title: Dominated convergence theorem

text: The assumption that the sequence is dominated by some integrable "g" cannot be dispensed with. This may be seen as follows: define for "x" in the interval and otherwise. Any "g" which dominates the sequence must also dominate the pointwise supremum . Observe that


title: Dominated convergence theorem

text: by the divergence of the harmonic series. Hence, the monotonicity of the Lebesgue integral tells us that there exists no integrable function which dominates the sequence on [0,1]. A direct calculation shows that integration and pointwise limit do not commute for this sequence:


title: Dominated convergence theorem

text: because the pointwise limit of the sequence is the zero function. Note that the sequence ("f") is not even uniformly integrable, hence also the Vitali convergence theorem is not applicable.


title: Dominated convergence theorem

text: One corollary to the dominated convergence theorem is the bounded convergence theorem, which states that if ("f") is a sequence of uniformly bounded complex-valued measurable functions which converges pointwise on a bounded measure space (i.e. one in which μ("S") is finite) to a function "f", then the limit "f" is an integrable function and


title: Dominated convergence theorem

text: Remark: The pointwise convergence and uniform boundedness of the sequence can be relaxed to hold only almost everywhere, provided the measure space is complete or "f" is chosen as a measurable function which agrees μ-almost everywhere with the everywhere existing pointwise limit.


title: Dominated convergence theorem

text: Since the sequence is uniformly bounded, there is a real number "M" such that for all and for all "n". Define for all . Then the sequence is dominated by "g". Furthermore, "g" is integrable since it is a constant function on a set of finite measure. Therefore, the result follows from the dominated convergence theorem.


title: Dominated convergence theorem

text: If the assumptions hold only everywhere, then there exists a set such that the functions "f"1 satisfy the assumptions everywhere on "S".


title: Dominated convergence theorem

text: Let formula_31 be a measure space, a real number and formula_1 a sequence of formula_33-measurable functions formula_34.


title: Dominated convergence theorem

text: Assume the sequence formula_1 converges formula_36-almost everywhere to an formula_33-measurable function formula_2, and is dominated by a formula_39 (cf. Lp space), i.e., for every natural number formula_40 we have: formula_41, μ-almost everywhere.


title: Dominated convergence theorem

text: Then all formula_42 as well as formula_2 are in formula_44 and the sequence formula_1 converges to formula_2 in the sense of formula_44, i.e.:


title: Dominated convergence theorem

text: Idea of the proof: Apply the original theorem to the function sequence formula_49 with the dominating function formula_50.


title: Dominated convergence theorem

text: The dominated convergence theorem applies also to measurable functions with values in a Banach space, with the dominating function still being non-negative and integrable as above. The assumption of convergence almost everywhere can be weakened to require only convergence in measure.


title: P.O

text: Pyo Ji-hoon (born February 2, 1993), better known by his stage name P.O, is a South Korean rapper, singer and actor. He is the youngest member of the boy group Block B and its sub-unit Bastarz.


title: P.O

text: P.O was born Pyo Ji-hoon on February 2, 1993, in Seoul, South Korea. He attended Hanlim Multi Art School, graduating in 2012.


title: P.O

text: P.O got acting lessons in elementary school and entered Hanlim Multi Art School to chase after his original dream of becoming an actor. He then fell in love with Hip hop together with his bestfriend Mino. He decided to rejoin Stardom Entertainment, after they kicked him out previously before he lost weight and ignored offers from other Agencies, to debut with Block B.


title: P.O

text: P.O debuted with Block B in April 2011. In February 2012, the band received heavy criticism for their disrespectful behavior during an interview in Thailand, particularly jokes regarding about the previous year's flooding disaster. P.O reportedly fainted and was hospitalized for shock on February 24, after learning of a petition calling for the members to apologize by committing suicide.


title: P.O

text: To show his gratitude to BBC (Block B Club), Block B's official fanbase, P.O released a song written especially for them. "Dear My Wife" was released into his cyworld on September 25, featuring (previously part of BoM's) Winner's Mino.


title: P.O

text: Along with fellow Block B member, Zico, they both were chosen as MCs for SBS MTV's "The Show". During a November 2012 episode of "Weekly Idol", P.O stated that he came from a wealthy family background, explaining that his father runs a duty-free store.


title: P.O

text: On March 9, P.O released the first song "Amino Acid" from his Mixtape "Bigboi is Ready 2 Showtime," featuring Winner's Mino. He continued releasing songs each day until March 21. Rookie girl group Delight featured P.O in their song "Mega-Yak". In September 2013, P.O starred in Kye Bum-zu's "Something Special" music video alongside Hello Venus's Yoon-jo.


title: P.O

text: In 2014, P.O was featured in the digital single "It's not a Big Deal" by V.O.S's Kim Kyung Rok, released January 6. P.O also co-wrote the lyrics for the title track of the SBS drama "Secret Door", which was performed by Block B and released September 22.


title: P.O

text: On April 5, it was announced that P.O would participate in Block B's first sub-unit, Bastarz, along with members U-Kwon and B-Bomb. The sub-unit's album was released April 13, along with a video for the title track, "Zero for Conduct," and it debuted at No. 3 on the Gaon album chart.


title: P.O

text: P.O was significantly involved with the creation of the Bastarz album, receiving a lyrics credit for "Zero for Conduct," sole lyrics credit and a composition credit for "Charlie Chaplin," a lyrics credit for "Thief," and a lyrics and composition credit for "Sue Me," which he performed along with the rapper Incredivle.


title: P.O

text: On May 23, P.O appeared with fellow Block B member Taeil on the KBS show , where they performed a remake of the song "I Don't Know Why" by Kim Soo-chul. P.O featured in Kye Bum Zu's "Give It 2 U," which was released in late July.


title: P.O

text: Bastarz released a Japanese version of "Conduct Zero" in October; the CD single containing the song reached No. 20 on the Oricon weekly chart.


title: P.O

text: In February, P.O appeared in the theatrical play "Superman.com," which he also helped write and produce as part of a new theatrical troupe, Company Boy (극단 소년).


title: P.O

text: In October, Block B announced that the Bastarz sub-unit would be having a comeback featuring a lead single composed by P.O, which was released October 24. The sub-unit's second mini-album, "Welcome to BASTARZ," was released October 31; P.O received lyrics credits for all five songs on the album, and composition credits for three.


title: P.O

text: Also in October, the OnStyle network announced that P.O and fellow Block B member U-Kwon would be on the new show "Lipstick Prince." The first season aired from December 1, 2016, to February 16, 2017.


title: P.O

text: P.O was cast in "Living Together in Empty Room," a special variety show broadcast on MBC for the Korean New Year in three episodes from January 26 to 27, 2017. In the course of the show, two women, trot singer Hong Jin-young and comedian Kim Shin-young, moved into P.O's house. The show ranked No. 1 among New Year's specials. In March it was reported that the show would be picked up and aired as a series, and that P.O would be among the cast members.


title: P.O

text: In addition, P.O was cast as an MC for the cooking variety show "Strange Restaurant," which premiered on the O'live television channel March 13. P.O hosted the show, in which guests attempted to cook dishes they have ordered, along with Kim Jong-min, Kim Yong-man, and Seo Jang-hoon.


title: P.O

text: On April 5, it was announced that P.O had been cast in the upcoming drama "Our First Romance," starring Lee Jong-hyun and Lee Yu-bi, and written by Go Sun Hee, who also wrote the tvN drama "Cheese in the Trap." Later that month, it was reported that P.O had been cast on a pilot MBC variety show called "Secret Variety Institute."


title: P.O

text: In May, it was announced that P.O would be an MC for the SBS MTV music program "The Show," along with Jeonghwa of EXID and Yeonwoo of Momoland. P.O appeared in a second play by the Company Boy troupe, "Manitoz," which ran from June 17 to 25. Also in June, he and fellow group member U-Kwon received the Maxim K-Model Icon Idol Award. In July, it was reported that P.O had been cast in the SBS drama "Temperature of Love," which began airing in September. The show's debut episode had the highest ratings in its time slot.


title: P.O

text: P.O took part in the Japanese special project album, "Block B: Project-1," released September 20, performing the song "Winner" along with fellow Block B member U-Kwon and Japanese rapper Chanmina.


title: P.O

text: On September 19, it was announced that P.O would make his solo debut. His song, the funk tune "Men'z Night," was released September 27 and featured the singer Chancellor.


title: P.O

text: In December, P.O took part in a tribute album for the late singer Yoo Jae-ha to commemorate the 30th anniversary of his debut.


title: P.O

text: In spring of 2018, P.O appeared again as a cast member on "Living Together in Empty Room", living with stylist Han Hye-yeon and Jinyoung of Got7. In addition, the Company Boy troupe staged another production of "Superman.com" in which P.O starred. Later in the year, he became a regular cast member for "Great Escape" and "New Journey to the West 5/6".


title: P.O

text: In addition to his work on variety shows, in 2018 P.O acted in two dramas, "Encounter" (broadcast by tvN) and "Love Alert" (broadcast by MBN).


title: P.O

text: P.O released a new song, "Comme des Garçons," on November 11, 2018. The song features a funky sound and personal lyrics that discuss P.O's life from before his debut to the present.


title: P.O

text: During the broadcast of the last episode of "New Journey to the West 6" on December 2, 2018, it was announced that P.O would be joining the upcoming second season of "Kang's Kitchen."


title: P.O

text: In February 2019, it was announced that P.O would star in a new theatrical production by the Company Boy troupe, a live version of the 2005 film "Boy Goes to Heaven" scheduled to run from February 16 to March 3.


title: P.O

text: In November 2019, it was revealed that P.O would act as master of ceremony for the upcoming MBC Entertainment Awards, along with Hwasa of Mamamoo and Jun Hyun-moo.


title: P.O

text: In December 2020, P.O starred in another Company Boy theatrical production, the play "Almost, Maine." P.O played the characters of Randy and Dave in the production, which ran from December 25, 2020, to February 14, 2021. P.O also starred in the play's Busan production, which took place in June 2021.


title: P.O

text: In September 2021, P.O's label, Seven Seasons, announced that he would not be renewing his contract with them at the end of the month.


title: P.O

text: On February 10, 2022, it was reported that P.O would be recording his last show "Amazing Saturday" in March, three days before his military service.


title: P.O

text: In February 24, 2012, P.O (real name Pyo Ji-hoon) was diagnosed with "stress-induced schizophrenia" shortly after being hospitalized for fainting. Though his uncle Pyo Jin-in would later dispute the accuracy of the diagnosis on his Twitter account. Jin-in criticized it for its vagueness, and the fact that it was given quickly. He cited that symptoms might have arisen due to SPD, schizoaffective disorder, brief psychotic disorder or PTSD and they would have been shown for at least six months if it were to match those of schizophrenia.


title: P.O

text: P.O enlisted in the Republic of Korea Marine Corps on March 28, 2022. Later in June 2022, the agency said that P.O. had just been assigned to the Marine Corps headquarters in Hwaseong, Gyeonggi-do and was planning to serve in a military band. Previously, he has postponed his military service until December 2021 to focus on broadcasting and acting.


title: Shayne Ward

text: Shayne Thomas Ward (born 16 October 1984) is an English actor and singer. He rose to fame as the winner of the second series of "The X Factor". His debut single, "That's My Goal", was released in the United Kingdom on 21 December 2005 and reached number one on the UK Singles Chart and was that year's Christmas number one. It sold 313,000 copies on its first day of sales, making it the third-fastest-selling single of all time in the UK, behind Elton John's "Candle in the Wind 1997" and Will Young's "Evergreen", which sold 685,000 and 400,000 copies in their first days of sale, respectively.


title: Shayne Ward

text: Ward was the first "X Factor" winner to release an original song as his winner's single. His prize, as winner, was a recording contract with Simon Cowell's Syco record label, which is co-owned by Sony Music. His eponymous debut album was released in April 2006. It debuted at number one on both the Irish and UK Albums Charts, going 4× Platinum in Ireland and Platinum in the UK. It spawned two hit singles: "No Promises" and "Stand by Me". The follow-up album, "Breathless", featuring the top 10 hits "If That's OK with You" and "No U Hang Up", was released in November 2007 and topped the Irish charts, where it went 5× Platinum.


title: Shayne Ward

text: In November 2010, after a three-year hiatus, Ward released his third album, "Obsession". In contrast to "Shayne Ward" and "Breathless", it underperformed with first-week sales of under 23,000, and missed the top 10 in both the UK and Ireland. In 2011, Ward was dropped by Syco. In 2015, he released a new album "Closer" as an independent artist, funded through PledgeMusic.


title: Shayne Ward

text: In 2015, he began appearing as Aidan Connor in TV's "Coronation Street" as a regular character. He made his last appearance in August 2018. He made voiceover appearance on 22 October 2021.


title: Shayne Ward

text: Ward was born on 16 October 1984 in Tameside, Greater Manchester, England to Irish Traveller parents who settled in England. He attended St. Peter’s RC High School in Manchester. In 2002, he reached the final thirty of "". Prior to his participation in "The X Factor", Ward was in a band called Destiny with two women named Tracy Murphy and Tracey Lyle, performing at pubs, clubs and weddings.


title: Shayne Ward

text: In early 2005, Ward auditioned for the second series of "The X Factor" in front of judges Simon Cowell, Sharon Osbourne and Louis Walsh. He impressed all three judges and passed through to the next round. His category, 16 to 24-year-olds, was then mentored by Walsh, and Ward was chosen to be among Walsh's top four contestants and perform on the live shows. Ward quickly became the bookmakers' favourite to win the show, and after making it to the grand final, he defeated Cowell's duo Journey South and Osbourne's over-25 singer Andy Abraham and was crowned as the winner. He had not fallen into the bottom two throughout the entire competition, and won by a margin of 1.2% of the vote, out of a reported 10.8 million phone votes cast by viewers. Immediately after the competition, his "X Factor" mentor Walsh became his manager under a joint venture with Global Publishing and Walsh Global Management.


title: Shayne Ward

text: Immediately after his victory on "The X Factor", Ward signed a recording contract with Syco Music and his first single, "That's My Goal", was released in the UK on Wednesday, 21 December 2005. After selling 742,000 copies in the first week, including 313,000 on its first day, it became the Christmas number one single of 2005, held the top spot for four weeks and stayed in the top 75 until June 2006, a 21-week run. It became, at that time the fourth-fastest-selling UK single of all time, beaten only by Elton John's "Candle in the Wind", Will Young's "Anything Is Possible/Evergreen", and Gareth Gates' "Unchained Melody" which sold 685,000, 403,000 and 335,000 copies in their first days of sale, respectively. To date, "That's My Goal" has sold over 1.3 million copies in the UK. Ward also won an Ivor Novello Award for being the Best Selling Single. Ward's second single, "No Promises", a cover of a Bryan Rice song was released on 10 April 2006, and peaked at number two (behind "Crazy" by Gnarls Barkley) in the UK Singles Chart. "Shayne Ward", his self-titled debut album was released on 17 April 2006. It sold 201,266 copies in the first week and entered the albums chart at number one. To date, the album has sold 520,000 copies in the UK and a further 2,000,000 worldwide, reaching number one in eight other countries. The album was certified platinum. Ward's third single was "Stand by Me".


title: Shayne Ward

text: It was confirmed in Gary Barlow's autobiography "My Take", that in 2006, fellow Take That member, Jason Orange threatened to quit the band, and Ward was seriously considered as his replacement. Orange, however, later changed his mind and a replacement was not required. In August 2006, it was reported that Ward had developed vocal cord nodules — the same condition that stopped the singing career of Julie Andrews — and was to be flown out to Los Angeles in early September to see a specialist surgeon. Walsh released a statement that he was confident Ward would be fine and would be back at work by the end of the month. Ward had a successful treatment and was indeed able to return to his singing career. In November 2006, he released his autobiography entitled "My Story". He travelled to several places around the UK for book signings, which hundreds of people attended. In early 2007, Ward embarked on a solo tour of UK & Republic of Ireland venues, taking in eighteen concerts in twenty-eight days from late January to mid-February. The tour commenced in Dublin on 21 January and ended in Birmingham on 17 February 2007.


title: Shayne Ward

text: After the completion of his successful debut tour, Ward's fourth single and first from his second album, "If That's OK with You" was given a release date of 20 August 2007, but was then delayed and became a double A-side single with "No U Hang Up". It was finally released on 24 September 2007, and charted at number two in the UK being held off by the Sugababes with "About You Now". "No U Hang Up" and "If That's OK with You" charted separately in Ireland, the former reaching number eleven and the latter entering at number one. Ward's second album, "Breathless", was released on 26 November 2007, and after selling over 95,000 copies in its first week, debuted at number two on the UK Albums Chart, held off the top spot by his "X Factor" successor, Leona Lewis's, multi-platinum selling debut, "Spirit". In Ireland, the album debuted at number one, removing Lewis's album from the top spot, a position it held for three weeks, and was later certified five times platinum. The second single from Ward's album was announced as "Breathless", and was released on 19 November 2007. It peaked at number six in the UK and number two in Ireland. On 10 November, Ward performed "Breathless" on the live results show of the fourth series of "The X Factor", although the single was not available for download until 18 November, followed by a performance on "The Paul O'Grady Show" on 19 November. In the UK the album has been certified platinum with sales of over 450,000. In May 2008, Ward embarked on his month-long UK tour, The Breathless Tour 2008. He made his stage debut at London's O2 Arena and visited his home town Manchester at the MEN Arena. He also performed his complete show as a support act for Westlife's 2008 tour in front of a crowd of over 80,000 at Ireland's Croke Park. Ward also played on the opening night at The O2, Dublin, at the Cheerios Childline concert on 16 December 2008.


title: Shayne Ward

text: Ward began working on his third album in 2009 with producers RedOne and Taio Cruz. The album, titled "Obsession", was released on 15 November 2010. The singer worked with songwriters such as Savan Kotecha, Quiz & Larossi and Lucas Secon, while the songs produced by RedOne and Taio Cruz will not be included. The first single from the album is a cover version of Nickelback's 2008 single, "Gotta Be Somebody". Ward's version was released on 7 November 2010 and reached number 12 in the UK and number 10 in Ireland. The video for the song premiered on 29 October 2010 and he performed the song on "The X Factor" on 7 November. Ward also performed at the Miss World Pageant, which was held in Sanya, China. He did his first television appearance in over two years, on "Live from Studio Five" the day after his "X Factor" appearance, where he also performed his single. The album reached number 11 in Ireland on 19 November and peaked at number 15 in the UK on 21 November. On 8 March 2011, Ward performed the title track from the album "Obsession" on "The Alan Titchmarsh Show". In an interview with Digital Spy Ward stated that he hoped he could release a second single from the album.


title: Shayne Ward

text: On 9 June 2011, it was announced that Ward would star as Stacee Jaxx in 1980s-themed musical "Rock of Ages" at the Shaftesbury Theatre, London. For this role, Ward received a nomination for The DEWYNTERS London Newcomer of the Year award from the 2012 What's on Stage Awards. He announced that he would return to the studio in September 2012, after the end of his contract with "Rock of Ages". In February 2014, Ward released a version of "Falling Slowly" with Louise Dearman. In 2014, Ward joined the cast of "Jeff Wayne's Musical Version of The War of the Worlds" for the final arena tour of that production, as the Artilleryman.


title: Shayne Ward

text: On 19 September 2014, Ward announced was working on a new album with Mike Stock, with a then-projected release of February 2015 through PledgeMusic. Ward later postponed the release to April, with the video for the first single "My Heart Would Take You Back", due to be filmed on 25 February 2015 in London.


title: Shayne Ward

text: The album was released in April 2015 and peaked at No.17 in the UK albums chart. It featured two further singles; "The Way You Were" and "Moving Target".


title: Shayne Ward

text: On 12 May 2015, ITV announced they had signed Ward to a one-year contract deal to appear on "Coronation Street" as Aidan Connor, a "distant cousin of Michelle who grew up on the same estate as her and knicker boss Carla Connor". He made his on-screen debut in August 2015. For his performance, he received 2016 National Television Award and 2016 Inside Soap Award, both for the Best Newcomer. His contract was renewed the following year due to the character's popularity and he continued in the role for another two years.


title: Shayne Ward

text: In early 2018, Ward announced that he was leaving the role. He made his last appearance as Aidan Connor on 7 May 2018, in a storyline highlighting male suicide. The storyline gained much attention from the press. Ward has also spoken of his significant weight gain during his time on the show. He revealed that he gained three stone (42 lbs) and said that the tempting canteen food at Granada studios was partly to blame, although he was largely unconcerned by negative comments he received regarding this. He subsequently slimmed-down towards the end of his time on the show.


title: Shayne Ward

text: After leaving the show, he was cast as a lead in the film, "Stairs", a psychological drama. Upon release, however, the film was titled "The Ascent", with its US title being "Black Ops".


title: Shayne Ward

text: In November 2022, it was announced that Ward would be releasing a compilation retrospective of his musical career to date, titled "Anthology", which is due for release 9 December 2022. In an interview with "Retro Pop Magazine", Ward shared that he had begun work on his next studio album, which was following a more country pop approach.


title: Shayne Ward

text: On 2 August 2016, Ward announced he and his partner were expecting their first child. On 3 December 2016, the pair welcomed their first child, a daughter named Willow May. In December 2017, Ward announced his engagement to Austin. On 3 January 2022, the couple announced they are expecting their second child. On 11 June 2022, the pair welcomed their second child, a boy.


title: Shayne Ward

text: In September 2017, Ward spoke out about his noticeable weight gain since becoming a father and through TV's "Loose Women" appeared in a photo shoot, promoting body confidence for men, along with several other celebrities.


title: Mercedes-Benz M112 engine

text: The Mercedes-Benz M112 engine is a gasoline-fueled, 4-stroke, spark-ignition, internal-combustion automobile piston V6 engine family used in the 2000s. Introduced in 1998, it was the first V6 engine ever built by Mercedes. A short time later the related M113 V8 was introduced.


title: Mercedes-Benz M112 engine

text: All are built in Bad Cannstatt, Germany except the supercharged C32 AMG, which is assembled in Affalterbach, Germany.


title: Mercedes-Benz M112 engine

text: All M112 engines have silicon/aluminum (Alusil) engine blocks with a 90° vee angle. The aluminum SOHC cylinder heads have 3 valves per cylinder. All use sequential fuel injection with two spark plugs per cylinder. All have forged steel connecting rods, a one-piece cast camshaft, iron-coated aluminum pistons and a magnesium intake manifold. To deal with the vibration problems of a 90 degree V6, a balancer shaft was installed in the engine block between the cylinder banks. This essentially eliminated first and second order vibration problems (see engine balance). A dual-length Variable Length Intake Manifold is fitted to optimise engine flexibility.


title: Mercedes-Benz M112 engine

text: The E24 is a version. Bore and stroke is . The engine produces between 5500 and 6000 rpm and of torque between 3000 and 5500 rpm. The compression ratio is 10.0:1.


title: Mercedes-Benz M112 engine

text: The E26 is a version. Bore and stroke is . Output is ECE at 5,500 rpm of torque at 4,500 rpm in all applications except in the 2003-2005 W211 E-Class where power rose to . The compression ratio is raised to 10.5:1.


title: Mercedes-Benz M112 engine

text: The E28 is a version. Bore and stroke is . It produces (W220 S280 and W210 E280) or (W202 C280) at 5,700 rpm and of torque between 3,000 and 5,000 rpm. The compression ratio is 10.0:1.


title: Mercedes-Benz M112 engine

text: The E32 is a version. Bore remains at but the engine is stroked to . Output is 215-224 bhp ECE at 5,700 rpm (depending on model) with of torque at 3,000-4,800 rpm. The compression ratio is 10.0:1. It has fracture-split forged steel connecting rods.


title: Mercedes-Benz M112 engine

text: The E 32 ML is a special version of the , fitted with a helical Twin-screw type supercharger. The supercharger was developed in conjunction with IHI and features Teflon-coated rotors producing overall boost of with the factory 74mm clutch-activated pulley. A water-to-air intercooler made by Garrett is fitted beneath the supercharger inside the V, with a 0.8L Heat-Exchanger mounted under the bumper run by an electric water pump. Output is ECE at 6,100 rpm with of torque at 3,000-4,600 rpm. The compression ratio is 9.0:1.


title: Mercedes-Benz M112 engine

text: The E37 is a version. It retains the stroke of the E32 but is bored to . Output is ECE at 5,750 rpm with of torque at 3,000-4,500 rpm. The compression ratio is 10.0:1.


title: Beauden Barrett

text: Beauden John Barrett (born 27 May 1991) is a New Zealand rugby union player. He plays as a First five-eighth (fly-half) and fullback for Taranaki in the Mitre 10 Cup, the Blues in Super Rugby and New Zealand's national team, the All Blacks. He was a key member of the 2015 Rugby World Cup winning team.


title: Beauden Barrett

text: Barrett won the World Rugby Player of the Year award in 2016 and 2017, was also a nominee for the award in 2018, and is only the second player to win the award in back-to-back years, after former teammate Richie McCaw. He also won the overall Sportsperson of the Year Award in the Taranaki Sports Awards in 2013, 2016 and 2019.


title: Beauden Barrett

text: Barrett played at under-20 and Sevens levels for New Zealand before being called into the All Blacks' squad in May 2012, and made his international debut as a replacement in the final test against Ireland in Hamilton, when he kicked nine points, on 23 June 2012. He debuted for Taranaki in 2010, and debuted in Super Rugby with the Hurricanes in 2011.


title: Beauden Barrett

text: Barrett was born in New Plymouth to parents Robyn and Kevin Barrett. He grew up on a farm in Pungarehu, a small town in South Taranaki near Ōpunake, with his seven siblings. He has four brothers and three sisters, including Kane, a former Blues representative and Taranaki captain and current All Blacks, Scott and Jordie. Barrett spent a year in Ireland when he was eight years old. He attended St Fiach's National School in Ballinacree, where he and his brother Kane learned how to play Gaelic football. He played for the Rahotu and Coastal Rugby clubs throughout his early childhood rugby, whilst he also represented Francis Douglas Memorial College in New Plymouth, alongside All Black teammate Liam Coltman, where he excelled in its first XV.


title: Beauden Barrett

text: Barrett came to the attention of national selectors at the age of 19, after he was selected in the New Zealand Sevens team for the final two legs of the 2010 IRB Sevens World Series in England and Scotland and debuted for Taranaki in the ITM Cup against Northland.


title: Beauden Barrett

text: Barrett made his debut for Taranaki in the 2010 ITM Cup competition, coming on as a replacement against Northland. The 19-year-old had made a huge impression in his opening season for the province, especially in his ability to attack the line and create space which saw him named most promising player of the year. Barrett soon enough caught the eyes of coaches, after a solid performance against Manawatu. Coming off the bench to score a 65-metre solo try that secured his side a bonus point win with 10 minutes to play. Barrett's try, his third of the season, helped Taranaki to their eighth win of the season, maintaining their position in the top four.


title: Beauden Barrett

text: With his season over with Taranaki, it left Barrett with tough decisions to make on his Super Rugby future. Weighing up whether to take up a wider training group contract with the Hurricanes or look at other offers, including one from the Blues. Barrett decided to opt with the Hurricanes to become a Hurricanes wider squad member in 2011 after turning down the offer from the Blues. He was called up by the Hurricanes before the side's 2011 tour to South Africa where he saw time off the bench, earning his first four Hurricanes caps. He made his debut in a 50–47 win over the Cheetahs in Bloemfontein, a match that saw the Hurricanes prevail on full-time with a try to lock Jeremy Thrush that Barrett converted.


title: Beauden Barrett

text: In his second season with the Taranaki squad for the 2011 ITM Cup, Barrett scored 90 points for the season, including an ITM Cup record after he kicked nine penalties in a 39–33 win over Bay of Plenty. With Barrett playing, Taranaki finished a respectable third placing in the ITM Cup and was instrumental in securing his side the Ranfurly Shield off Southland. Barrett was crowned Taranaki best back of the year for his efforts.


title: Beauden Barrett

text: In 2012, Barrett began with his first Super Rugby match-day start with the Hurricanes against the Stormers. He produced a man of the match performance during a 39–26 loss. Barrett lead effectively with two try assists, one for second five Tim Bateman and another for reserve hooker Motu Matu'u that was later disallowed by the television match official. He scored one himself and landed all of his six attempts at goal. Barrett also celebrated a record-setting display of goal kicking during the Hurricanes' 66–24 win over the Melbourne Rebels. It saw his 21 points break several franchise records previously held by Jon Preston, including his 1997 mark of 152 points for the season. He landed all nine of his conversion attempts, eclipsing the previous mark of six shared by Christian Cullen, Willie Ripia and Jimmy Gopperth. It was only the second time the Hurricanes have scored nine tries in a match and their total of 66 bettered the 64 scored against Northern Transvaal in 1997.


title: Beauden Barrett

text: In June 2012, Barrett was named in the All Blacks squad for the Irish tour of New Zealand. Barrett's Test debut was a memorable one; the first five-eighth coming off the bench after 24 minutes and helping the All Blacks contribute 9 points to a record 60–0 win over the Irish. He went on to play five Tests in 2012.


title: Beauden Barrett

text: Due to his international duties, Barrett appeared only four times in 2012 for Taranaki, recording a respectable 60 points. He began the season with a win over Bay of Plenty, whilst scoring a 70-meter intercept try and converting all his goals. Barrett was then released from New Zealand national coach Steve Hansen to start in his first run-on against Wellington since Taranaki's successful Ranfurly Shield defence against Tasman on 1 September. He also featured in 2012 rugby semifinals, when Taranaki took on Canterbury. The match had to go into extra-time after a 27-all draw at full time.


title: Beauden Barrett

text: In 2013, Barrett represented the Hurricanes in his third Super Rugby campaign and finished with 186 points for the year. He found his best form of the season playing majority in the number 10 position but was switched to fullback now and then throughout the season after he showed his versatility for the Hurricanes in the position that year. With his international commitments, Barrett was kept from running out for Taranaki. Although he did feature at the launch of the side's 2013 alternative rugby jersey revealing.


title: Beauden Barrett

text: Barrett returned to international rugby in 2013, being named in the All Blacks squad for the French tour of New Zealand. Barrett was a key player, playing in the historic 30–0 victory over France, scoring his first test try, which was subsequently voted International Rugby Players' Association's Try of the Year for 2013.


title: Beauden Barrett

text: Barrett ended speculation concerning his future by signing a two-year contract extension with the Hurricanes in 2014. The then 23-year-old only signed a 12-month deal the previous year after reportedly almost joining the Blues. Along with Julian Savea, he started all sixteen matches for the Hurricanes and by early April, in the 2014 Super Rugby season, Barrett had already scored 100 points. He finished the season scoring 209 points.


title: Beauden Barrett

text: In June 2014, Barrett featured in all of the three Tests against England starting on the bench, in the mid-year Test series. He played in the opening 2 Bledisloe Cup Test games against Australia starting from the bench in August.


title: Beauden Barrett

text: In September 2014, Barrett got the opportunity to start in the All Blacks No. 10 jersey for the first time in his career. He played against Argentina at McLean Park in Napier following an injury to Aaron Cruden. Despite having a tough night with his goal-kicking, succeeding with only one from five attempts, he produced a strong 55-minute performance and were involved in setting up the team's three tries. He was then subbed-off by Colin Slade in the 55th minute. The following week, he was benched for the home-game clash against South Africa and came on to replace Aaron Cruden in the 58th minute of the All Blacks' 14–10 win over South Africa, kicking a successful penalty goal.


title: Beauden Barrett

text: Following Cruden's boozy night out and off-field drama, Barrett got more opportunity to start in the All Blacks No. 10 (Fly Half) role, starting for the last two Tests of the Rugby Championship. He guided the All Blacks to a third straight Rugby Championship Title in the All Blacks' 34–13 win over Argentina in La Plata and then featured in the 25–27 loss to South Africa in Johannesburg. He finished the Rugby Championship with 30 points (6 conversion goals and 6 penalty goals) as 5th highest point-scorer (behind teammate Aaron Cruden with 37 points).


title: Beauden Barrett

text: On 18 October 2014, despite Cruden returning to the team squad for the third Bledisloe Cup match in Brisbane, coach Steve Hansen selected Barrett to start at No. 10 for the team's clash against the Wallabies. He played for 72 minutes, kicking 3 goals from 4 attempts and produced a strong performance, before being replaced by Colin Slade. The All Blacks won the game 29–28.


title: Beauden Barrett

text: Barrett was selected for the 2015 Rugby World Cup, starting in one fixture against Namibia, and coming off the bench to cover wing and fullback in the rest.


title: Beauden Barrett

text: In 2015, Barrett had a couple of injuries throughout the Hurricanes 2015 season. He first had a frustrating month of rehabilitation for a knee injury suffered against the Crusaders on 2 May after Barrett's scans revealed a grade-two tear of the medial collateral ligament (MCL) in his right knee. He had been ruled out of the Hurricanes' Super Rugby derby match against the Chiefs with a calf strain. Barrett returned to Hurricanes just in time for the 2015 Super Rugby final in which the Highlanders created an upset and heaped heartbreak on the Hurricanes with a 21–14 win in Wellington.


title: Beauden Barrett

text: Barrett returned to Taranaki in 2015, after missing the 2013 and 2014 seasons for the province after featuring at first five-eighth against Otago in round three of the competition. His performance did not go unnoticed after a break, from set play, saw him break the Otago line with ease, and speed, to find wing Jackson Ormond in support to take his pass for the opening try in the 12th minute. With three minutes left in the first half, he sized up his options perfectly again to slip a kick across field where right wing Codey Rei was waiting in clear space to secure the ball and score.


title: Beauden Barrett

text: All Black Head Coach, Steve Hansen, selected Barrett for the 2015 Rugby World Cup. Barrett started in one fixture against Namibia, and coming off the bench to cover wing and fullback in the rest. On 31 October 2015, Barrett scored the final try in the 2015 Rugby World Cup Final match against Australia, having been substituted on for the injured Nehe Milner-Skudder. Dan Carter converted his try to make the final score 34–17.


title: Beauden Barrett

text: In 2016, Barrett scored the most individual points that season with 223, in addition he was the only player in the 2016 Super Rugby season to surpass 200 points. He was named man of the match in the Super Rugby final, scoring 15 points as the Hurricanes beat the Lions 20-3 to win their first title.


title: Beauden Barrett

text: During the Wales tour to New Zealand, Barrett came off the bench in the second test after Aaron Cruden was injured, he scored 11 points in the second test which New Zealand won 36-22. Barrett started in the final test against Wales; he was praised heavily for his 26-point haul in a 46-6 demolition of a tired Wales side.


title: Beauden Barrett

text: Due to his superb form for the Hurricanes and against Wales during their tour; Barrett supplanted an injury-plagued Aaron Cruden at fly-half for the 2016 Rugby Championship. He seemed to cement his position as New Zealand's first choice fly-half as New Zealand beat Australia by a record 42-8, away; he followed this with another 29-9 victory over Australia in round 2. Barrett only seemed to get better as the Rugby Championship continued as New Zealand comfortably beat Argentina 57-22 and South Africa 41-13, winning the Championship with two rounds to spare. Barrett finished as the highest point scorer of the tournament, scoring 81 points across the 6 matches played. Barrett supplanted Aaron Cruden as New Zealand's first-choice by the end of the competition and carried on being a regular starter in the end of year tour.


title: Beauden Barrett

text: Barrett managed to convert his brother Scott Barrett's first test try in the All Blacks' 40-29 loss against Ireland in November, after Scott scored on debut.


title: Beauden Barrett

text: Barrett won the award for World Rugby Player of the Year, later in the year, beating teammate Dane Coles to the award and becoming the next All Blacks player after Dan Carter to win that award. Barrett's 95-meter individual try against France in New Zealand's final match for the year saw Barrett overtake Ben Smith as the second to highest try scorer in the All Blacks for the year, scoring 9 tries throughout the calendar year, having doubled his career total. Barrett finished behind winger Israel Dagg, who scored 10 tries that year.


title: Beauden Barrett

text: Barrett played in most Hurricanes fixtures, during the 2017 Super Rugby season, but lent his kicking duties to younger brother, Jordie Barrett, during the season due to a leg problem. Despite this, Barrett still scored 58 points in the season. Barrett's discipline was also notably off, with Barrett ending the season as the most-carded player of the year. Barrett received four yellow cards, as well as a red card during the season. Barrett earned this red card, which was the first of his career, for being awarded two yellow cards against the Waratahs, having performed a deliberate knock-down and an offside against the Waratahs.


title: Beauden Barrett

text: Barrett was selected for the All Blacks' 33-man squad to face Manu Samoa and the British and Irish Lions in 2017. His brothers Scott and fellow Hurricane Jordie were selected too. This meant the Barrett family were the first to have three siblings selected for the same All Blacks squad. Barrett scored 24 points including two tries in his 50th test match, against Samoa, on 16 June 2017, which was also his brother Jordie's debut. Although Beauden and Jordie were not on the pitch at the same time, Scott shared game time with both of them.


title: Beauden Barrett

text: Barrett went on to score 41 points in the three tests against the British and Irish Lions, being the highest points scorer of the series. The All Blacks drew the series with the Lions, with Barrett missing three of his ten kicks during the second test of the series.


title: Beauden Barrett

text: Barrett was retained as a regular starter for the 2017 Rugby Championship, despite calls from the public to replace Barrett with outstanding Highlanders first-five Lima Sopoaga. Barrett was named as the All Black Vice-Captain, for the rest of 2017, replacing Ben Smith who took a sabbatical leave. In the final match of the Rugby Championship against South Africa, Barrett was subbed off after only 33 minutes for a concussion test, being replaced by Lima Sopoaga. The All Blacks went on to win 25-24 after Barrett failed to make it back on the field.


title: Beauden Barrett

text: Barrett returned from concussion to captain the All Blacks for the first time, in a non-cap match over the Barbarians on 4 November, which the All Blacks won 31-22 (Barrett slotting 3 conversions). Barrett started in all three tests on the end-of-year tour, scoring the winning try against Scotland in a tense 22-17 win.


title: Beauden Barrett

text: Barrett was awarded World Rugby Player of the Year for the second time in 2017, beating team-mate Rieko Ioane to the award, joining former team-mates Richie McCaw and Dan Carter to become the third player to win the award on more than one occasion, as well as becoming only the second player to win the award twice in successive years. Barrett also scored the second-to-most tries of any All Black in 2017, tying with Waisake Naholo and scoring six tries in 2017. Ioane was the only All Black to score more than Barrett, scoring 10 tries in 2017.


title: Beauden Barrett

text: On 10 March 2018, Barrett as well as his Hurricanes team-mate Ben May, played their 100th game for the Hurricanes, in Round 4, against the Crusaders. The Hurricanes won the match 29-19, with Barrett lasting the full 80 minutes. Barrett finished the Super Rugby season with 117 points, including five tries.


title: Beauden Barrett

text: Barrett scored the first All Black try of 2018, but he had limited participation in the three-test 2018 Steinlager series against France, due to injury. On 16 June 2018, Barrett was replaced by Damian McKenzie only 12 minutes into the test. Barrett was taken off the field for a concussion test, which he failed, due to a mid-air clash with French fullback Benjamin Fall. Fall was controversially red-carded, by referee Angus Gardner, for causing Barrett's dangerous landing, although Fall was later cleared and was not suspended for doing so. Barrett did not play in the third test of the series, with the All Blacks going on to win all three tests.


title: Beauden Barrett

text: The 2018 Rugby Championship was somewhat of a mixed competition for Barrett. He was the second-to-highest point scorer in the Rugby Championship, with 61 points. This included five tries, bringing Barrett's career try tally to 30 tries, a major career milestone. Four of the tries Barrett scored in the competition, were all in one test, on 25 August 2018, against the Wallabies. Barrett became the first All Black to score four tries in a test since his former team-mate Zac Guildford scored four against Canada in 2011. Barrett also won Man of the Match for that performance, becoming the first player to ever score more than three tries against the Wallabies, scoring 30 points in the process. Barrett was deemed to have silenced critics who wanted him replaced by Crusaders first-five and new All Black, Richie Mo'unga, but also arguably cost the All Blacks a win with his follow-up performance.


title: Beauden Barrett

text: On 15 September 2018, in his following performance, Barrett managed to kick only two of the six goals he attempted against South Africa. The All Blacks then narrowly lost to South Africa, by 34-36. Had Barrett kicked two more of his goals, the All Blacks could have won by two points. Barrett's performance against South Africa was answered by the All Black selectors, with Mo'unga chosen over Damian McKenzie as Barrett's back-up off the bench. Barrett performed well in the last round of the competition, when he was moved to fullback, after Richie Mo'unga replaced winger Waisake Naholo. Barrett, Mo'unga and Hurricanes loose forward, Ardie Savea, had a commanding teamwork in the last 20 minutes, allowing the All Blacks to beat South Africa 32-30.


title: Beauden Barrett

text: Barrett's 2018 end-of-year tour saw him surpass Dan Carter as the most prolific try-scorer to ever play at first-five, as he scored the 31st of his career in the third Bledisloe Cup test, against the Wallabies, off a pass from Rieko Ioane, during a 37-20 win.


title: Beauden Barrett

text: After being rested and missing out on a test against Japan, Barrett was retained in the starting lineup for the test against England, on 10 November 2018, after New Zealand went for four years without playing England. With Richie Mo'unga on the bench, and Damian McKenzie at fullback, Barrett was one of three first-fives fielded by New Zealand on the day. Barrett's performance against England also saw him kick the first drop-goal of his professional career, in the 46th minute, answering the ongoing criticism for his goal-kicking. Barrett's performance made a big contribution to the final score, 16-15, a win for New Zealand. However, Barrett did concede what could have been the match-winning try to England. England's then third-choice openside flanker, Sam Underhill, outran Barrett to score what would have been a try. Underhill's try was ruled out due to an offside charge down from replacement forward, Courtney Lawes, which left Barrett's 100% kicking percentage as the way New Zealand won the test.


title: Beauden Barrett

text: The week following the England test, Barrett also kicked a drop goal against Ireland in an ill-fated loss, 9-16. Barrett was New Zealand's only point-scorer in the loss, also kicking two penalty goals. Barrett was subbed off in the final test of the year, against Italy, scoring a 15-point haul during the 66-3 win.


title: Beauden Barrett

text: Following the 2019 Super Rugby season, Barrett re-signed with New Zealand Rugby through to 2023, also announcing that he would be switching Super Rugby clubs, from the Hurricanes, to the Auckland-based Blues. Barrett finished his career with the Hurricanes as their all-time leading points-scorer, with 1238 points, also finishing as the fourth-to-most capped Hurricane of all-time, behind Conrad Smith, Ma'a Nonu and current All Blacks teammate, TJ Perenara.


title: Beauden Barrett

text: In the All Black's 2019 Rugby Championship campaign, Barrett started one game at first five and two games at fullback. Even after partially handing over the kicking duties to Richie Mo'unga, Barrett was able to score a total of 20 points across the All Black's 3 games, making him the All Black's top point scorer (10 points vs Argentina, 5 points vs South Africa, and 5 points vs Australia.


title: Beauden Barrett

text: After continued poor performances by Ben Smith and Rieko Ioane, Barrett started his third consecutive test at fullback, against Australia during the second Bledisloe Cup test of 2019. The 36-0 win was also a success for Barrett's partnership with Richie Mo'unga, the new regular at first-five, with Mo'unga having overtaken Barrett as the first-choice.


title: Beauden Barrett

text: All Blacks Head Coach, Steve Hansen named Barrett in New Zealand's 31-man squad for the 2019 Rugby World Cup on 28 August 2019, with the competition set to be Barrett's second World Cup. Barrett went on to play in five tests during the competition, although it ended in disappointment for New Zealand, who finished in third place.


title: Beauden Barrett

text: In a season disrupted by COVID-19 Barrett played for the Blues in the 2020 Super Rugby season until it was suspended and in the subsequent 2020 Super Rugby Aotearoa season.


title: Beauden Barrett

text: In October and November the All Blacks played six tests and Barrett appeared in five of them, three against Australia and two against Argentina. He started as first five-eighth in the last test against Australia but in the other four tests he started at Fullback. He did not score any tries or points, Richie Mo’unga and Jordie attended to goal kicking duties.


title: Beauden Barrett

text: In 2021 Barrett had a sabbatical in Japan with Top League club Suntory Sungoliath so he did not appear for the Blues in the 2021 Super Rugby Aotearoa or Super Rugby Trans-Tasman.


title: Beauden Barrett

text: Barrett returned for the international season and on 30 October 2021 he played his 100th test match, in the fixture against Wales at Principality Stadium in Cardiff. He scored two tries.


title: Beauden Barrett

text: Barret is known for his speed and quickness. Barrett clocked in an All Blacks record 4.18 in the infamous Bronco fitness test requires players to run 20, 40 and 60m and back, five times over – a total distance of 1.2km – as fast as possible. It’s considered one of the best indicators of aerobic endurance.


title: Beauden Barrett

text: Barrett proposed to his long-time partner Hannah Laity in 2018 and they married the following year in a private ceremony on Rakino Island. Together they have two children.


title: Andrea True

text: Andrea Marie Truden (July 26, 1943 – November 7, 2011), better known by her pseudonym Andrea True, was an American pornographic actress and singer from the disco era. In addition to her given name, she had multiple stage names, including Inger Kissin, Singe Low, Sandra Lips, Andrea Travis, and Catherine Warren. As a singer, she is best known for the 1976 pop-disco hit "More, More, More" (performed as part of her recording project, the Andrea True Connection), which peaked at no. 4 on the US "Billboard" Hot 100 and no. 5 on the UK Singles Chart.


title: Andrea True

text: Andrea Marie Truden was born in Nashville, Tennessee, where she attended St. Cecilia Academy, a Catholic school for girls dedicated to the performing arts. She studied music at George Peabody College at Vanderbilt University. Her father, Frank, was an engineer, who died when True was 16 years old. Her mother Anne owned a silverplating business and was a professional singer, specializing in polka, who recorded her own record and had performed with Frankie Yankovic's band. Her parents were immigrants from Slovenia.


title: Andrea True

text: As a child, True studied classical piano and was given a high rating for her piano audition for St. Cecilia Academy in 1954. At age 15, she hosted her own television program "Teen Beat" for Nashville station WLAC. While a junior at St. Cecilia, True participated in Junior Achievement, serving as vice-president of a TV production enterprise. In 1960, she received an award for her work from the Radio and Television Council of Middle Tennessee.


title: Andrea True

text: In a recorded interview published by "The Rialto Report", True stated that she married David L. Wolfe at age 19, leaving college to follow her husband for his academic career, first to Oklahoma and then eventually to New York City in the late 1960s.


title: Andrea True

text: True performed in a few pornographic films in Scandinavia in the 1960s and, by the end of the decade, began appearing in American adult films. Her first prominent role was in the film "Head Nurse" in 1972. She also appeared as an extra in non-adult films "The Way We Were" and "40 Carats". In 1975, she directed her first pornographic film, "Once Over Nightly". Eventually, she performed in more than fifty hardcore porn films throughout the 1970s and early to mid-1980s in the early New York adult film industry.


title: Andrea True

text: During her heyday as a porn actress, around 1975, True was hired by a real estate business in Jamaica to appear in their commercials. While she was working there, the Jamaican government banned asset transfers in response to sanctions imposed by the U.S. after the election of Michael Manley, a supporter of Fidel Castro. In order to return to the U.S., True would have had to either forfeit her pay or spend the money before she went home. True, who by this time was trying to break into the music industry, chose to invest the money in recording a demo of "More, More, More", a song she had been working on with record producer Gregg Diamond, her partner in a project called The Andrea True Connection. Remixed by recording engineer Tom Moulton, "More, More, More" became a favorite in nightclubs. It reached no. 4 on the U.S. "Billboard" Hot 100, no. 1 on the U.S. disco chart, and no. 1 on the national singles chart in Canada. It also peaked at no. 5 in the UK and no. 9 in Germany. A full album with the same title followed, which performed moderately in North America and spawned the second single, "Party Line", a minor chart hit.


title: Andrea True

text: By the time of her singing career, True admitted she was burned out and tired of porn, saying, "I'd rather be a waitress or a typist than make another adult film", and also, "Don't think of me as a porn star any more, think of me as a recording star. I just want to record and perform". She was performing extensively and went on to play around 300 shows within a year from June 1976. Andrea True Connection came fifth in ASCAP's ranking of disco artists of the year.


title: Andrea True

text: In early 1977, True released the single "N.Y., You Got Me Dancing". It became a considerable hit, reaching no. 27 on "Billboard"s pop chart and no. 4 on the disco chart. In early 1978, she had another hit with "What's Your Name, What's Your Number", which peaked at no. 56 in the U.S. and no. 34 in the UK. Both singles were included in her second album, "White Witch". It was a commercial flop and did not chart due to a lack of promotion from Buddah Records as the label was struggling financially at the time. In 1980, she released her third and final album, "War Machine", promoted by the anti-war title song. A more rock and new wave-oriented album, it was released only in Europe, but it flopped.


title: Andrea True

text: True never returned to adult film industry and for some time performed in clubs in Florida. After that, a growth developed on her vocal cords that required surgery, essentially ending her singing ability. She did, however, perform two sold out shows at the Paramount Theater in New York City in 1994, and worked on new music, which eventually never materialised. True received a renewed burst of publicity in 1999 when the Canadian group Len sampled the instrumental break from "More, More, More" in their single "Steal My Sunshine". Subsequently, True appeared on several VH1 specials including "100 Greatest Dance Songs" in 2000 ("More, More, More" was the no. 45 greatest dance song), "Where Are They Now?" and "100 Greatest One-Hit Wonders" (both in 2002), in which she said she wanted to be remembered as a person who "gave people pleasure" — then emphasized the words — "with my music". She also made an appearance in the 2005 documentary movie "Inside Deep Throat".


title: Andrea True

text: In her later years, she was reported as working as a counselor for people struggling with substance abuse, and as an astrologer. "More, More, More" remained a popular song on TV and in movies, and Andrea was eventually able to claim outstanding royalties from the track's usage and sales. She spent her final years living in Woodstock, New York, suffering from declining health.


title: Andrea True

text: True died on November 7, 2011, at a hospital in Kingston, New York. She was 68 years old. The cause was given as heart failure. In line with her wishes, True's body was cremated.


title: Shannon–Hartley theorem

text: In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise. It is an application of the noisy-channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise. The theorem establishes Shannon's channel capacity for such a communication link, a bound on the maximum amount of error-free information per time unit that can be transmitted with a specified bandwidth in the presence of the noise interference, assuming that the signal power is bounded, and that the Gaussian noise process is characterized by a known power or power spectral density. The law is named after Claude Shannon and Ralph Hartley.


title: Shannon–Hartley theorem

text: The Shannon–Hartley theorem states the channel capacity formula_1, meaning the theoretical tightest upper bound on the information rate of data that can be communicated at an arbitrarily low error rate using an average received signal power formula_2 through an analog communication channel subject to additive white Gaussian noise (AWGN) of power


title: Shannon–Hartley theorem

text: During the late 1920s, Harry Nyquist and Ralph Hartley developed a handful of fundamental ideas related to the transmission of information, particularly in the context of the telegraph as a communications system. At the time, these concepts were powerful breakthroughs individually, but they were not part of a comprehensive theory. In the 1940s, Claude Shannon developed the concept of channel capacity, based in part on the ideas of Nyquist and Hartley, and then formulated a complete theory of information and its transmission.


title: Shannon–Hartley theorem

text: In 1927, Nyquist determined that the number of independent pulses that could be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel. In symbolic notation,


title: Shannon–Hartley theorem

text: where formula_10 is the pulse frequency (in pulses per second) and formula_5 is the bandwidth (in hertz). The quantity formula_12 later came to be called the "Nyquist rate", and transmitting at the limiting pulse rate of formula_12 pulses per second as "signalling at the Nyquist rate". Nyquist published his results in 1928 as part of his paper "Certain topics in Telegraph Transmission Theory".


title: Shannon–Hartley theorem

text: During 1928, Hartley formulated a way to quantify information and its line rate (also known as data signalling rate "R" bits per second). This method, later known as Hartley's law, became an important precursor for Shannon's more sophisticated notion of channel capacity.


title: Shannon–Hartley theorem

text: Hartley argued that the maximum number of distinguishable pulse levels that can be transmitted and received reliably over a communications channel is limited by the dynamic range of the signal amplitude and the precision with which the receiver can distinguish amplitude levels. Specifically, if the amplitude of the transmitted signal is restricted to the range of [−"A" ... +"A"] volts, and the precision of the receiver is ±Δ"V" volts, then the maximum number of distinct pulses "M" is given by


title: Shannon–Hartley theorem

text: By taking information per pulse in bit/pulse to be the base-2-logarithm of the number of distinct messages "M" that could be sent, Hartley constructed a measure of the line rate "R" as:


title: Shannon–Hartley theorem

text: Hartley then combined the above quantification with Nyquist's observation that the number of independent pulses that could be put through a channel of bandwidth formula_5 hertz was formula_12 pulses per second, to arrive at his quantitative measure for achievable line rate.


title: Shannon–Hartley theorem

text: Hartley's law is sometimes quoted as just a proportionality between the analog bandwidth, formula_5, in Hertz and what today is called the digital bandwidth, formula_20, in bit/s.


title: Shannon–Hartley theorem

text: Other times it is quoted in this more quantitative form, as an achievable line rate of formula_20 bits per second:


title: Shannon–Hartley theorem

text: Hartley did not work out exactly how the number "M" should depend on the noise statistics of the channel, or how the communication could be made reliable even when individual symbol pulses could not be reliably distinguished to "M" levels; with Gaussian noise statistics, system designers had to choose a very conservative value of formula_23 to achieve a low error rate.


title: Shannon–Hartley theorem

text: The concept of an error-free capacity awaited Claude Shannon, who built on Hartley's observations about a logarithmic measure of information and Nyquist's observations about the effect of bandwidth limitations.


title: Shannon–Hartley theorem

text: Hartley's rate result can be viewed as the capacity of an errorless "M"-ary channel of formula_12 symbols per second. Some authors refer to it as a capacity. But such an errorless channel is an idealization, and if M is chosen small enough to make the noisy channel nearly errorless, the result is necessarily less than the Shannon capacity of the noisy channel of bandwidth formula_5, which is the Hartley–Shannon result that followed later.


title: Shannon–Hartley theorem

text: Claude Shannon's development of information theory during World War II provided the next big step in understanding how much information could be reliably communicated through noisy channels. Building on Hartley's foundation, Shannon's noisy channel coding theorem (1948) describes the maximum possible efficiency of error-correcting methods versus levels of noise interference and data corruption. The proof of the theorem shows that a randomly constructed error-correcting code is essentially as good as the best possible code; the theorem is proved through the statistics of such random codes.


title: Shannon–Hartley theorem

text: Shannon's theorem shows how to compute a channel capacity from a statistical description of a channel, and establishes that given a noisy channel with capacity formula_1 and information transmitted at a line rate formula_20, then if


title: Shannon–Hartley theorem

text: there exists a coding technique which allows the probability of error at the receiver to be made arbitrarily small. This means that theoretically, it is possible to transmit information nearly without error up to nearly a limit of formula_1 bits per second.


title: Shannon–Hartley theorem

text: the probability of error at the receiver increases without bound as the rate is increased. So no useful information can be transmitted beyond the channel capacity. The theorem does not address the rare situation in which rate and capacity are equal.


title: Shannon–Hartley theorem

text: The Shannon–Hartley theorem establishes what that channel capacity is for a finite-bandwidth continuous-time channel subject to Gaussian noise. It connects Hartley's result with Shannon's channel capacity theorem in a form that is equivalent to specifying the "M" in Hartley's line rate formula in terms of a signal-to-noise ratio, but achieving reliability through error-correction coding rather than through reliably distinguishable pulse levels.


title: Shannon–Hartley theorem

text: If there were such a thing as a noise-free analog channel, one could transmit unlimited amounts of error-free data over it per unit of time (Note that an infinite-bandwidth analog channel couldn’t transmit unlimited amounts of error-free data absent infinite signal power). Real channels, however, are subject to limitations imposed by both finite bandwidth and nonzero noise.


title: Shannon–Hartley theorem

text: Bandwidth and noise affect the rate at which information can be transmitted over an analog channel. Bandwidth limitations alone do not impose a cap on the maximum information rate because it is still possible for the signal to take on an indefinitely large number of different voltage levels on each symbol pulse, with each slightly different level being assigned a different meaning or bit sequence. Taking into account both noise and bandwidth limitations, however, there is a limit to the amount of information that can be transferred by a signal of a bounded power, even when sophisticated multi-level encoding techniques are used.


title: Shannon–Hartley theorem

text: In the channel considered by the Shannon–Hartley theorem, noise and signal are combined by addition. That is, the receiver measures a signal that is equal to the sum of the signal encoding the desired information and a continuous random variable that represents the noise. This addition creates uncertainty as to the original signal's value. If the receiver has some information about the random process that generates the noise, one can in principle recover the information in the original signal by considering all possible states of the noise process. In the case of the Shannon–Hartley theorem, the noise is assumed to be generated by a Gaussian process with a known variance. Since the variance of a Gaussian process is equivalent to its power, it is conventional to call this variance the noise power.


title: Shannon–Hartley theorem

text: Such a channel is called the Additive White Gaussian Noise channel, because Gaussian noise is added to the signal; "white" means equal amounts of noise at all frequencies within the channel bandwidth. Such noise can arise both from random sources of energy and also from coding and measurement error at the sender and receiver respectively. Since sums of independent Gaussian random variables are themselves Gaussian random variables, this conveniently simplifies analysis, if one assumes that such error sources are also Gaussian and independent.


title: Shannon–Hartley theorem

text: Comparing the channel capacity to the information rate from Hartley's law, we can find the effective number of distinguishable levels "M":


title: Shannon–Hartley theorem

text: The square root effectively converts the power ratio back to a voltage ratio, so the number of levels is approximately proportional to the ratio of signal RMS amplitude to noise standard deviation.


title: Shannon–Hartley theorem

text: This similarity in form between Shannon's capacity and Hartley's law should not be interpreted to mean that formula_23 pulse levels can be literally sent without any confusion. More levels are needed to allow for redundant coding and error correction, but the net data rate that can be approached with coding is equivalent to using that formula_23 in Hartley's law.


title: Shannon–Hartley theorem

text: In the simple version above, the signal and noise are fully uncorrelated, in which case formula_35 is the total power of the received signal and noise together. A generalization of the above equation for the case where the additive noise is not white (or that the is not constant with frequency over the bandwidth) is obtained by treating the channel as many narrow, independent Gaussian channels in parallel:


title: Shannon–Hartley theorem

text: Note: the theorem only applies to Gaussian stationary process noise. This formula's way of introducing frequency-dependent noise cannot describe all continuous-time noise processes. For example, consider a noise process consisting of adding a random wave whose amplitude is 1 or −1 at any point in time, and a channel that adds such a wave to the source signal. Such a wave's frequency components are highly dependent. Though such a noise may have a high power, it is fairly easy to transmit a continuous signal with much less power than one would need if the underlying noise was a sum of independent noises in each frequency band.


title: Shannon–Hartley theorem

text: in which case the capacity is logarithmic in power and approximately linear in bandwidth (not quite linear, since increases with bandwidth, imparting a logarithmic effect). This is called the bandwidth-limited regime.


title: Shannon–Hartley theorem

text: In this low-SNR approximation, capacity is independent of bandwidth if the noise is white, of spectral density formula_47 watts per hertz, in which case the total noise power is formula_48.


title: M712 Copperhead

text: a fin-stabilized, terminally laser guided, explosive shell intended to engage hard point targets such as tanks, self-propelled howitzers or other high-value targets. It may be fired from different artillery pieces, such as the M114, M109, M198, M777 and CAESAR howitzers. The projectile has a minimum range of 3 km and a maximum range of 16 km.


title: M712 Copperhead

text: The concept for Copperhead was originally made in 1970 by engineers at the US Army's Rodman Laboratories, with feasibility studies conducted in 1971. In 1972 development contracts were awarded to Martin Marietta and Texas Instruments. After testing Martin Marietta was chosen for continued development through the 1970s.


title: M712 Copperhead

text: For Copperhead to function, the target must be illuminated with a laser designator. Once the laser signal is detected, the on-board guidance system will operate the steering vanes to maneuver the projectile to the target. The Copperhead targeting logic is designed to ensure (1) that the optical system will always be able to detect the target, and (2) that once the target has been detected there will be sufficient time and velocity to maneuver to hit the target. Copperhead must be below any cloud cover at critical parts of the trajectory, and there must be sufficient visibility to ensure that when the target is acquired the projectile will have sufficient time to maneuver.


title: M712 Copperhead

text: Copperhead has two modes of operation: ballistic mode and glide mode. Ballistic mode is used where the cloud ceiling is high and visibility is good. When the projectile is 3,000 meters from the target, the guidance vanes extend, the target is acquired, and then the on-board guidance system adjusts the guidance vanes to maneuver onto the target.


title: M712 Copperhead

text: Glide mode is used when the cloud ceiling and/or the visibility is too low to permit the use of the ballistic mode. A glide mode trajectory consists of two phases: a ballistic phase and a glide phase. At a predetermined point along the trajectory, the guidance vanes extend and there is a transition from ballistic phase to glide phase. Glide phase targeting logic is designed to ensure the largest possible angle of fall permitted by the cloud cover and the visibility. The target is acquired when the projectile is close enough to detect the laser illumination or when the projectile emerges from the cloud cover, whichever event occurs later in the trajectory. When a trajectory solution has been obtained, time-to-target and terminal velocity are checked to ensure that there will be enough time to maneuver and that the projectile is aerodynamically stable—that it will not stall while maneuvering.


title: M712 Copperhead

text: Copperhead was used in Operation Desert Storm, with 90 rounds fired against hardened Iraqi fortifications and radar stations. One of these strikes caused an Iraqi unit to surrender.


title: M712 Copperhead

text: Lebanese Armed Forces fired several hundred Copperhead shells at ISIL targets in east Lebanon during the Qalamoun offensive (July–August 2017). At least five technicals, five occupied buildings, and several troop formations were struck with precision.


title: My Name Is Nobody

text: My Name Is Nobody () is a 1973 Italian/French/German international co-production comedy Spaghetti Western starring Terence Hill and Henry Fonda. The film was directed by Tonino Valerii and based on an idea by Sergio Leone.


title: My Name Is Nobody

text: The film follows the story of Nobody (Terence Hill) who attempts to get his idol Jack Beauregard (Henry Fonda) to take on the Wild Bunch gang of outlaws.


title: My Name Is Nobody

text: Jack Beauregard is an aging gunslinger who wants to retire peacefully to Europe. After watching him quickly shoot three gunmen who attempted to ambush him in a barbershop, the barber's son asks his father if there is anyone in the world faster than Beauregard, to which the barber replies, "Faster than him? Nobody!"


title: My Name Is Nobody

text: Beauregard pauses to watch a down-and-out catching fish before continuing to an old goldmine. He finds his friend Red dying after an attack by a gang. Beauregard asks Red about the whereabouts of "Nevada" but Red only manages to disclose Nevada's village before dying. At a horse relay station, the down-and-out is asked by three men to deliver a basket to Beauregard inside where he talks to Beauregard, revealing his detailed knowledge of Beauregard's feats. He throws the basket outside where the bomb that was hidden inside explodes. The bum introduces himself as "Nobody". He idolizes Beauregard and wants him to end his career in style by taking on all 150 of the Wild Bunch single-handed. The bandits are using a worthless goldmine to launder their stolen gold. Sullivan, the mine owner fronting for them, believes Beauregard is trying to kill him, so he tries to kill him first.


title: My Name Is Nobody

text: Arriving at Nevada's village, Beauregard finds Nobody already there who reveals that the Nevada Kid, Beauregard's brother, is dead. Nobody again unsuccessfully tries to get Beauregard to take on the Wild Bunch. Arriving in a town, Sullivan hires Nobody to kill Beauregard, but Nobody instead helps Beauregard to take out Sullivan's men. The Wild Bunch ride into town to collect sticks of dynamite, stashing them in their saddlebags.


title: My Name Is Nobody

text: Later, an old man tells Beauregard that he was bought out of a worthless gold mine by his partners Nevada and Red, only to have the mine produce much gold afterwards. Beauregard hurries off to the mine and catches Sullivan loading sacks of gold powder. Sullivan offers Beauregard Nevada's share, but Beauregard tells him he could not care less about his brother, and just takes two sacks, as well as $500 to pay for his passage to Europe. He then leaves to catch a train to New Orleans.


title: My Name Is Nobody

text: Nobody steals a train that is being loaded at a station with bars of gold, guarded by soldiers. Beauregard is waiting down the line when the Wild Bunch charge towards him across a featureless plain. Nobody arrives with the train, but refuses to rescue Beauregard until he "makes his name in the history books". Remembering the mirrored conchas on the gang’s dynamite-filled saddlebags, Beauregard shoots them and takes out most of the gang until Nobody lets him board the train.


title: My Name Is Nobody

text: In New Orleans, Beauregard and Nobody duel in the street, with a photographer and many spectators on hand. Nobody is faster, and Beauregard falls to the ground, apparently dead. The remaining members of the Wild Bunch see it and switch their search to the anonymous Nobody. Later, Nobody walks by the ship that was to take Beauregard to Europe where Beauregard is revealed to be in his cabin aboard, writing Nobody an affectionate farewell.


title: My Name Is Nobody

text: Shooting for "My Name Is Nobody" started on April 30, 1973. It was one of the few films related to Sergio Leone where 80% of the outdoor scenes were actually shot in the United States. The film was shot in nine weeks.


title: My Name Is Nobody

text: Filming took place at Acoma Pueblo, the ghost town of Cabezon, the former mining town of Mogollon, the mission of San Esteban Del Rey in New Mexico and in the gypsum dunes at White Sands. Leone predominantly stayed at home for the shoot and went to join the crew for five days in New Orleans. Leone replaced director Tonino Valerii, who was suffering from an ear infection, for one day on the set.


title: My Name Is Nobody

text: Tensions rose on set between cinematographer Armando Nannuzzi and Valerii. Fonda was being told how to pick up money off the ground and was told two different ways to pick up between Valerii and Nannuzzi. Their relationship became more intense, with Nannuzzi eventually leaving the film.


title: My Name Is Nobody

text: When the film began shooting in Spain in Almería and Guadix, Valerii had a new cinematographer Giuseppe Ruzzolini and Sergio Salvati. Salvati worked as a cameraman uncredited for the sequences of the duel among mirrors and Nobody's meeting with Sullivan in the gambling room. A new problem arose on set when costumes for Henry Fonda vanished, leading to production stopping for nine days. This led to paying a high penalty to keep Fonda for a few days or postpone shooting until he was free again. Leone proposed to Valerii that they either cut 30 or 40 pages from the script or create a second unit to finish the film. Leone offered to take the second unit shots, which Valerii accepted. Claudio Mancini warned Valerii, stating that Leone would take credit for the film when they go back to Rome if he let him shoot anything. Valerii took over scenes involving Henry Fonda and the action sequences in the desert, while Leone directed the saloon scene with Terence Hill showing his gunslinger skills and parts of the sequences in the village festival, and the public urinal scene which was not in the original script.


title: My Name Is Nobody

text: Assumptions range over how much Leone contributed to the film. Christopher Frayling wrote: "the most likely scenario is that Leone helped out on a duel, then took over second-unit work on 'the battle', and then directed the opening scenes and the carnival section of the film." John Landis, who has claimed to be an extra in the film, said: "We shot for a couple of weeks, among hundreds of extras on horseback, attacking and firing wildly. Fonda and Hill kept us all at bay. [...] Leone directed that battle on horseback." Neil Summers who played Squirrel stated that Leone "directed most of the scenes I was in [...] [Leone] worked slowly and was constantly trying new angles with his camera and new innovative shots with his actors." Valerii himself stated that "scenes filmed by Leone are: Terence Hill getting drunk in the saloon (but not the close-ups of that shattering glasses, I shot those myself; and also the footage of the betting, with Piero Lulli taking the money, is mine); the part of the sequence at the fair which starts from the moment where Nobody steals the apple from the boy, to the episode of the pies thrown at the negroes' faces; the digression in the public urinal, [...] and several close-ups of Nobody who, while Beauregard fights the Wild Bunch, takes note of the body count as if they were points at a game, another addition on the part of Leone, who thought it was a funny idea." Screenwriter Ernesto Gastaldi confirmed Valerii's comments stating that "Tonino shot the whole film, absolutely ON HIS OWN" and that Leone "organized a second unit crew and shot a couple of sequences, which in my opinion are the weakest in the film: the urinal, stretched in an abnormal way, and the glass contest in the saloon. Nothing else." Sergio Donati expanded on this, stating that some photographers were sent over by the press office, and asked Leone, who was on set for a single day, to sit behind camera in a director's pose with Valerii's permission. Donati stated that "inevitably, from that moment on, everyone, in and outside the movie business started saying "Yeah, actually the real director of the film was Leone, who saved it from the disaster of an incapable director". Leone's own discussion following the film's release often contradicted itself.


title: My Name Is Nobody

text: Prior to its release in Italy, "My Name Is Nobody" was released in West Germany and France on December 13 and 14 respectively. Italian audiences got to see it starting 21 December 1973, where it was distributed by Titanus. The film grossed over 3.6 billion lire and was the third highest-grossing film in Italy of the year, behind Salvatore Samperi's "Malicious" (5.5 billion lire) and Dino Risi's "Sessomatto". In the United States, it was cut to 111 minutes and "nearly flopped" according to Italian film historian Roberto Curti.


title: My Name Is Nobody

text: In 2015, a novelization of the film by Michael R. Hudson was published in the United States by Raven Head Press as part of a series of adaptations of several of Gastaldi's scripts, including "The Horrible Dr. Hichcock" and "The Case of the Bloody Iris".


title: My Name Is Nobody

text: Contemporary reviews are positive. Vincent Canby in "The New York Times" considered the film "very entertaining" and it "is the kind of Western that only an immensely appreciative and witty Italian film maker could make."


title: Fifty Shades of Black

text: Fifty Shades of Black is a 2016 American slapstick romantic comedy film directed by Michael Tiddes and starring Marlon Wayans, who also serves as co-writer and co-producer. A parody of the 2015 erotic romantic drama film "Fifty Shades of Grey", the film co-stars Kali Hawk, Affion Crockett, Jane Seymour, Andrew Bachelor, Florence Henderson, Jenny Zigrino, Fred Willard and Mike Epps.


title: Fifty Shades of Black

text: The film was released theatrically on January 29, 2016 to near universally negative reviews. Despite this, it was a box office success, grossing $22 million worldwide from a $5 million budget. It was also Florence Henderson's last film before her death on November 24, 2016, which was 10 months after the film was released.


title: Fifty Shades of Black

text: Christian Black introduces shy college student Hannah Steale to the world of "romance" after she interviews him for her school newspaper. Their kinky relationship stumbles forward despite Christian's shortcomings as a lover and the antics of his racist adoptive mother Claire, his well-endowed brother Eli and Hannah's hyper-sexual roommate Kateesha.


title: Fifty Shades of Black

text: On June 3, 2015, it was announced that Open Road Films had acquired the US distribution rights to the yet-to-be made film for $5 million.


title: Fifty Shades of Black

text: The film was released in North America on January 29, 2016, alongside "Kung Fu Panda 3", "The Finest Hours", and "Jane Got a Gun". The film was projected to gross $10–11 million from 2,075 theaters in its opening weekend. The film grossed $275,000 from its Thursday night previews, $2.3 million on its first day, and $5.9 million in its opening weekend, finishing 10th at the box office. The film was released on DVD and Blu-ray on April 19, 2016.


title: Fifty Shades of Black

text: On Rotten Tomatoes, the film has an approval rating of 4% based on 46 reviews; the average rating is 2.79/10. The site's consensus reads, "Wildly erratic even for a spoof movie, "Fifty Shades of Black" bears the unfortunate distinction of offering fewer laughs than the unintentionally funny film it's trying to lampoon." On Metacritic, the film has a score of 28 out of 100 based on 11 critics, indicating "generally unfavorable reviews". Audiences polled by CinemaScore gave the film an average grade of "C" on an A+ to F scale.


title: Fifty Shades of Black

text: Critic Mark Kermode dismissed "Fifty Shades of Black" as another lame parody film, among the likes of "Scary Movie" (2000), "Epic Movie" (2007) and "Vampires Suck" (2010). Austin film critic Korey Coleman ended his review by starting an online petition to stop Marlon Wayans from making any more parody films. He gave it the #1 spot for the worst movie of 2016, tying it with "Yoga Hosers".


title: Fifty Shades of Black

text: Kermode was critical of the humor: "Cue jokes about wallet and car theft, fried chicken and Bill Cosby, alongside glasshouse/brick complaints about EL James being a rubbish writer. When it all runs out of steam, the cock-and-ball routines downshift into riffs from "Whiplash" and "Magic Mike", but sadly, these aren’t funny either." J.R. Jones condemned the jokes as a set of "amplified racial stereotypes and misogynistic swipes", citing the running gag of male characters calling Hawk's character "ugly", as well as the rape jokes, as examples. Henry Barnes claimed there is a "Cosby joke, a Kanye joke and huge spaces where the laughs should be", particularly arguing that the "abuse is amplified out of the realm of satire into a weird hinterland of really unfunny gross-out and blaxploitation revenge flick".


title: Fifty Shades of Black

text: Jones did, however, highlight the "impressive attention to detail, meticulously re-creating the original film's costumes and sets, and Kali Hawk nails her Dakota Johnson impression as the virginal protagonist".


title: Fixed effects model

text: In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models and mixed models in which all or some of the model parameters are random variables. In many applications including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population. Generally, data can be grouped according to several observed factors. The group means could be modeled as fixed or random effects for each grouping. In a fixed effects model each group mean is a group-specific fixed quantity.


title: Fixed effects model

text: In panel data where longitudinal observations exist for the same subject, fixed effects represent the subject-specific means. In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression model including those fixed effects (one time-invariant intercept for each subject).


title: Fixed effects model

text: Such models assist in controlling for omitted variable bias due to unobserved heterogeneity when this heterogeneity is constant over time. This heterogeneity can be removed from the data through differencing, for example by subtracting the group-level average over time, or by taking a first difference which will remove any time invariant components of the model.


title: Fixed effects model

text: There are two common assumptions made about the individual specific effect: the random effects assumption and the fixed effects assumption. The random effects assumption is that the individual-specific effects are uncorrelated with the independent variables. The fixed effect assumption is that the individual-specific effects are correlated with the independent variables. If the random effects assumption holds, the random effects estimator is more efficient than the fixed effects estimator. However, if this assumption does not hold, the random effects estimator is not consistent. The Durbin–Wu–Hausman test is often used to discriminate between the fixed and the random effects models.


title: Fixed effects model

text: Unlike the random effects model where the unobserved formula_13 is independent of formula_9 for all formula_19, the fixed effects (FE) model allows formula_13 to be correlated with the regressor matrix formula_9. Strict exogeneity with respect to the idiosyncratic error term formula_14 is still required.


title: Fixed effects model

text: Since formula_13 is not observable, it cannot be directly controlled for. The FE model eliminates formula_13 by de-meaning the variables using the "within" transformation:


title: Fixed effects model

text: Since formula_13 is constant, formula_30 and hence the effect is eliminated. The FE estimator formula_31 is then obtained by an OLS regression of formula_32 on formula_33.


title: Fixed effects model

text: One is to add a dummy variable for each individual formula_34 (omitting the first individual because of multicollinearity). This is numerically, but not computationally, equivalent to the fixed effect model and only works if the sum of the number of series and the number of global parameters is smaller than the number of observations. The dummy variable approach is particularly demanding with respect to computer memory usage and it is not recommended for problems larger than the available RAM, and the applied program compilation, can accommodate.


title: Fixed effects model

text: Second alternative is to use consecutive reiterations approach to local and global estimations. This approach is very suitable for low memory systems on which it is much more computationally efficient than the dummy variable approach.


title: Fixed effects model

text: The third approach is a nested estimation whereby the local estimation for individual series is programmed in as a part of the model definition. This approach is the most computationally and memory efficient, but it requires proficient programming skills and access to the model programming code; although, it can be programmed even in SAS.


title: Fixed effects model

text: Finally, each of the above alternatives can be improved if the series-specific estimation is linear (within a nonlinear model), in which case the direct linear solution for individual series can be programmed in as part of the nonlinear model definition.


title: Fixed effects model

text: An alternative to the within transformation is the "first difference" transformation, which produces a different estimator. For formula_35:


title: Fixed effects model

text: When formula_40, the first difference and fixed effects estimators are numerically equivalent. For formula_41, they are not. If the error terms formula_14 are homoskedastic with no serial correlation, the fixed effects estimator is more efficient than the first difference estimator. If formula_14 follows a random walk, however, the first difference estimator is more efficient.


title: Fixed effects model

text: For the special two period case (formula_40), the fixed effects (FE) estimator and the first difference (FD) estimator are numerically equivalent. This is because the FE estimator effectively "doubles the data set" used in the FD estimator. To see this, establish that the fixed effects estimator is:


title: Fixed effects model

text: Gary Chamberlain's method, a generalization of the within estimator, replaces formula_13 with its linear projection onto the explanatory variables. Writing the linear projection as:


title: Fixed effects model

text: Partition the formula_55 and formula_56 variables such that formula_62 where formula_63 and formula_64 are uncorrelated with formula_13. Need formula_66.


title: Fixed effects model

text: Estimating formula_67 via OLS on formula_68 using formula_69 and formula_70 as instruments yields a consistent estimate.


title: Fixed effects model

text: When there is input uncertainty for the formula_71 data, formula_72, then the formula_73 value, rather than the sum of squared residuals, should be minimized. This can be directly achieved from substitution rules:


title: Fixed effects model

text: then the values and standard deviations for formula_75 and formula_76 can be determined via classical ordinary least squares analysis and variance-covariance matrix.


title: Fixed effects model

text: Random effects estimators may be inconsistent sometimes in the long time series limit, if the random effects are misspecified (i.e. the model chosen for the random effects is incorrect). However, the fixed effects model may still be consistent in some situations. For example, if the time series being modeled is not stationary, random effects models assuming stationarity may not be consistent in the long-series limit. One example of this is if the time series has an upward trend. Then, as the series becomes longer, the model revises estimates for the mean of earlier periods upwards, giving increasingly biased predictions of coefficients. However, a model with fixed time effects does not pool information across time, and as a result earlier estimates will not be affected.


title: Fixed effects model

text: In situations like these where the fixed effects model is known to be consistent, the Durbin-Wu-Hausman test can be used to test whether the random effects model chosen is consistent. If formula_77 is true, both formula_78 and formula_79 are consistent, but only formula_78 is efficient. If formula_81 is true the consistency of formula_78 cannot be guaranteed.


title: Ben (Michael Jackson album)

text: Ben is the second studio album by American singer Michael Jackson, released by Motown Records on August 4, 1972, while Jackson was still a member of The Jackson 5. The album received mixed reviews from contemporary music critics. "Ben", however, was more successful on the music charts than Jackson's previous studio album, peaking within the top 10 on the "Billboard" 200 in the United States. Internationally, the album was less successful, peaking at number 12 in Canada, while charting within the top 200 positions in Australia and France.


title: Ben (Michael Jackson album)

text: The album released one single, the title track "Ben", which was a commercial success on the music charts, topping both the US "Billboard" Hot 100 and the Australian ARIA charts, giving Jackson his first number-one single domestically and internationally. "Ben" also charted within the top 10 in other territories worldwide. "Everybody's Somebody's Fool" was planned to be released as the second single from the album, but was cancelled for unspecified reasons. Two of the album's songs were "stripped" in 2009 as part of the three-disc compilation "".


title: Ben (Michael Jackson album)

text: In January 1972, while still a member of The Jackson 5, Jackson released his first studio album, entitled "Got to Be There", under Motown Records. The album received generally mixed reviews from contemporary music critics, but was commercially successful worldwide. The album's three singles had a good chart performance on the "Billboard" Hot 100, with all charting within the top 20 positions on the chart, two peaking within the top 5. "Got to Be There" was more successful in the U.S. than internationally, peaking at number 14 on the "Billboard" 200 while peaking at number 37 in the U.K. and number 121 in France.


title: Ben (Michael Jackson album)

text: Recording sessions for "Ben" began in November 1971, concluding by February 1972 before Jackson's voice began to deepen. It was produced by six people, and executive-produced by Berry Gordy. Songwriters for the 10 tracks of "Ben" include Mel Larson, Jerry Marcellino, Thom Bell, Linda Creed, The Corporation, Smokey Robinson, and Ronald White, among others. The album's songs have a tempo ranging from 69 beats per minute on "Ben", to 130 on "Shoo-Be-Doo-Be-Doo-Da-Day".


title: Ben (Michael Jackson album)

text: The album's title track, the theme song for the 1972 film of the same name (itself the sequel to the 1971 killer rat film "Willard"), won a Golden Globe and was nominated for an Academy Award for Best Song, losing to "The Morning After" by Maureen McGovern from another 1972 film, "The Poseidon Adventure". "What Goes Around Comes Around" has similarities to Jackson's older brother Jackie's single, "Didn't I (Blow Your Mind This Time)", which featured vocals from Jackson and his older brothers. For "Ben", Jackson recorded a cover of The Temptations' 1964 single, "My Girl", a cover of The Stylistics' 1971 hit "People Make The World Go Round", a cover of Lionel Hampton's "Everybody's Somebody's Fool", a cover of Brenda Holloway's 1965 single, "You Can Cry on My Shoulder" and a cover of Stevie Wonder's 1968 single, "Shoo-Be-Doo-Be-Doo-Da-Day". "My Girl" has a funk rhythm and the song's score includes some call-and-response interaction, which is similar to what Jackson and his brothers displayed in their Jackson 5 material. In 1966, The Jackson 5 won a talent show at Gary's Theodore Roosevelt High School, where they performed "My Girl". "You Can Cry on My Shoulder" is a mid-tempo song. "We've Got a Good Thing Going" was previously issued as the B-side to "Got to Be There"s "I Wanna Be Where You Are" and "In Our Small Way" was also featured on Jackson's previous album "Got to Be There".