title: Permian–Triassic extinction event

text: Prior to consideration of the inclusion of roasting carbonate sediments by volcanism, the only proposed mechanism sufficient to cause a global 1% reduction in the was the release of methane from methane clathrates. Carbon-cycle models confirm that it would have had enough effect to produce the observed reduction. It was also suggested that a large-scale release of methane and other greenhouse gases from the ocean into the atmosphere was connected to the anoxic events and euxinic (i.e. sulfidic) events at the time, with the exact mechanism compared to the 1986 Lake Nyos disaster


title: Permian–Triassic extinction event

text: The area covered by lava from the Siberian Traps eruptions is about twice as large as was originally thought, and most of the additional area was shallow sea at the time. The seabed probably contained methane hydrate deposits, and the lava caused the deposits to dissociate, releasing vast quantities of methane.


title: Permian–Triassic extinction event

text: A vast release of methane might cause significant global warming since methane is a very powerful greenhouse gas. Strong evidence suggests the global temperatures increased by about 6 °C (10.8 °F) near the equator and therefore by more at higher latitudes: a sharp decrease in oxygen isotope ratios (); the extinction of "Glossopteris" flora ("Glossopteris" and plants that grew in the same areas), which needed a cold climate, with its replacement by floras typical of lower paleolatitudes.


title: Permian–Triassic extinction event

text: However, the pattern of isotope shifts expected to result from a massive release of methane does not match the patterns seen throughout the Early Triassic. Not only would such a cause require the release of five times as much methane as postulated for the PETM, but would it also have to be reburied at an unrealistically high rate to account for the rapid increases in the (episodes of high positive ) throughout the early Triassic before it was released several times again.


title: Permian–Triassic extinction event

text: As of 2022, latest research suggests that greenhouse gas release during the extinction event was dominated by volcanic carbon dioxide: while methane release had to have contributed, isotopic signatures show that thermogenic methane released from the Siberian Traps had consistently played a larger role than methane from clathrates and any other biogenic sources such as wetlands during the event.


title: Permian–Triassic extinction event

text: Marine organisms are more sensitive to changes in (carbon dioxide) levels than terrestrial organisms for a variety of reasons. is 28 times more soluble in water than is oxygen. Marine animals normally function with lower concentrations of in their bodies than land animals, as the removal of in air-breathing animals is impeded by the need for the gas to pass through the respiratory system's membranes (lungs' alveolus, tracheae, and the like), even when diffuses more easily than oxygen. In marine organisms, relatively modest but sustained increases in concentrations hamper the synthesis of proteins, reduce fertilization rates, and produce deformities in calcareous hard parts. An analysis of marine fossils from the Permian's final Changhsingian stage found that marine organisms with a low tolerance for hypercapnia (high concentration of carbon dioxide) had high extinction rates, and the most tolerant organisms had very slight losses. The most vulnerable marine organisms were those that produced calcareous hard parts (from calcium carbonate) and had low metabolic rates and weak respiratory systems, notably calcareous sponges, rugose and tabulate corals, calcite-depositing brachiopods, bryozoans, and echinoderms; about 81% of such genera became extinct. Close relatives without calcareous hard parts suffered only minor losses, such as sea anemones, from which modern corals evolved. Animals with high metabolic rates, well-developed respiratory systems, and non-calcareous hard parts had negligible losses except for conodonts, in which 33% of genera died out. This pattern is also consistent with what is known about the effects of hypoxia, a shortage but not total absence of oxygen. However, hypoxia cannot have been the only killing mechanism for marine organisms. Nearly all of the continental shelf waters would have had to become severely hypoxic to account for the magnitude of the extinction, but such a catastrophe would make it difficult to explain the very selective pattern of the extinction. Mathematical models of the Late Permian and Early Triassic atmospheres show a significant but protracted decline in atmospheric oxygen levels, with no acceleration near the P–Tr boundary. Minimum atmospheric oxygen levels in the Early Triassic are never less than present-day levels and so the decline in oxygen levels does not match the temporal pattern of the extinction.


title: Permian–Triassic extinction event

text: In addition, an increase in concentration is inevitably linked to ocean acidification, consistent with the preferential extinction of heavily calcified taxa and other signals in the rock record that suggest a more acidic ocean. The decrease in ocean pH is calculated to be up to 0.7 units. Evidence from paralic facies spanning the Permian-Triassic boundary in western Guizhou and eastern Yunnan, however, shows a local marine transgression dominated by carbonate deposition, suggesting that ocean acidification did not occur across the entire globe and was likely limited to certain regions of the world's oceans.


title: Permian–Triassic extinction event

text: Evidence for widespread ocean anoxia (severe deficiency of oxygen) and euxinia (presence of hydrogen sulfide) is found from the Late Permian to the Early Triassic. Throughout most of the Tethys and Panthalassic Oceans, evidence for anoxia, including fine laminations in sediments, small pyrite framboids, high uranium/thorium ratios, and biomarkers for green sulfur bacteria, appear at the extinction event. However, at some sites, including Spiti, India, Meishan, China, and eastern Greenland, evidence for anoxia precedes the extinction. Biomarkers for green sulfur bacteria, such as isorenieratane, the diagenetic product of isorenieratene, are widely used as indicators of photic zone euxinia because green sulfur bacteria require both sunlight and hydrogen sulfide to survive. Their abundance in sediments from the P–T boundary indicates hydrogen sulfide was present even in shallow waters. The disproportionate extinction of high-latitude marine species provides further evidence for oxygen depletion as a killing mechanism; low-latitude species living in warmer, less oxygenated waters are naturally better adapted to lower levels of oxygen and are able to migrate to higher latitudes during periods of global warming, whereas high-latitude organisms are unable to escape from warming, hypoxic waters at the poles.


title: Permian–Triassic extinction event

text: This spread of toxic, oxygen-depleted water would have devastated marine life, causing widespread die-offs. Models of ocean chemistry suggest that anoxia and euxinia were closely associated with hypercapnia (high levels of carbon dioxide). This suggests that poisoning from hydrogen sulfide, anoxia, and hypercapnia acted together as a killing mechanism. Hypercapnia best explains the selectivity of the extinction, but anoxia and euxinia probably contributed to the high mortality of the event. The persistence of anoxia through the Early Triassic may explain the slow recovery of marine life after the extinction. Models also show that anoxic events can cause catastrophic hydrogen sulfide emissions into the atmosphere (see below).


title: Permian–Triassic extinction event

text: The sequence of events leading to anoxic oceans may have been triggered by carbon dioxide emissions from the eruption of the Siberian Traps. In that scenario, warming from the enhanced greenhouse effect would reduce the solubility of oxygen in seawater, causing the concentration of oxygen to decline. Increased weathering of the continents due to warming and the acceleration of the water cycle would increase the riverine flux of phosphate to the ocean. The phosphate would have supported greater primary productivity in the surface oceans. The increase in organic matter production would have caused more organic matter to sink into the deep ocean, where its respiration would further decrease oxygen concentrations. Once anoxia became established, it would have been sustained by a positive feedback loop because deep water anoxia tends to increase the recycling efficiency of phosphate, leading to even higher productivity.


title: Permian–Triassic extinction event

text: A severe anoxic event at the end of the Permian would have allowed sulfate-reducing bacteria to thrive, causing the production of large amounts of hydrogen sulfide in the anoxic ocean, turning it euxinic. Upwelling of this water may have released massive hydrogen sulfide emissions into the atmosphere and would poison terrestrial plants and animals and severely weaken the ozone layer, exposing much of the life that remained to fatal levels of UV radiation.


title: Permian–Triassic extinction event

text: Indeed, biomarker evidence for anaerobic photosynthesis by Chlorobiaceae (green sulfur bacteria) from the Late-Permian into the Early Triassic indicates that hydrogen sulfide did upwell into shallow waters because these bacteria are restricted to the photic zone and use sulfide as an electron donor. The hypothesis has the advantage of explaining the mass extinction of plants, which would have added to the methane levels and should otherwise have thrived in an atmosphere with a high level of carbon dioxide. Fossil spores from the end-Permian further support the theory: many show deformities that could have been caused by ultraviolet radiation, which would have been more intense after hydrogen sulfide emissions weakened the ozone layer.


title: Permian–Triassic extinction event

text: Analysis of the fossil river deposits of the floodplains indicate a shift from meandering to braided river patterns, indicating a very abrupt drying of the climate. The climate change may have taken as little as 100,000 years, prompting the extinction of the unique "Glossopteris" flora and its associated herbivores, followed by the carnivorous guild. In the North China Basin, highly arid climatic conditions are recorded during the latest Permian, near the Permian-Triassic boundary, with a swing towards increased precipitation during the Early Triassic, the latter likely assisting biotic recovery following the mass extinction.


title: Permian–Triassic extinction event

text: Evidence from the Sydney Basin of eastern Australia, on the other hand, suggests that the expansion of semi-arid and arid climatic belts across Pangaea was not immediate but was instead a gradual, prolonged process. Apart from the disappearance of peatlands, there was little evidence of significant sedimentological changes in depositional style across the Permian-Triassic boundary. Instead, a modest shift to amplified seasonality and hotter summers is suggested by palaeoclimatological models based on weathering proxies from the region's Late Permian and Early Triassic deposits.


title: Permian–Triassic extinction event

text: In the Kuznetsk Basin of southwestern Siberia, an increase in aridity led to the demise of the humid-adapted cordaites forests in the region a few hundred thousand years before the Permian-Triassic boundary. This has been attributed to a broader poleward shift of drier, more arid climates during the late Changhsingian before the more abrupt main phase of the extinction at the Permian-Triassic boundary that disproportionately affected tropical and subtropical species.


title: Permian–Triassic extinction event

text: A minority hypothesis holds that the impact event which formed the Araguainha crater, whose formation has been dated to , a possible temporal range overlapping with the end-Permian extinction, to have precipitated the mass extinction. The impact occurred around extensive deposits of oil shale in the shallow marine Paraná–Karoo Basin, whose perturbation by the seismicity resulting from impact likely discharged about 1.6 teratonnes of methane into Earth's atmosphere, buttressing the already rapid warming caused by hydrocarbon release due to the Siberian Traps. The large earthquakes generated by the impact would have additionally generated massive tsunamis across much of the globe. Despite this, most palaeontologists reject the impact as being a significant driver of the extinction, citing the relatively low energy (equivalent to 10 to 10 of TNT, around two orders of magnitude lower than the impact energy believed to be required to induce mass extinctions) released by the impact.


title: Permian–Triassic extinction event

text: In the mid-Permian (during the Kungurian age of the Permian's Cisuralian epoch), Earth's major continental plates joined, forming a supercontinent called Pangaea, which was surrounded by the superocean, Panthalassa.


title: Permian–Triassic extinction event

text: Oceanic circulation and atmospheric weather patterns during the mid-Permian produced seasonal monsoons near the coasts and an arid climate in the vast continental interior.


title: Permian–Triassic extinction event

text: As the supercontinent formed, the ecologically diverse and productive coastal areas shrank. The shallow aquatic environments were eliminated and exposed formerly protected organisms of the rich continental shelves to increased environmental volatility.


title: Permian–Triassic extinction event

text: Pangaea's formation depleted marine life at near catastrophic rates. However, Pangaea's effect on land extinctions is thought to have been smaller. In fact, the advance of the therapsids and increase in their diversity is attributed to the late Permian, when Pangaea's global effect was thought to have peaked.


title: Permian–Triassic extinction event

text: While Pangaea's formation certainly initiated a long period of marine extinction, its impact on the "Great Dying" and the end of the Permian is uncertain.


title: Permian–Triassic extinction event

text: A hypothesis published in 2014 posits that a genus of anaerobic methanogenic archaea known as "Methanosarcina" was responsible for the event. Three lines of evidence suggest that these microbes acquired a new metabolic pathway via gene transfer at about that time, enabling them to efficiently metabolize acetate into methane. That would have led to their exponential reproduction, allowing them to rapidly consume vast deposits of organic carbon that had accumulated in the marine sediment. The result would have been a sharp buildup of methane and carbon dioxide in the Earth's oceans and atmosphere, in a manner that may be consistent with the C/C isotopic record. Massive volcanism facilitated this process by releasing large amounts of nickel, a scarce metal which is a cofactor for enzymes involved in producing methane. On the other hand, in the canonical Meishan sections, the nickel concentration increases somewhat after the concentrations have begun to fall.


title: Permian–Triassic extinction event

text: Possible causes supported by strong evidence appear to describe a sequence of catastrophes, each worse than the last: the Siberian Traps eruptions were bad enough alone, but because they occurred near coal beds and the continental shelf, they also triggered very large releases of carbon dioxide and methane. The resultant global warming may have caused perhaps the most severe anoxic event in the oceans' history: according to this theory, the oceans became so anoxic, anaerobic sulfur-reducing organisms dominated the chemistry of the oceans and caused massive emissions of toxic hydrogen sulfide.


title: Permian–Triassic extinction event

text: However, there may be some weak links in this chain of events: the changes in the C/C ratio expected to result from a massive release of methane do not match the patterns seen throughout the early Triassic; and the types of oceanic thermohaline circulation that may have existed at the end of the Permian are not likely to have supported deep-sea anoxia.


title: Houston Texans

text: The Houston Texans are a professional American football team based in Houston. The Texans compete in the National Football League (NFL) as a member club of the American Football Conference (AFC) South division, and play their home games at NRG Stadium.


title: Houston Texans

text: The Texans were founded in 1999, and were owned by Bob McNair until his death in 2018; following McNair's death, the majority ownership of the team went to his wife, Janice. The team replaced the city's previous NFL franchise, the Houston Oilers, who played from 1960 to 1996 before moving to Nashville and eventually becoming the Tennessee Titans. The Texans began play as an expansion team in , making them the youngest franchise currently competing in the NFL.


title: Houston Texans

text: While the Texans mainly struggled in the 2000s, which was their first decade of play, their fortunes would take a turn for the better in the 2010s when they first found success in the 2011 season, winning their first division championship and clinching their first playoff berth. The Texans have gone on to win five more AFC South championships in 2012, 2015, 2016, 2018, and 2019. They are the only franchise to have never won a road playoff game along with the only one to have never appeared in a conference championship game; they are also one of four franchises to never have appeared in a Super Bowl, alongside the Cleveland Browns, Detroit Lions, and division rival Jacksonville Jaguars.


title: Houston Texans

text: In 1997, Houston entrepreneur Bob McNair had a failed bid to bring a National Hockey League (NHL) expansion team to the city, and Bud Adams relocated the city's NFL team, the Houston Oilers, to Nashville, Tennessee, where they were renamed the Tennessee Titans in 1999. In 1996, the Cleveland Browns had controversially relocated to become the Baltimore Ravens. As part of the settlement between the NFL, the city of Cleveland, and the team owned by Art Modell, the league promised to return football to Cleveland within the next three years.


title: Houston Texans

text: In order to even out the franchises to 32, the NFL contemplated adding another expansion franchise. As Houston was one of the favorites for the extra franchise, along with Toronto and Los Angeles (the latter of whom had lost the Rams and the Raiders in 1995), McNair then decided to join the football project and founded Houston NFL Holdings with partner Steve Patterson. With Houston Livestock Show and Rodeo, they would push for a domed stadium as part of the bid to lure the NFL back to Houston. On October 6, 1999, the NFL awarded the 32nd team to Houston at a cost of $700 million.


title: Houston Texans

text: In the process of naming the new franchise leadership conducted an extensive review and research process; the final list of names was determined after several months of research conducted jointly by Houston NFL 2002 and NFL Properties. This included an online survey asking fans and the community to weigh in which received more than 65,000 responses in one week. On March 2, 2000, it was announced that the team name search had been narrowed down to five choices: Apollos, Bobcats, Stallions, Texans, and Wildcatters. On September 6, 2000, the NFL's 32nd franchise was officially christened the Houston Texans before thousands at a downtown rally in Houston. McNair explained that the name and logo were chosen to "embody the pride, strength, independence and achievement that make the people of Houston and our area special." The name "Texans" had been used by several now-defunct football teams, including the Canadian Football League franchise in San Antonio; the World Football League franchise in Houston, which moved to Louisiana to become the Shreveport Steamer; the Dallas Texans of the NFL which played in only the 1952 season; and by the precursor of the present-day Kansas City Chiefs, when they were the second incarnation of the Dallas Texans in the American Football League (AFL). Owner Bob McNair received permission from Chiefs' owner Lamar Hunt to use the Texans name for his new team.


title: Houston Texans

text: The Houston Texans joined the NFL in the 2002 season, playing at the newly opened Reliant Stadium under head coach Dom Capers. With their opening game victory over the Dallas Cowboys on September 8, 2002, the Texans became the first expansion team to win its opening game since the Minnesota Vikings beat the Chicago Bears in 1961.


title: Houston Texans

text: While the team struggled in its early seasons, results began to improve when native Houstonian Gary Kubiak became the head coach in 2006. The Texans finished with a .500 season (8–8) in 2007 and 2008, and nearly qualified for the 2009–10 playoffs with a 9–7 result in 2009. The Texans started the 2010 season on a 4–2 record going into a Week 7 bye week, but promptly collapsed 2–8 in the second half of the season, finishing 6–10. In the 2011 NFL Draft, the Texans acquired Wisconsin star defensive end J. J. Watt 11th overall. The following season, former Cowboys head coach Wade Phillips was hired as the defensive coordinator for the Texans, and the improved defense led to them finishing 10–6, winning their first AFC South title. The Texans then beat wild card Cincinnati Bengals 31–10 in the first round of the 2011–12 playoffs, before a 20–13 defeat by the Ravens in the Divisional Round.


title: Houston Texans

text: The Texans surged as the team to beat in the AFC South in , starting 5–0 and holding an 11–1 record by week 14. However, they lost three of their last four games to finish 12–4; beating the rival Indianapolis Colts in that four-game stretch allowing them to clinch their 2nd AFC South title. The Texans beat the Bengals again in the wild-card round, but they lost in the Divisional Round to the New England Patriots.


title: Houston Texans

text: In the 2013 NFL Draft, the Texans acquired Clemson wide receiver DeAndre Hopkins 27th overall. In 2013, the Texans started 2–0 but went into a tailspin and lost every game afterwards. Kubiak was fired as head coach after being swept by the rival Jacksonville Jaguars, who themselves started 0–8. Wade Phillips filled in as head coach, but the Texans' poor form did not change, and they finished 2–14, tying, with 2005, their worst record in franchise history. The 14-game losing streak is the worst in franchise history.


title: Houston Texans

text: The Texans entered the 2014 season with a 14-game losing streak. Former Penn State head coach Bill O'Brien became the Texans' new head coach, and the third in franchise history, during the offseason. In 2014, the Texans won three of their first four games, defeating the Redskins in the season opener, the Raiders, and the Bills, losing to the New York Giants. They lost three of their next four games, losing to the Dallas Cowboys, the Indianapolis Colts, and the Pittsburgh Steelers, respectively. The Texans went on to finish 9–7 in the 2014 season and barely missed the playoffs.


title: Houston Texans

text: In the 2015 season, they were featured on HBO, on the show "Hard Knocks". That year, the Texans started with a 2–5 record. Quarterback Ryan Mallett was released amidst controversy regarding his benching in favor of Brian Hoyer during a loss against the Indianapolis Colts. After a poor start, the Texans finished with a 9–7 record and won their third AFC South title. However, they were shut out by the Kansas City Chiefs in the Wild Card round 30–0, ending their championship hopes for the year.


title: Houston Texans

text: On March 9, 2016, the Texans signed former Denver Broncos quarterback Brock Osweiler to a 4-year, $72 million deal. Despite Osweiler's lucrative deal, he struggled significantly during the 2016 season. After throwing two interceptions in Week 15 against the Jaguars, coach Bill O'Brien benched the offseason acquisition in favor of backup quarterback Tom Savage. Savage led a comeback effort against the Jaguars, and was named the starter for the remainder of the season. The Texans clinched their fourth AFC South division title in six years in Savage's first career start against the Bengals in Week 16. They defeated the wildcard Oakland Raiders 27–14 in the opening round of the playoffs with Osweiler as the starting quarterback due to Savage being out with a concussion. Osweiler started in the Divisional Playoffs game against the New England Patriots, throwing three interceptions in the second half. The Texans lost 34–16.


title: Houston Texans

text: In the 2017 NFL Draft, the Texans traded up to the 12th overall selection to select Clemson star quarterback Deshaun Watson. Watson started six games his rookie year, going 3–3 and having arguably the greatest and most decorated rookie season by a quarterback in NFL history, eventually rising up to become the Texans' franchise quarterback. However, his success would come up very short, following a Week 8 41–38 loss to the Seattle Seahawks, Watson tore his ACL in practice and was ruled out the remainder of the season, which caused the Texans to have one of their worst seasons. Plagued by a series of unexpected injuries (including a second consecutive season-ending injury to J. J. Watt) and controversy involving the team's suspected violation of the league's concussion protocol, after backup quarterback Tom Savage suffered a seizure following a Week 14 game against the San Francisco 49ers, the Texans went 1–9 the rest of the season and eventually finish 4–12 and last in the AFC South in 2017, missing the playoffs for the first time since 2014 and giving Bill O'Brien his first losing season as Texans head coach.


title: Houston Texans

text: In 2018, the Texans started the season 0–3, losing by a combined 15 points to the New England Patriots, Tennessee Titans, and New York Giants, before winning a 37–34 overtime shootout on the road in Indianapolis. This win sparked a nine-game winning streak for the Texans, their first since starting 5–0 in 2012, which included a Week 8 win against the Miami Dolphins that included five touchdown passes from Deshaun Watson. This streak was the longest ever for a team that started the season 0–3; the previous record was a seven-game win-streak set by the New York Giants in 1918 after starting out 0–3.


title: Houston Texans

text: On November 23, 2018, the owner of the Houston Texans, Bob McNair, died from skin cancer. On November 26, 2018, McNair's wife, Janice McNair, became the principal owner and Senior Chair of the Houston Texans, while their son, D. Cal McNair, became the Chairman and Chief Operating Officer.


title: Houston Texans

text: The Texans finished the season 11–5, and won another AFC South division championship under Bill O'Brien. They then lost 21–7 in the first round of the playoffs to their AFC South division rival Indianapolis Colts.


title: Houston Texans

text: In 2019, the Texans won the AFC South division championship and qualified for the NFL playoffs on the back of a 10–6 record. They went on to defeat the Buffalo Bills by a score of 22–19 in overtime in the AFC wild-card round. However, the Texans' 2019 season came to an end the following week, as they lost to the eventual Super Bowl champion Kansas City Chiefs by a score of 51–31 in the AFC divisional round.


title: Houston Texans

text: On March 22, 2020, the Texans traded away all-pro wide receiver DeAndre Hopkins and a fourth-round pick in the 2020 NFL Draft to the Arizona Cardinals. In return, Houston received running back David Johnson, a 2020 second-round pick, and a 2021 fourth-round pick. The move was confusing and controversial among fans and sportswriters alike, as many claimed that the Texans should have received more valuable assets for Hopkins, who was among the best receivers in the NFL.


title: Houston Texans

text: The Texans began the 2020 NFL season with a record of 0–4, and Bill O'Brien was consequentially fired following a disappointing loss to the Minnesota Vikings in Week 4. Romeo Crennel, who was the head coach of the Cleveland Browns from 2005 to 2008 and of the Kansas City Chiefs in 2011-12, was named the interim head coach for the remainder of the season. Crennel managed to win more than half of his first 7 games as Houston's head coach, giving Houston a record of 4-7. However, the Texans ended the season on a 5-game losing streak. With a final record of 4–12, the Texans were unable to make the playoffs.


title: Houston Texans

text: On January 27, 2021, the Texans hired David Culley as the team's head coach. Culley most recently worked as the Baltimore Ravens assistant head coach, wide receivers coach and passing game coordinator. On February 12, 2021, the Texans released all-pro defensive end J.J. Watt. It was confirmed that Watt personally requested owner Cal McNair for his release.


title: Houston Texans

text: On January 13, 2022, the Texans fired David Culley. as the team's head coach and promoted defensive coordinator Lovie Smith as the team's fifth head coach on February 7, 2022. The team traded away their starting quarterback Deshaun Watson to the Cleveland Browns and a 2024 fifth round pick for three 1st round picks, a 3rd round pick and a 4th round pick on March 20, 2022. The Texans opened their 2022 season in a tie game against the Indianapolis Colts, the franchise’s first tie in their 20 year existence.


title: Houston Texans

text: The Texans are the youngest expansion team in the NFL, having only been competing in the NFL since 2002. For that reason, they have not had the history or the reputation on which to build classic rivalries like the ones that often exist between older franchises. Despite this, the team has developed some rivalries. Its natural rivals are its fellow AFC South teams such as the Tennessee Titans, Jacksonville Jaguars, and Indianapolis Colts.


title: Houston Texans

text: The Tennessee Titans, who were formerly the Houston Oilers before their relocation in 1996, are viewed by many Houston fans as the Texans' chief rival as members of the AFC South ever since the early 2000s.


title: Houston Texans

text: Ever since the early 2000s, the Texans also have an AFC South Division rivalry with the Indianapolis Colts, whom the Texans had never defeated in Indianapolis until the 2006 season. The first time that the Texans would sweep the Colts was in the 2016 NFL season. More recently, Houston has increased bitterness with the Indianapolis Colts due to their young Houston-native quarterback Andrew Luck having been drafted by the Colts in 2012 and the franchise's first ever sweep of the Colts against Luck in 2016. In 2018 the two teams met in the , with the Colts winning 21–7.


title: Houston Texans

text: The Texans also have an intrastate/interconference rivalry with the Dallas Cowboys, with whom they contest the so-called Governor's Cup every year (a tradition started between the cities prior to the Oilers relocating) either in the preseason or the regular season for bragging rights in the state of Texas. In 2017, the destruction and flooding caused during Hurricane Harvey a few days before their Week 4 pre-season match up time scheduled caused the game to be relocated to AT&T Stadium in Arlington, Texas. However, out of concern for the safety of the fans and the condition of the player's families & communities, the game was canceled.


title: Houston Texans

text: Along with the team name, McNair unveiled the team logo, an abstract depiction of a bull's head, split in such a way to resemble the flag of Texas and the state of Texas, including a lone star to stand for the eye, the five points of which representing pride, courage, strength, tradition and independence. McNair described the colors as "Deep Steel Blue", "Battle Red" and "Liberty White". A year later the Texans unveiled their uniforms during another downtown rally.


title: Houston Texans

text: The Texans' helmet is dark blue with the Texans bull logo. The helmet was initially white when the team name and logo were unveiled, but was later changed to dark blue. The uniform design consists of red trim and either dark blue or white jerseys. The team typically wears white pants with its blue jerseys and blue pants with its white jerseys. Starting with the 2006 season, the Texans wore all-white for their home opener, and the team began to wear an all-blue combination for home games vs. the Indianapolis Colts. In 2003, the Texans introduced an alternative red jersey with blue trim; they wear this jersey at one home game each year, usually against a division rival. In 2007, the Texans introduced red pants for the first time, pairing them with the red jerseys for an all-red look. (This uniform combination was not well-received and has since been retired). In October 2008 the Texans paired blue socks (instead of the traditional red) with their blue pants and white jerseys, eventually becoming the team's primary road uniform combination. In 2016, the Texans unveiled a new uniform combo against the Jacksonville Jaguars, pairing the red jersey with blue pants and red socks. In 2017, the Texans unveiled a Color Rush uniform, using an all-blue uniform but with minimal white elements. In 2022, the Texans began using an alternate red helmet, worn exclusively with the red jerseys.


title: Houston Texans

text: In 2002, the team wore a patch commemorating their inaugural season. Also, they celebrated 10 years as a franchise by wearing an anniversary patch throughout 2012. From 2018 to 2019, the Texans wore a memorial patch to honor Bob McNair after his death.


title: Houston Texans

text: On November 19, 2017, Andre Johnson was the first-ever inductee into the Texans Ring of Honor. On October 6, 2019, Bob McNair was posthumously the second inductee into the Texans Ring of Honor.


title: Houston Texans

text: The team's official mascot is Toro, an anthropomorphic blue bull. The team also has a cheerleading squad simply named the Houston Texans Cheerleaders.


title: Houston Texans

text: Community outreach by the Houston Texans is primarily operated by the Houston Texans Foundation, who works with multiple community partners. The Houston Texans organization is also a supporter of the character education program, Heart of a Champion. In 2017, the 15th annual Houston Texans Charity Golf Classic raised more than $380,000 for the Foundation. More than $27.2 million has been raised for the Foundation since its creation in 2002.


title: Houston Texans

text: Former Texans DE J. J. Watt raised $41.6 million in relief funds for Hurricane Harvey after the storm devastated the city in 2017.


title: Houston Texans

text: , the Texans' flagship radio stations were KILT SportsRadio 610AM and KILT 100.3FM. The AM station has an all-sports format, while the FM station plays contemporary country music. Both are owned by Entercom. Marc Vandermeer is the play-by-play announcer. Heisman Trophy winner Andre Ware provides color commentary, and SportsRadio 610 host Rich Lord serves as the sideline reporter. Preseason and regular season Monday night games from ESPN are telecast by KTRK, an ABC owned and operated station. Kevin Kugler calls the preseason games on TV, with former Oilers running back Spencer Tillman providing color commentary. Regular season games are aired over CBS affiliate KHOU, FOX affiliate KRIV if the Texans host an NFC team, and NBC affiliate KPRC for Sunday night games.


title: Houston Texans

text: Spanish-language radio broadcasts of the team's games are aired on KGOL ESPN Deportes 1180AM. Enrique Vásquez is the play-by-play announcer. José Jojo Padrón provides color commentary, and Fernando Hernández serves as sideline reporter.


title: Sunshine (2007 film)

text: Sunshine is a 2007 science fiction psychological thriller film directed by Danny Boyle and written by Alex Garland. Taking place in the year 2057, the story follows a group of astronauts on a dangerous mission to reignite the dying Sun. The ensemble cast features Cillian Murphy, Chris Evans, Rose Byrne, Michelle Yeoh, Cliff Curtis, Troy Garity, Hiroyuki Sanada, Benedict Wong, Chipo Chung, and Mark Strong. The director cast a group of international actors for the film, and had the actors live together and learn about topics related to their roles, as a form of method acting.


title: Sunshine (2007 film)

text: The film was a co-production between the motion picture studios of Moving Picture Company, DNA Films, UK Film Council, and Ingenious Film Partners. Theatrically, it was commercially distributed by Fox Searchlight Pictures, while the 20th Century Fox Home Entertainment division released the film in the video rental market. "Sunshine" explores physics, science and religion. Following its wide release in theatres, the film garnered several award nominations for its acting, directing, and production merits. It also won an award for Best Technical Achievement for production designer Mark Tildesley from the British Independent Film Awards. was composed by John Murphy and was released by the Fox Music Group on 25 November 2008.


title: Sunshine (2007 film)

text: Previous science fiction films that Boyle cited as influences included Stanley Kubrick's 1968 film "", Andrei Tarkovsky's 1972 film "Solaris", and Ridley Scott's 1979 science-fiction horror film "Alien". "Sunshine" was released in the United Kingdom on 6 April 2007 and in the United States on 20 July 2007. The film took £3.2 million in the UK over twelve weeks, and in the USA it was placed no. 13 in the box office on the first weekend of its wide release. With a budget of US$40 million, it ultimately grossed US$32 million worldwide. Preceding its initial screening to the public, the film was generally met with positive critical reviews, but was not considered a box office success. Widescreen DVD and Blu-ray editions of the film, also including the hi-definition theatrical trailer, scene selections, and director's commentary among other highlights, were released in the United States on 8 January 2008.


title: Sunshine (2007 film)

text: In 2057, the Sun is dying and Earth is freezing. Eight international astronauts pilot a colossal stellar bomb aboard the spaceship "Icarus II", with the intent of jump-starting the Sun and then returning to Earth. As they pass near Mercury, "Icarus II" picks up the distress beacon of "Icarus I". That ship was the first to attempt a similar mission, and disappeared seven years earlier. The ship's proximity to the sun kept its signals from reaching Earth. The iron core of Mercury acts as an antenna, amplifying the signal and allowing "Icarus II" to intercept it. Reasoning that two payloads have a better chance of success than one, and that the last of Earth's fissile materials had been used to make their bomb, the ship's physicist Capa recommends to captain Kaneda that they change course and attempt to commandeer "Icarus I". Mace, the ship's engineer, opposes the deviation as risky. Navigator Trey calculates and implements a trajectory to intercept "Icarus I", but forgets to realign the shields that protect the ship from the sun, causing damage to four shield panels which if not repaired could destroy the whole ship and kill the crew.


title: Sunshine (2007 film)

text: Kaneda and Capa embark on a spacewalk to make repairs, assisted by the pilot, Cassie, who angles the damaged portion of the shield away from the Sun. As expected, this leads to the loss of two protruding communications towers; however, reflected light also destroys the ship's oxygen garden and oxygen reserves, much to the horror of botanist Corazon. As "Icarus II"s autopilot returns the shield to its original alignment, Kaneda orders Capa to retreat to safety as he repairs the final panel himself, and is burned to death moments later. Trey is unable to cope with the loss of Kaneda, and the ship's psychiatrist Searle assesses him as a suicide risk and places him under heavy sedation.


title: Sunshine (2007 film)

text: Without enough oxygen to reach the release point for its explosive payload, "Icarus II" has no choice but to dock with "Icarus I". Capa, Searle, Mace, and communications officer Harvey, now the acting captain, search the vessel, leaving Cassie and Corazon onboard "Icarus II" with Trey. They discover that despite the ship's systems being mostly operational, including a lush, overgrown, oxygen garden, the mainframe has been sabotaged, rendering delivery of the payload impossible. The ship's log contains a rambling message from Pinbacker, its captain, who abandoned his mission and has severe burns on his face. Mace deduces that the transmission was made six and a half years ago, around the time when the crew should have delivered their payload. The crew of "Icarus I" is found in the solar observation room, burned to death long ago by unfiltered exposure to the Sun.


title: Sunshine (2007 film)

text: Suddenly, the two ships explosively decouple, destroying "Icarus I"s outer airlock and stranding the four crewmembers. With only one spacesuit available, Capa wears it due to being the only crewmember able to operate the payload, while the rest wrap themselves in salvaged insulation material from the walls of the ship and then jettison between airlocks, using the vacuum release for propulsion. Searle realizes that one of them must stay behind to manually operate the airlock and volunteers himself. Searle releases the airlock, shooting Capa, Harvey and Mace out into open space. Harvey misses the airlock, freezes, and dies from asphyxiation, while Capa and Mace make it back to "Icarus II". Searle, having spent the mission obsessed with looking into the shielded sun, voluntarily exposes himself to its full, deadly force in the observation room, killing himself in the process.


title: Sunshine (2007 film)

text: Corazon calculates that there is only enough oxygen left for four of the five survivors to reach the Sun. The group reluctantly decides to have Mace kill Trey, but discovers Trey has already committed suicide. With the remaining crew somewhat relieved that they will now at least make the trip to the Sun, Capa is informed by "Icarus" that there is still not enough oxygen to complete the mission because an unknown fifth person is on board the ship. Capa investigates and discovers an insane and disfigured Pinbacker, who is revealed to have been behind the decoupling of the airlocks. Pinbacker attacks, wounds, and pursues Capa into the airlock, who seals it from his side. Pinbacker locks his side of the airlock to trap Capa, then kills Corazon and removes the four mainframes from their coolant baths, shutting down the ship's computer, before going after Cassie.


title: Sunshine (2007 film)

text: Mace manually lowers two of the computers back into the freezing coolant, but when his leg catches on the third descending mainframe, he becomes trapped, and the computer system is disabled. As he freezes to death, he begs Capa to complete the mission. Capa blows the airlock and separates the bomb from the ship, which is burned away by the sun. He then enters the bomb, where he finds Cassie, but they are ambushed by Pinbacker, who claims he spent the last seven years "conversing" with God (the sun) and was told to send all humanity to Heaven. As they hurtle into the Sun, Capa escapes Pinbacker by ripping the skin off one of his arms. Cassie encourages Capa to ignite the bomb, and he manages to reach the controls. Unsure if it will work under these extreme conditions, he watches as the bomb begins to ignite at the edge of the Sun, killing Cassie and Pinbacker. As time and space distort, Capa uses his final moments to blissfully reach out and touch the surface of the Sun. On Earth, at the frozen Sydney Harbour, Capa's sister and her children listen to Capa's last transmission and witness the Sun's light starting to shine again.


title: Sunshine (2007 film)

text: In March 2005, following the completion of "Millions" (2004), director Danny Boyle was briefly attached to direct "3000 Degrees", a Warner Bros. project about the 1999 Worcester Cold Storage Warehouse fire in Massachusetts. Opposition from surviving victims and firefighters prevented the project from entering production. At the same time, Boyle received a script from screenwriter Alex Garland, who had paired with Boyle for "The Beach" (2000) and "28 Days Later" (2002). Producer Andrew Macdonald, working with Boyle and Garland, pitched the script to 20th Century Fox, who were reluctant to finance the film based on its similarities to the 2002 remake "Solaris", which performed dismally for the studio. The project was instead financed by Fox's specialised film unit Fox Searchlight Pictures. Since the preliminary budget at US$40 million was too demanding for Fox Searchlight, Macdonald sought outside financing from British lottery funds, U.K. rebates, and outside investor Ingenious Film Partners. With financing in place, Boyle entered pre-production work for "Sunshine", for which he planned to commence production by the following July. Since Boyle had previously worked with Fox Searchlight on "28 Days Later", the existing relationship permitted the director freedom in production, working in a small studio.


title: Sunshine (2007 film)

text: Boyle and Garland worked on the script for a year, spent a second year preparing for production, filmed for three months, and spent a third full year editing and completing visual effects for "Sunshine". After completion of filming for "Sunshine", Boyle said that he would not revisit the science fiction genre, citing production as a spiritually exhausting experience. The director said making the film had conquered his fear of the difficulty encountered in producing a science fiction film, and that he would move on from the genre.


title: Sunshine (2007 film)

text: Director Danny Boyle chose to have an ensemble cast for "Sunshine" to encourage a more democratic process, similar to the ensemble cast in "Alien". Boyle also chose to have the cast be international in order to reflect the mission's purpose "on behalf of all mankind". The space crew in the film also consisted of American/Asian nationality because of the filmmakers' belief that the American and Chinese space programs would be the most developed and economically empowered 50 years in the future. The director had also received advice that there would be advanced space programs with India and Brazil, but the advice was overlooked to avoid creating a cast that was too disparate. According to producer Andrew Macdonald, the actors were required to speak with American accents to target the US audience as much as audiences from other parts of the world due to the budget level of the project.


title: Sunshine (2007 film)

text: To prepare the international actors for the film, Boyle had the cast undergo method acting. At the beginning of the film, the characters had been together for sixteen months, so Boyle desired to capture a sense of togetherness among the actors by assigning them to live together. He also enrolled the cast members in space training and scuba diving, as well as watching films together, such as "The Right Stuff" (1983) and the documentary "For All Mankind" (1989). Boyle also took the cast on a tour of a nuclear submarine to comprehend claustrophobic living conditions. He also had the cast experience weightlessness in the zero G environment of an acrobatic plane.


title: Sunshine (2007 film)

text: Cast members operated a Boeing 747 flight simulator and were introduced to futurologist Richard Seymour. The book "Moondust" by Andrew Smith, a collection of accounts of the men who had walked on the Moon, was required reading for cast members. The book had been assigned by Boyle because it described the lasting psychological changes experienced by that particular group of astronauts. The director sought to manifest the effect by showing the Sun's awesome, radiant power influencing the psyches of the ship's crew.


title: Sunshine (2007 film)

text: Screenwriter Alex Garland was inspired to write "Sunshine" based on scientific ideas about the heat death of the universe. Garland had wondered about what would result from the Sun's death after reading in an American scientific periodical "an article projecting the future of mankind from a physics-based, atheist perspective". Garland said of the project: "What interested me was the idea that it could get to a point when the entire planet's survival rests on the shoulders of one man, and what that would do to his head."


title: Sunshine (2007 film)

text: Garland brought the script to director Danny Boyle, who enthusiastically took up the project due to his long-time desire to direct a science fiction film set in space. Boyle and Garland worked on the script for a year, creating 35 drafts in their experimenting.


title: Sunshine (2007 film)

text: Boyle also considered the story of "Sunshine" as a counterintuitive approach for the contemporary issue of global warming, with the death of the Sun being a threat. Originally, "Sunshine" was scripted to begin with a voiceover talking about how parents tell their children not to look into the Sun, but once told, the children would be compelled to look. Boyle described the Sun as a godlike personality in the film, creating a psychological dimension for the astronauts due to its scale and power. The director also described the film's villain as based on light, explaining: "That's quite a challenge because the way you generate fear in cinema is darkness." The director also sought to have the characters experience a psychological journey in which each person is worn mentally, physically, and existentially and is experiencing doubt in their faiths. To capture the dangers of the voyage that the crew members went through, the director cited Bill Bryson's "A Short History of Nearly Everything" as influential in "articulating the universe's power".


title: Sunshine (2007 film)

text: The story was also written in part to reflect the brilliance and "necessary arrogance" of real life science when the world's scientists are presented with the crisis that threatens Earth. The time period of the story, 50 years in the future, was chosen to enable the level of technology to advance to the ability to travel to the Sun, but to simultaneously keep a feel of familiarity for the audience. Scientific advisers, futurists, and people who developed products for the future were consulted to shape an idea of the future.


title: Sunshine (2007 film)

text: To shape the science of the film, Boyle and Garland hired scientific advisers, including NASA employees and astrophysicists. Brian Cox, a professor of particle physics at the University of Manchester, was hired to advise the cast and crew after the director had seen Cox on the science TV series "Horizon". Cox gave regular lectures to the film's cast members about solar physics, and also advised the filmmakers to scale down the nuclear device in the film from the mass of the Moon to the size of Manhattan in America. In the film's backstory, a Q-ball enters and is caught in the Earth's Sun, and begins to eat it away. According to Cox, the Sun would not be dense enough in real life to stop a Q-ball, but filmmakers took creative licence in writing the backstory. Cox noted in the DVD commentary that several inaccuracies were permitted to allow for plot. He also dismissed criticisms of the film by scientists: ""Sunshine" is not a documentary. It's trying to just, in an hour and forty minutes, get across a feeling of what it's like – not only to be a scientist, because obviously there's much more in it than that. So, I found it interesting to watch the kind of people that get upset because the gravity is wrong."


title: Sunshine (2007 film)

text: Boyle originally included romantic subplots, including a sex scene planned between the characters Capa (Murphy) and Cassie (Byrne) in the ship's oxygen garden. However, the director considered the attempt for relationships in space too "embarrassing" and excluded the subplots. Boyle further distanced the characters from possible relationships by ensuring that the cast members wore little to no make-up to avoid any romantic overtures. The director also avoided including humour in the script with the exception of a few gags, believing that humour was a difficult fit for the story. "You get intensity of experience in space movies but not joy. So there's not much room for comedy or sex – everything is waiting to destroy you", explained Boyle.


title: Sunshine (2007 film)

text: Slow motion during weightlessness was inaccurately portrayed; the director had discovered this when riding the Vomit Comet, but he kept the slow motion to meet audiences' expectations. Another purposeful inaccuracy was the "whooshing" of the ship, despite there actually being no sound in the vacuum of space; Cox later mentioned in the BBC's "Stargazing Live" programme in January 2011 that this was simply because without accompanying sound, the CGI shots seemed "cheap".


title: Sunshine (2007 film)

text: The film's scientific content has been criticised by specialists. For example, the science periodical "New Scientist" said that the nuclear stellar bomb used by the crew would be woefully inadequate to reignite the dying Sun (billions of such devices would be required). The periodical found the film to be confusing and disappointing. Similarly, solar physicist Anjana Ahuja, a columnist for "The Times", commented on the lack of source of artificial gravity on board the spacecraft, saying "Danny Boyle could have achieved the same level of scientific fidelity in "Sunshine" by giving a calculator to a schoolboy". Ahuja was, however, more positive about the psychological aspect of the film, joking that "the psychology of extended space travel is covered well, although we could have done with a space bonk".


title: Sunshine (2007 film)

text: Filming for "Sunshine" took place at 3 Mills Studios in east London. An elaborate set was constructed, containing eight stages, 17 sets, and detailed models. The filmmakers employed three film units.


title: Sunshine (2007 film)

text: Filming began on 23 August 2005, lasting for 15 weeks, with August and September being difficult months due to the heat and the cast's requirement to wear spacesuits for their roles. Cinematographer Alwin H. Küchler chose to film in anamorphic format to capture a physical sense of the light. "We shot certain sequences in a very dark environment, which you get used to, so when the Sun plays a role, we wanted the audience to have a physical reaction to it", Kuchler said. Due to filming with the actors taking place on a stage, director Danny Boyle constructed live effects so the actors could realistically respond to computer-generated effects that were later implemented.


title: Sunshine (2007 film)

text: To increase the feeling of claustrophobia in "Sunshine", Boyle refused to cut back to scenes on Earth, a traditional technique in most films about the planet in jeopardy. The director also maintained an atmosphere of confinement in "Sunshine" by avoiding filming the primary ship, "Icarus II", from the outside. There are only a few outside shots of the ship. He also attempted to avoid filming star field backgrounds, keeping the ship's exterior pitch black, but he was ultimately compelled to show stars outside the spacecraft to help convey a sense of the ship's movement.


title: Sunshine (2007 film)

text: A scene in a snow-covered park with three stone monoliths was a homage to a similar scene in "". The scene was filmed at a May Day memorial in Stockholm, Sweden. The Sydney Opera House in Sydney, Australia, was chosen by Boyle out of six monuments that he considered universally recognisable. The Opera House, according to the director, possessed a "heat-thing" quality that decided it as his choice for a final establishing shot on Earth.


title: Sunshine (2007 film)

text: The snowy territory of the final scene was shot in Stockholm, Sweden, and a composite shot was created combining Stockholm's background and the Sydney Opera House. A slightly different ending was shot after the original but was not chosen as the director felt that it did not fit the film. The alternative ending became available on the DVD of "Sunshine".


title: Sunshine (2007 film)

text: The presspack says that the claustrophobic environment in the film was inspired by Wolfgang Petersen's "Das Boot" (1981). Boyle also cited inevitable visual influences from science fiction films in space by Andrei Tarkovsky ("Solaris" in 1972), Stanley Kubrick ("" in 1968), and Ridley Scott ("Alien" in 1979). Influences from other science fiction films also included Paul W. S. Anderson's "Event Horizon" (1997), John Carpenter's "Dark Star" (1974), and Douglas Trumbull's "Silent Running" (1971).


title: Sunshine (2007 film)

text: Filmmakers consulted NASA in designing the scientific aspects of the film. Technical specifications for the ship were provided in order to make it more realistic. An oxygen garden was also recommended to provide oxygen for the ship and to enable the crew to grow their own food rather than rely completely on pre-packaged sustenance. Boyle met with a department within NASA that was focused on the psychology of deep-space travel, and they advised the director that regular Earth routines like preparing one's own food, enjoying its consumption and cleaning up afterwards are activities crucial to an astronaut's sanity.


title: Sunshine (2007 film)

text: The gold-leaf shielding in "Sunshine" was influenced by NASA satellite designs for deflecting heat and other forms of radiant energy. Boyle designed the gold-coloured space suits along these lines despite persistent encouragement to model them after the NASA template. The helmets were designed to have cameras mounted in them. This further enhanced a sense of claustrophobia useful to the actors in delivering more heartfelt performances. The helmets were also limited to a horizontal slit for visibility instead of a full-face visor as further consideration toward protecting the characters from the ambient radiation of outer space. According to Boyle, the funnel shape of the helmet was influenced by the character Kenny from "South Park".


title: Sunshine (2007 film)

text: Boyle included "Icarus" in the name of the ship to continue a theme of bleakness, opining that no American would give their craft such an ill-fated name. According to the director, "They'd call it "Spirit of Hope" or "Ship of Destiny". They'd call it something optimistic ... in America they would sacrifice all plausibility, because there would be hope." The ship's exterior was designed to look like an oil tanker. The ship's interior was influenced by the design of a nuclear submarine that filmmakers had visited in Scotland, though the space was larger due to NASA's advice that smaller quarters would adversely affect the crewmembers' sanity. The corpses of burn victims in the film were modelled on the Pompeii victims from the Mount Vesuvius eruption.


title: Sunshine (2007 film)

text: Cinematographer Alwin H. Küchler provided an idea to render the interior of the ship in the colours of grey, blue, and green, with no reference to orange, red, or yellow. Scenes were intended to be shot inside the ship at long intervals, and when the shot changed to the outside, yellow-starved audiences would be "penetrated" by sunlight. The visual effects of the sunlight were based on photographs from the Solar and Heliospheric Observatory project. Boyle also sought to pursue inexpensive methods in filming sequences involving actors and visual effects. In a scene where Cillian Murphy's character dreams of falling into the Sun, the actor was placed in a gantry around which 20 assistants rotated an assembly of bright lights.


title: Sunshine (2007 film)

text: In another scene in which a character dies from solar exposure among the ashes from cremated bodies, massive wind turbines propelled biodegradable dust at the actor in the director's attempt to have the computer-generated effects follow the actor instead of vice versa. Boyle commented on his approach to using effects, "There is part of our brain where we admire the effect, but we put it in a side compartment of our experience because you know there's no way an actor can live through that, or be there in that moment." During the post-production process, Boyle hired one visual effects company, London's Moving Picture Company, to work on the film's 750 visual effects. The assignment of a single company was contrary to the industry trend of hiring multiple vendors to work on a film's effects. Boyle chose one company for ease of quality control, though the decision resulted in a prolonged post-production process.


title: Sunshine (2007 film)

text: When the film was mostly complete, director Danny Boyle provided the footage to the band Underworld, who improvised a score. Karl Hyde of Underworld was influenced by the music of avant garde composer György Ligeti which had been used in Stanley Kubrick's "" (1968). "Lux Aeterna" by Ligeti particularly influenced Hyde. When Underworld finished recording, the band sent its work to composer John Murphy, who completed the score. The final result was a hybrid product of Underworld and Murphy's efforts. The band I Am Kloot also contributed to the score with the track "Avenue of Hope".


title: Sunshine (2007 film)

text: Despite high praise for the score from fans of the film, a soundtrack release was significantly delayed. This was partly due to "disputes" between the lawyers of Underworld and Fox Searchlight. Although not available close to the film's debut, the soundtrack was finally released on iTunes USA on 25 November 2008.


title: Sunshine (2007 film)

text: "Sunshine" was originally slated for a theatrical release in October 2006, but the release was later changed to March 2007. The film was finally set to debut in April 2007. "Sunshine" made its world premiere at Fantasy Filmfest in Bochum, Germany, on 23 March 2007.


title: Sunshine (2007 film)

text: The film was originally slated to be released in the United States in September 2007, but the release date was moved earlier to July 2007. "Sunshine" was released in the United States and Canada at select locations in Los Angeles, New York City, Chicago, San Francisco, Boston, and Toronto on 20 July 2007. "Sunshine" opened in 10 cinemas in the United States and took US$242,964 over the opening weekend.


title: Sunshine (2007 film)

text: Following its cinematic release in theatres, the Region 2 Code widescreen edition of the film was released on DVD in the United Kingdom on 27 August 2007. Extras include deleted scenes with audio commentary by Danny Boyle; alternative ending; web production diaries; two short films – "Dad's Dead" and "Mole Hills" with an intro by Danny Boyle; audio commentary by director Danny Boyle; and an audio commentary by Dr. Brian Cox, University of Manchester. In the United States, the Region 1 Code widescreen edition of the film was released on DVD on 8 January 2008 with the same features.


title: Sunshine (2007 film)

text: A Blu-ray version was released in the UK in October of the same year. In the United States, "Sunshine" was released on high-definition Blu-ray Disc. Special features include deleted scenes with optional commentary by director Boyle; web production diaries; 2 short films with introduction by Boyle; commentary by director Boyle; commentary by Dr. Brian Cox, University of Manchester; enhanced viewing mode with the filmmakers of "Sunshine"; Journey Into Sound – surround sound enhancement; and the theatrical trailer in high definition. As of 17 February 2008, Sunshine had grossed $15.83 million in rental sales. A UMD version of the film for the Sony PlayStation Portable was released on 17 December 2008. A supplemental viewing option for the film in the media format of Video on demand is available as well.


title: Sunshine (2007 film)

text: The film was moderately well received in the UK by critics. However, many found the last reels disappointing, with one critic suggesting the switch to "slasher movie" mode might have been inserted to appease teenage audiences.


title: Sunshine (2007 film)

text: Among mainstream critics in the US, the film received generally positive reviews. , the film holds a 77% approval rating on Rotten Tomatoes based on 171 reviews, with an average rating of 6.80/10, and the consensus that "Danny Boyle continues his descent into mind-twisting sci-fi madness, taking us along for the ride. "Sunshine" fulfills the dual requisite necessary to become classic sci-fi: dazzling visuals with intelligent action." At Metacritic, which assigns a weighted average out of 100 to critics' reviews, the film received a score of 64 based on 34 reviews.


title: Sunshine (2007 film)

text: Sean Axmaker, writing in the "Seattle Post-Intelligencer", said the film presented a "visionary odyssey with a grace and awe and visual scope that calls to mind Stanley Kubrick's "" for a new millennium, with echoes of the industrial grunge and crew friction of "Alien," the greenhouse ecology of "Silent Running," even the unraveling sanity of "Dark Star."" Film critic Roger Ebert in the "Chicago Sun-Times" referred to the special effects in the film as "convincing and remorseless" and that the film was at its strongest point when it "focuses on the sheer enormity of the mission and its consequences". In "Variety", Derek Elley wrote that the film was "gripping enough with its solid performances, good-looking CGI, underlying tension and resonant, iron-hard digital soundtrack. This film reflects education excellence." He reserved praise for the production merits, noting, "Boyle generally directs fluidly, making the most of p.d. Mark Tildesley's sensible, not-too-futuristic sets, lensed with cool reserve by Alwin Kuchler."


title: Sunshine (2007 film)

text: Conversely, writing for the "San Francisco Chronicle", Mick Lasalle bluntly noted that the motion picture starts out "bad" and later "gets worse". He summed up his displeasure by stating, """Sunshine"" has nothing to offer, and this nothing is going to be offered relentlessly and earnestly, like a holy missive." In a primarily negative review, Joanne Kaufman writing for "The Wall Street Journal", called the film "a warmed-over stew of sci-fi and gothic horror". Unenthusiastic, she affirmed, "There are the predictable malfunctions that compromise the space craft, the banal speechifying about the fate of mankind, the issue of who will live and who will die. Who cares? The characters are so sketchily drawn that it's hard to keep them straight, let alone get worked up about their survival." Also describing an unfavourable opinion, Marrit Ingman of "The Austin Chronicle" professed the film exhibited "problems which arise in the film's third act" which causes "a profoundly implausible plot turn that sends the movie skidding into bogeyman horror. It cheapens the sentiment, and the film doesn't recover."


title: Sunshine (2007 film)

text: Nathan Lee of "The Village Voice" said the film "works despite feeling both over-familiar and over-ambitious. It crescendos with a legitimate sense of wonder (if not profundity) thanks in large part to the luminous and uncanny score by electro legends Underworld." Writing for "The New York Times", Manohla Dargis viewed director Boyle as a "first-rate, seemingly sweat-free entertainer" who always "sells the goods smoothly, along with the chills, the laughs and, somewhat less often, the tears." She went on to say, "He's wickedly good at making you jump and squirm in your seat, which he does often in "Sunshine," but he tends to avoid tapping into deep wells of emotion." Wesley Morris in "The Boston Globe" mused that if the film didn't "float your boat as a work of science-fiction, action, philosophy, heliocentrism, or staggering visual spectacle (although, it really should), then it certainly succeeds as a parable for cinematic ambition." He emphatically added, "The surface of this movie is plenty enthralling on its own." Desson Thomson of "The Washington Post" commented that for the film, "The voyage works, beautifully. While we don't get the ticklish conceit of Scottish profanities in the celestial outer realm, we do get something surprisingly consoling: a deep sense of the humanity that we always carry with us, no matter how far we venture from home."


title: Sunshine (2007 film)

text: The film was released commercially in its home country of the United Kingdom on 6 April 2007, taking £1,021,063 in 407 cinemas for its opening weekend. The film also opened the same weekend in seven other markets, performing most strongly in Hong Kong (US$267,000), Taiwan (US$442,000) and Singapore (US$198,000). On the weekend of 13 April 2007, "Sunshine" opened in 22 more countries, garnering US$5.3 million for the weekend. Its French debut was the strongest with US$1.2 million in 380 cinemas, but the film only had an average performance in New Zealand (US$120,149 from 36 cinemas), Switzerland (US$60,285 from 11 cinemas) and Finland (US$42,745 from 15 cinemas).


title: Sunshine (2007 film)

text: The following weekend of 20 April 2007, the film's release expanded to 44 countries, garnering US$5.9 million for a total of US$18.6 million thus far, considered a disappointing amount. "Sunshine" had poor debuts in Spain (US$1 million), Germany (US$638,549), and Italy (US$453,000). By the end of April, "Sunshine" had opened to most countries, with the notable exception of the United States, for which a release date had yet to be established at the time. The film's cinematic run in the UK lasted twelve weeks, totaling £3,175,911.


title: Sunshine (2007 film)

text: The film was released everywhere else in the two countries the following weekend of 27 July 2007. In the film's first wide release weekend in Canada and the United States, "Sunshine" took US$1,262,996 in 461 cinemas, ranking no. 13 at the weekend box office. In its theatrical run, the film took a worldwide gross of US$32,017,803.


title: Sunshine (2007 film)

text: The film won the award for Best Technical Achievement from the British Independent Film Awards 2008 and was nominated for several other awards in 2007–08.


title: Don King

text: Donald King (born August 20, 1931) is an American boxing promoter, known for his involvement in several historic boxing matchups. He has been a controversial figure, partly due to a manslaughter conviction and civil cases against him, as well as allegations of dishonest business practices by numerous boxers.


title: Don King

text: King's career highlights include, among multiple other enterprises, promoting "The Rumble in the Jungle" and the "Thrilla in Manila". King has promoted some of the most prominent names in boxing, including Muhammad Ali, Joe Frazier, George Foreman, Larry Holmes, Tomasz Adamek, Mike Tyson, Evander Holyfield, Chris Byrd, John Ruiz, Julio César Chávez, Ricardo Mayorga, Andrew Golota, Bernard Hopkins, Félix Trinidad, Roy Jones Jr., Azumah Nelson, Gerald McClellan, Marco Antonio Barrera, and Christy Martin. Some of these boxers sued him for allegedly defrauding them. Most of the lawsuits were settled out of court. Mike Tyson was quoted as saying, “He did more bad to black fighters than any white promoter ever in the history of boxing.”


title: Don King

text: King has been charged with killing two people in incidents 13 years apart. In 1954, King shot a man in the back after spotting him trying to rob one of his gambling houses; this incident was ruled a justifiable homicide. In 1967, King was convicted of voluntary manslaughter for stomping one of his employees to death. For this, he served three years and eleven months in prison.


title: Don King

text: King was born in Cleveland, Ohio, where he attended school and graduated from John Adams High in 1951. After dropping out of Kent State University, he ran an illegal bookmaking operation out of the basement of a record store on Kinsman Road, and was charged with killing two men in incidents 13 years apart. The first was determined to be justifiable homicide after it was found that King shot Hillary Brown in the back and killed him while he was attempting to rob one of King's gambling houses in 1954. In 1967, King was convicted of second-degree murder for the second killing after he was found guilty of stomping to death an employee, Sam Garrett, who owed him $600. While he served his term at the Marion Correctional Institution, he began self-education; according to his own words, he read everything in the prison library he could get his hands on.


title: Don King

text: Having been released in 1972, King was pardoned in 1983 by Ohio Governor Jim Rhodes, with letters from Jesse Jackson, Coretta Scott King, George Voinovich, Art Modell, and Gabe Paul, among others, being written in support of King.


title: Don King

text: King entered the boxing world after convincing Muhammad Ali to box in a charity exhibition for a local hospital in Cleveland with the help of singer Lloyd Price. Early on he formed a partnership with a local promoter named Don Elbaum, who already had a stable of fighters in Cleveland and years of experience in boxing. In 1974, King negotiated to promote a heavyweight championship fight between Muhammad Ali and George Foreman in Zaire, popularly known as "The Rumble in the Jungle". The fight between Ali and Foreman was a much-anticipated event. King's rivals all sought to promote the bout, but King was able to secure the then-record $10 million purse through an arrangement with the government of Zaire.


title: Don King

text: King arranged Ali's 1975 fight against journeyman Chuck Wepner. It is widely believed the fight inspired Sylvester Stallone to write the screenplay for "Rocky" (1976).


title: Don King

text: King solidified his position as one of boxing's preeminent promoters the following year with the third fight between Ali and Joe Frazier in Manila, the capital of the Philippines, which King deemed the "Thrilla in Manila". Aside from promoting the premier heavyweight fights of the 1970s, King was also busy expanding his boxing empire. Throughout the decade, he compiled an impressive roster of fighters, many of whom would finish their career with Hall of Fame credentials. Fighters including Larry Holmes, Wilfred Benítez, Roberto Durán, Salvador Sánchez, Wilfredo Gómez, and Alexis Argüello would all fight under the Don King Productions promotional banner in the 1970s.


title: Don King

text: For the next two decades, King continued to be among boxing's most successful promoters. Mike Tyson, Evander Holyfield, Julio César Chávez, Aaron Pryor, Bernard Hopkins, Ricardo López, Félix Trinidad, Terry Norris, Carlos Zárate, Azumah Nelson, Andrew Gołota, Mike McCallum, Gerald McClellan, Meldrick Taylor, Marco Antonio Barrera, Tomasz Adamek, John Ruiz, and Ricardo Mayorga are some of the boxers who chose King to promote many of their biggest fights.


title: Don King

text: Outside of boxing, he was the concert promoter for The Jacksons' 1984 Victory Tour. In 1998, King purchased a Cleveland-based weekly newspaper serving the African-American community in Ohio, the "Call and Post", and as of 2011 continued as its publisher.


title: Don King

text: Don King's wife, Henrietta, died on December 2, 2010, at the age of 87. He has one biological daughter, Debbie, a son, Eric and adopted son Carl, five grandchildren and three great grandchildren.


title: Don King

text: King is politically active and supported Barack Obama in the 2008 and 2012 presidential elections. During the previous election, he had made media appearances promoting George W. Bush, which had included attendance at the 2004 Republican National Convention in New York City.


title: Don King

text: On June 10, 1987, King was made a 'Mason-at-Sight' by 'Grand Master' Odes J. Kyle Jr. of the Most Worshipful Prince Hall 'Grand Lodge' of Ohio, thereby making him a Prince Hall Freemason. In the following year, he was awarded an honorary Doctorate of Humane letters degree from Central State University in Wilberforce, Ohio, by University President Dr. Arthur E. Thomas.


title: Don King

text: King has conducted an annual turkey giveaway each Christmas for several years, in which he distributes two thousand free turkeys to needy South Floridians.


title: Don King

text: King has been investigated for possible connections with organized crime. During a 1992 Senate investigation, King invoked the Fifth Amendment when questioned about his connection to mobster John Gotti.


title: Don King

text: When IBF president Robert W. "Bobby" Lee, Sr. was indicted for racketeering in 1999, King was not indicted, nor did he testify at Lee's trial, though prosecutors reportedly "called him an unindicted co-conspirator who was the principal beneficiary of Lee's machinations."


title: Don King

text: King has been involved in many litigation cases with boxers that were focused on fraud. In 1982, he was sued by Muhammad Ali for underpaying him $1.1 million for a fight with Larry Holmes. King called in an old friend of Ali, Jeremiah Shabazz, and handed him a suitcase containing $50,000 in cash and a letter ending Ali's lawsuit against King. He asked Shabazz to visit Ali (who was in the hospital due to his failing health) and get him to sign the letter and then give Ali the $50,000. Ali signed. The letter even gave King the right to promote any future Ali fights. According to Shabazz, "Ali was ailing by then and mumbling a lot. I guess he needed the money." Shabazz later regretted helping King. Ali's lawyer cried when he learned that Ali had ended the lawsuit without telling him.


title: Don King

text: Larry Holmes has alleged that over the course of his career King cheated him out of $10 million in fight purses, including claiming 25% of his purses as a hidden manager. Holmes says he received only $150,000 of a contracted $500,000 for his fight with Ken Norton, and $50,000 of $200,000 for facing Earnie Shavers, and claims King cut his purses for bouts with Muhammad Ali, Randall "Tex" Cobb, and Leon Spinks, underpaying him $2 million, $700,000, and $250,000, respectively. Holmes sued King over the accounting and auditing for the Gerry Cooney fight, charging that he was underpaid by $2 to $3 million. Holmes sued King after King deducted a $300,000 'finder's fee' from his fight purse against Mike Tyson; Holmes settled for $150,000 and also signed a legal agreement pledging not to give any more negative information about King to reporters.


title: Don King

text: Tim Witherspoon was threatened with being blackballed if he did not sign exclusive contracts with King and his stepson Carl. Not permitted to have his own lawyer present, he signed four "contracts of servitude" (according to Jack Newfield). One was an exclusive promotional contract with Don King, two were managerial contracts with Carl King, identical except one was "for show" that gave Carl King 33% of Witherspoon's purses and the other gave King a 50% share, more than is allowed by many boxing commissions. The fourth contract was completely blank.


title: Don King

text: Other examples include Witherspoon being promised $150,000 for his fight with Larry Holmes, but receiving only $52,750. King's son Carl took 50% of Witherspoon's purse, illegal under Nevada rules, and the WBC sanctioning fee was also deducted from his purse. He was forced to train at King's own training camp at Orwell, Ohio, instead of Ali's Deer Lake camp which Ali allowed Witherspoon to use for free. For his fight with Greg Page he received a net amount of $44,460 from his guaranteed purse of $250,000. King had deducted money for training expenses, sparring partners, fight and airplane tickets for his friends and family. Witherspoon was never paid a stipulated $100,000 for his training expenses and instead was billed $150 a day for using King's training camp. Carl King again received 50% of his purse, despite Don King Productions falsely claiming he had only been paid 33%. HBO paid King $1,700,000 for Witherspoon to fight Frank Bruno. Witherspoon got a purse of $500,000, but received only $90,000 after King's deductions. Carl King received $275,000. In 1987, Witherspoon sued King for $25 million in damages. He eventually settled for $1 million out of court.


title: Don King

text: Former undisputed World Heavyweight Boxing Champion Mike Tyson has described King, his former promoter, as "ruthless", "deplorable", and "greedy." In 1998, Tyson sued King for $100 million, alleging that the boxing promoter had cheated him out of millions over more than a decade. The lawsuit was later settled out of court, with Tyson receiving $14 million.


title: Don King

text: In 1996, Terry Norris sued King, alleging that King had stolen money from him and conspired with his manager to underpay him for fights. The case went to trial, but King settled out of court for $7.5 million in 2003. King also acceded to Norris's demand that the settlement be made public.


title: Don King

text: In 2005, King launched a $2.5 billion defamation suit against the Walt Disney Pictures–owned ESPN, the makers of "SportsCentury", after a documentary alleged that King had "killed, not once, but twice", threatened to break Larry Holmes' legs, had a hospital invest into a film that was never made, cheated Meldrick Taylor out of $1 million, and then threatened to have Taylor killed. Though the documentary repeated many claims that were already made, King said he had now had enough. King's attorney said "It was slanted to show Don in the worst way. It was one-sided from day one, Don is a strong man, but he has been hurt by this."


title: Don King

text: The case was dismissed on summary judgment with a finding that King could not show "actual malice" from the defendants, and that King had failed to prove that any of the challenged statements were false. The judgement also pointed out that the studio had tried on a number of occasions to interview King for the documentary, but he had declined; while not suggesting that King had a legal obligation to do so, the court sympathized with ESPN's circumstances on those grounds. King appealed the decision and, 3 years later, the Second District Court of Appeals upheld the summary judgement, but disagreed with the original finding that none of the statements were false. In any case, Judge Dorian Damoorgian ruled, "Nothing in the record shows that ESPN purposefully made false statements about King in order to bolster the theme of the program or to inflict harm on King".


title: Don King

text: In May 2003, King was sued by Lennox Lewis, who wanted $385 million from the promoter, claiming King used threats to pull Tyson away from a rematch with Lewis.


title: Don King

text: In early 2006, Chris Byrd sued Don King for breach of contract, and the two eventually settled out of court under the condition that Byrd would be released from his contract with King.


title: Don King

text: On September 21, 2016, King caused controversy when introducing Donald Trump at a campaign event at a black church in Cleveland by using the word "nigga" seemingly by accident. In King's speech, he was giving his thoughts on how black people cannot achieve success in the United States by acting like white people, stating: "If you're poor, you are a poor negro -- I would use the n-word -- but if you're rich, you are a rich negro. If you are intelligent, intellectual, you are intellectual negro. If you are a dancing and sliding and gliding nigga -- I mean negro -- you are a dancing and sliding and gliding negro."


title: Don King

text: King acted in a small role as more or less himself in "The Last Fight" (1982) and in the comedy "Head Office" (1985). He also had another brief cameo as himself in the film "The Devil's Advocate" (1997). He also appeared in a season 4 episode of "Knight Rider", titled "Redemption of a Champion".


title: Dirac delta function

text: In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one.


title: Dirac delta function

text: The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., formula_1) to its value at zero of its domain (formula_2), or as the weak limit of a sequence of bump functions (e.g., formula_3


title: Dirac delta function

text: Then "δ" is obtained by applying a power of the Laplacian to the integral with respect to the unit sphere measure dω of for "ξ" in the unit sphere "S":


title: Dirac delta function

text: The Laplacian here is interpreted as a weak derivative, so that this equation is taken to mean that, for any test function "φ",


title: Dirac delta function

text: The result follows from the formula for the Newtonian potential (the fundamental solution of Poisson's equation). This is essentially a form of the inversion formula for the Radon transform because it recovers the value of "φ"("x") from its integrals over hyperplanes. For instance, if "n" is odd and , then the integral on the right hand side is


title: Dirac delta function

text: In the study of Fourier series, a major question consists of determining whether and in what sense the Fourier series associated with a periodic function converges to the function. The "n"th partial sum of the Fourier series of a function "f" of period 2 is defined by convolution (on the interval ) with the Dirichlet kernel:


title: Dirac delta function

text: A fundamental result of elementary Fourier series states that the Dirichlet kernel tends to the a multiple of the delta function as . This is interpreted in the distribution sense, that


title: Dirac delta function

text: Despite this, the result does not hold for all compactly supported "continuous" functions: that is "D" does not converge weakly in the sense of measures. The lack of convergence of the Fourier series has led to the introduction of a variety of summability methods to produce convergence. The method of Cesàro summation leads to the Fejér kernel


title: Dirac delta function

text: for every compactly supported "continuous" function "f". The implication is that the Fourier series of any continuous function is Cesàro summable to the value of the function at every point.


title: Dirac delta function

text: The Dirac delta distribution is a densely defined unbounded linear functional on the Hilbert space L of square-integrable functions. Indeed, smooth compactly supported functions are dense in "L", and the action of the delta distribution on such functions is well-defined. In many applications, it is possible to identify subspaces of "L" and to give a stronger topology on which the delta function defines a bounded linear functional.


title: Dirac delta function

text: The Sobolev embedding theorem for Sobolev spaces on the real line R implies that any square-integrable function "f" such that


title: Dirac delta function

text: Thus "δ" is a bounded linear functional on the Sobolev space "H". Equivalently "δ" is an element of the continuous dual space "H" of "H". More generally, in "n" dimensions, one has provided .


title: Dirac delta function

text: In complex analysis, the delta function enters via Cauchy's integral formula, which asserts that if "D" is a domain in the complex plane with smooth boundary, then


title: Dirac delta function

text: for all holomorphic functions "f" in "D" that are continuous on the closure of "D". As a result, the delta function "δ" is represented in this class of holomorphic functions by the Cauchy integral:


title: Dirac delta function

text: Moreover, let "H"(∂"D") be the Hardy space consisting of the closure in "L"(∂"D") of all holomorphic functions in "D" continuous up to the boundary of "D". Then functions in "H"(∂"D") uniquely extend to holomorphic functions in "D", and the Cauchy integral formula continues to hold. In particular for , the delta function "δ" is a continuous linear functional on "H"(∂"D"). This is a special case of the situation in several complex variables in which, for smooth domains "D", the Szegő kernel plays the role of the Cauchy integral.


title: Dirac delta function

text: Given a complete orthonormal basis set of functions {"φ"} in a separable Hilbert space, for example, the normalized eigenvectors of a compact self-adjoint operator, any vector "f" can be expressed as


title: Dirac delta function

text: a form of the bra–ket notation of Dirac. Adopting this notation, the expansion of "f" takes the dyadic form:


title: Dirac delta function

text: is called a resolution of the identity. When the Hilbert space is the space "L"("D") of square-integrable functions on a domain "D", the quantity:


title: Dirac delta function

text: The right-hand side converges to "f" in the "L" sense. It need not hold in a pointwise sense, even when "f" is a continuous function. Nevertheless, it is common to abuse notation and write


title: Dirac delta function

text: With a suitable rigged Hilbert space where contains all compactly supported smooth functions, this summation may converge in Φ*, depending on the properties of the basis "φ". In most cases of practical interest, the orthonormal basis comes from an integral or differential operator, in which case the series converges in the distribution sense.


title: Dirac delta function

text: Cauchy used an infinitesimal "α" to write down a unit impulse, infinitely tall and narrow Dirac-type delta function "δ" satisfying formula_30 in a number of articles in 1827. Cauchy defined an infinitesimal in "Cours d'Analyse" (1827) in terms of a sequence tending to zero. Namely, such a null sequence becomes an infinitesimal in Cauchy's and Lazare Carnot's terminology.


title: Dirac delta function

text: Non-standard analysis allows one to rigorously treat infinitesimals. The article by contains a bibliography on modern Dirac delta functions in the context of an infinitesimal-enriched continuum provided by the hyperreals. Here the Dirac delta can be given by an actual function, having the property that for every real function "F" one has formula_31 as anticipated by Fourier and Cauchy.


title: Dirac delta function

text: A so-called uniform "pulse train" of Dirac delta measures, which is known as a Dirac comb, or as the Sha distribution, creates a sampling function, often used in digital signal processing (DSP) and discrete time signal analysis. The Dirac comb is given as the infinite sum, whose limit is understood in the distribution sense,


title: Dirac delta function

text: Up to an overall normalizing constant, the Dirac comb is equal to its own Fourier transform. This is significant because if formula_33 is any Schwartz function, then the periodization of formula_33 is given by the convolution


title: Dirac delta function

text: More generally, this formula remains to be true if formula_33 is a tempered distribution of rapid descent or, equivalently, if formula_38 is a slowly growing, ordinary function within the space of tempered distributions.


title: Dirac delta function

text: The Sokhotski–Plemelj theorem, important in quantum mechanics, relates the delta function to the distribution p.v. 1/"x", the Cauchy principal value of the function 1/"x", defined by


title: Dirac delta function

text: Here the limit is understood in the distribution sense, that for all compactly supported smooth functions "f",


title: Dirac delta function

text: for all integers "i", "j". This function then satisfies the following analog of the sifting property: if formula_43 is any doubly infinite sequence, then


title: Dirac delta function

text: Similarly, for any real or complex valued continuous function "f" on R, the Dirac delta satisfies the sifting property


title: Dirac delta function

text: In probability theory and statistics, the Dirac delta function is often used to represent a discrete distribution, or a partially discrete, partially continuous distribution, using a probability density function (which is normally used to represent absolutely continuous distributions). For example, the probability density function "f"("x") of a discrete distribution consisting of points x = {"x", ..., "x"}, with corresponding probabilities "p", ..., "p", can be written as


title: Dirac delta function

text: As another example, consider a distribution in which 6/10 of the time returns a standard normal distribution, and 4/10 of the time returns exactly the value 3.5 (i.e. a partly continuous, partly discrete mixture distribution). The density function of this distribution can be written as


title: Dirac delta function

text: The delta function is also used to represent the resulting probability density function of a random variable that is transformed by continuously differentiable function. If "Y" = g("X") is a continuous differentiable function, then the density of "Y" can be written as


title: Dirac delta function

text: The delta function is also used in a completely different way to represent the local time of a diffusion process (like Brownian motion). The local time of a stochastic process "B"("t") is given by


title: Dirac delta function

text: and represents the amount of time that the process spends at the point "x" in the range of the process. More precisely, in one dimension this integral can be written


title: Dirac delta function

text: The delta function is expedient in quantum mechanics. The wave function of a particle gives the probability amplitude of finding a particle within a given region of space. Wave functions are assumed to be elements of the Hilbert space "L" of square-integrable functions, and the total probability of finding a particle within a given interval is the integral of the magnitude of the wave function squared over the interval. A set {formula_51} of wave functions is orthonormal if they are normalized by


title: Dirac delta function

text: where formula_53 is the Kronecker delta. A set of orthonormal wave functions is complete in the space of square-integrable functions if any wave function formula_54 can be expressed as a linear combination of the {formula_51} with complex coefficients:


title: Dirac delta function

text: with formula_57. Complete orthonormal systems of wave functions appear naturally as the eigenfunctions of the Hamiltonian (of a bound system) in quantum mechanics that measures the energy levels, which are called the eigenvalues. The set of eigenvalues, in this case, is known as the spectrum of the Hamiltonian. In bra–ket notation, as above, this equality implies the resolution of the identity:


title: Dirac delta function

text: Here the eigenvalues are assumed to be discrete, but the set of eigenvalues of an observable may be continuous rather than discrete. An example is the position observable, . The spectrum of the position (in one dimension) is the entire real line and is called a continuous spectrum. However, unlike the Hamiltonian, the position operator lacks proper eigenfunctions. The conventional way to overcome this shortcoming is to widen the class of available functions by allowing distributions as well: that is, to replace the Hilbert space of quantum mechanics with an appropriate rigged Hilbert space. In this context, the position operator has a complete set of eigen-distributions, labeled by the points "y" of the real line, given by


title: Dirac delta function

text: The eigenfunctions of position are denoted by formula_60 in Dirac notation, and are known as position eigenstates.


title: Dirac delta function

text: Similar considerations apply to the eigenstates of the momentum operator, or indeed any other self-adjoint unbounded operator "P" on the Hilbert space, provided the spectrum of "P" is continuous and there are no degenerate eigenvalues. In that case, there is a set Ω of real numbers (the spectrum), and a collection "φ" of distributions indexed by the elements of Ω, such that


title: Dirac delta function

text: where the operator-valued integral is again understood in the weak sense. If the spectrum of "P" has both continuous and discrete parts, then the resolution of the identity involves a summation over the discrete spectrum "and" an integral over the continuous spectrum.


title: Dirac delta function

text: The delta function also has many more specialized applications in quantum mechanics, such as the delta potential models for a single and double potential well.


title: Dirac delta function

text: The delta function can be used in structural mechanics to describe transient loads or point loads acting on structures. The governing equation of a simple mass–spring system excited by a sudden force impulse "I" at time "t" = 0 can be written


title: Dirac delta function

text: As another example, the equation governing the static deflection of a slender beam is, according to Euler–Bernoulli theory,


title: Dirac delta function

text: where "EI" is the bending stiffness of the beam, "w" the deflection, "x" the spatial coordinate and "q"("x") the load distribution. If a beam is loaded by a point force "F" at "x" = "x", the load distribution is written


title: Dirac delta function

text: As the integration of the delta function results in the Heaviside step function, it follows that the static deflection of a slender beam subject to multiple point loads is described by a set of piecewise polynomials.


title: Dirac delta function

text: Also, a point moment acting on a beam can be described by delta functions. Consider two opposing point forces "F" at a distance "d" apart. They then produce a moment "M" = "Fd" acting on the beam. Now, let the distance "d" approach the limit zero, while "M" is kept constant. The load distribution, assuming a clockwise moment acting at "x" = 0, is written


title: Dirac delta function

text: Point moments can thus be represented by the derivative of the delta function. Integration of the beam equation again results in piecewise polynomial deflection.


title: Kalman filter

text: For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory.


title: Kalman filter

text: This digital filter is sometimes termed the "Stratonovich–Kalman–Bucy filter" because it is a special case of a more general, nonlinear filter developed somewhat earlier by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before summer 1960, when Kalman met with Stratonovich during a conference in Moscow.