While reduction of sodium intake to less than 2,300 mg per day is recommended by developed countries, one review recommended that sodium intake be reduced to at least 1,200 mg (contained in 3g of salt) per day, as a further reduction in salt intake the greater the fall in systolic blood pressure for all age groups and ethinicities. Another review indicated that there is inconsistent/insufficient evidence to conclude that reducing sodium intake to lower than 2,300 mg per day is either beneficial or harmful.  More recent evidence is showing a much more complicated relationship between salt and cardiovascular disease. According to a systematic review of multiple large studies, "mortality caused by levels of salt the association between sodium consumption and cardiovascular disease or mortality is U-shaped, with increased risk at both high and low sodium intake" The findings showed that increased mortality from excessive salt intake was primarily associated with individuals with hypertension. The levels of increased mortality among those with restricted salt intake appeared to be similar regardless of blood pressure. This evidence shows that while those with hypertension should primarily focus on reducing sodium to recommended levels, all groups should seek to maintain a healthy level of sodium intake of between 4 and 5 grams a day.  One of the two most prominent dietary risks for disability in the world is eating too much sodium.

Non-dietary uses.

Only about 6% of the salt manufactured in the world is used in food. Of the remainder, 12% is used in water conditioning processes, 8% goes for de-icing highways and 6% is used in agriculture. The rest (68%) is used for manufacturing and other industrial processes, and sodium chloride is one of the largest inorganic raw materials used by volume. Its major chemical products are caustic soda and chlorine, which are separated by the electrolysis of a pure brine solution. These are used in the manufacture of PVC, plastics, paper pulp and many other inorganic and organic compounds. Salt is also used as a flux in the production of aluminium. For this purpose, a layer of melted salt floats on top of the molten metal and removes iron and other metal contaminants. It is also used in the manufacture of soaps and glycerine, where it is added to the vat to precipitate out the saponified products. As an emulsifier, salt is used in the manufacture of synthetic rubber, and another use is in the firing of pottery, when salt added to the furnace vaporises before condensing onto the surface of the ceramic material, forming a strong glaze.  When drilling through loose materials such as sand or gravel, salt may be added to the drilling fluid to provide a stable "wall" to prevent the hole collapsing. There are many other processes in which salt is involved. These include its use as a mordant in textile dying, to regenerate resins in water softening, for the tanning of hides, the preservation of meat and fish and the canning of meat and vegetables.

Production.

Food-grade salt accounts for only a small part of salt production in industrialized countries (7% in Europe), although worldwide, food uses account for 17.5% of total production.  In 2018, total world production of salt was 300 million tonnes, the top six producers being China (68 million), the United States (42 million), India (29 million), Germany (13 million), Canada (13 million) and Australia (12 million). The manufacture of salt is one of the oldest chemical industries. A major source of salt is seawater, which has a salinity of approximately 3.5%. This means that there are about of dissolved salts, predominantly sodium () and chloride () ions, per kilogram (2.2 lbs) of water. The world's oceans are a virtually inexhaustible source of salt, and this abundance of supply means that reserves have not been calculated. The evaporation of seawater is the production method of choice in marine countries with high evaporation and low precipitation rates. Salt evaporation ponds are filled from the ocean and salt crystals can be harvested as the water dries up. Sometimes these ponds have vivid colours, as some species of algae and other micro-organisms thrive in conditions of high salinity.  Elsewhere, salt is extracted from the vast sedimentary deposits which have been laid down over the millennia from the evaporation of seas and lakes. These are either mined directly, producing rock salt, or are extracted in solution by pumping water into the deposit. In either case, the salt may be purified by mechanical evaporation of brine. Traditionally, this was done in shallow open pans which were heated to increase the rate of evaporation. More recently, the process is performed in pans under vacuum. The raw salt is refined to purify it and improve its storage and handling characteristics. This usually involves recrystallization during which a brine solution is treated with chemicals that precipitate most impurities (largely magnesium and calcium salts). Multiple stages of evaporation are then used to collect pure sodium chloride crystals, which are kiln-dried. Some salt is produced using the Alberger process, which involves vacuum pan evaporation combined with the seeding of the solution with cubic crystals, and produces a grainy-type flake. The Ayoreo, an indigenous group from the Paraguayan Chaco, obtain their salt from the ash produced by burning the timber of the Indian salt tree ("Maytenus vitis-idaea") and other trees.  One of the largest salt mining operations in the world is at the Khewra Salt Mine in Pakistan. The mine has nineteen storeys, eleven of which are underground, and of passages. The salt is dug out by the room and pillar method, where about half the material is left in place to support the upper levels. Extraction of Himalayan salt is expected to last 350 years at the present rate of extraction of around 385,000 tons per annum.

In religion.

Salt has long held an important place in religion and culture. At the time of Brahmanic sacrifices, in Hittite rituals and during festivals held by Semites and Greeks at the time of the new moon, salt was thrown into a fire where it produced crackling noises. The ancient Egyptians, Greeks and Romans invoked their gods with offerings of salt and water and some people think this to be the origin of Holy Water in the Christian faith. In Aztec mythology, Huixtocihuatl was a fertility goddess who presided over salt and salt water.  Salt is considered to be a very auspicious substance in Hinduism and is used in particular religious ceremonies like house-warmings and weddings. In Jainism, devotees lay an offering of raw rice with a pinch of salt before a deity to signify their devotion and salt is sprinkled on a person's cremated remains before the ashes are buried. Salt is believed to ward off evil spirits in Mahayana Buddhist tradition, and when returning home from a funeral, a pinch of salt is thrown over the left shoulder as this prevents evil spirits from entering the house. In Shinto, is used for ritual purification of locations and people (harae, specifically shubatsu), and small piles of salt are placed in dishes by the entrance of establishments for the two-fold purposes of warding off evil and attracting patrons.  In the Hebrew Bible, there are thirty-five verses which mention salt. One of these mentions Lot's wife, who was turned into a pillar of salt when she looked back at the cities of Sodom and Gomorrah (Genesis 19:26) as they were destroyed. When the judge Abimelech destroyed the city of Shechem, he is said to have "sown salt on it," probably as a curse on anyone who would re-inhabit it (Judges 9:45). The Book of Job contains the first mention of salt as a condiment. "Can that which is unsavoury be eaten without salt? or is there any taste in the white of an egg?" (Job 6:6). In the New Testament, six verses mention salt. In the Sermon on the Mount, Jesus referred to his followers as the "salt of the earth". The apostle Paul also encouraged Christians to "let your conversation be always full of grace, seasoned with salt" (Colossians 4:6). Salt is mandatory in the rite of the Tridentine Mass. Salt is used in the third item (which includes an Exorcism) of the Celtic Consecration ("cf." Gallican Rite) that is employed in the consecration of a church. Salt may be added to the water "where it is customary" in the Roman Catholic rite of Holy water.  In Judaism, it is recommended to have either a salty bread or to add salt to the bread if this bread is unsalted when doing Kiddush for Shabbat. It is customary to spread some salt over the bread or to dip the bread in a little salt when passing the bread around the table after the Kiddush. To preserve the covenant between their people and God, Jews dip the Sabbath bread in salt.  In Wicca, salt is symbolic of the element Earth. It is also believed to cleanse an area of harmful or negative energies. A dish of salt and a dish of water are almost always present on an altar, and salt is used in a wide variety of rituals and ceremonies.

Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of salts; salt in its natural form as a crystalline mineral is known as rock salt or halite. Salt is present in vast quantities in seawater, where it is the main mineral constituent. The open ocean has about of solids per liter of sea water, a salinity of 3.5%.

食盐是一种调味剂,能产生人类能感知的咸味,常在烹饪和享用食物时用作调味。常见的餐桌盐是一种含有97至99%的氯化钠的精制盐,另外还有未经提纯的粗盐、以氯化钾取代氯化钠的低钠盐、加入了碘化合物以防止使用者出现碘缺乏的碘盐等。