title: John Tesh

text: Tesh is a Christian. He was raised a Baptist and was involved in the church during his youth. He played organ, sang in the choir, and went to church camp. He became inactive in the church during his adult life, but became involved again after his future wife introduced him to pastor Louis Lapides. Since then, he has written and performed Christian music.


title: John Tesh

text: In 2018 John Tesh was inducted into the North Carolina Music Hall of Fame. In 2019 he was inducted into the National Radio Hall of Fame. In 2007, Tesh won the Syndicated Personality/Show of the Year award by "Radio & Records" magazine for his radio show. Other finalists included Delilah, Blair Garner, Steve Harvey, Kidd Kraddick, and "The Lia Show". Tesh was nominated in 2003 for the Grammy for "Best Pop Instrumental Album" for "Power of Love". John has also earned three gold albums, six Emmys for his sports themes, and a Keyboard Magazine Award.


title: Public sector

text: The public sector, also called the state sector, is the part of the economy composed of both public services and public enterprises. Public sectors include the public goods and governmental services such as the military, law enforcement, infrastructure, public transit, public education, along with health care and those working for the government itself, such as elected officials. The public sector might provide services that a non-payer cannot be excluded from (such as street lighting), services which benefit all of society rather than just the individual who uses the service. Public enterprises, or state-owned enterprises, are self-financing commercial enterprises that are under public ownership which provide various private goods and services for sale and usually operate on a commercial basis.


title: Public sector

text: Organizations that are not part of the public sector are either part of the private sector or voluntary sector. The private sector is composed of the economic sectors that are intended to earn a profit for the owners of the enterprise. The voluntary, civic, or social sector concerns a diverse array of non-profit organizations emphasizing civil society. In the United Kingdom, the term "wider public sector" is often used, referring to public sector organisations outside central government.


title: Public sector

text: "Infrastructure" includes areas that support both the public's members and the public sector itself. Streets and highways are used both by those who work for the public sector and also by the citizenry. The former, who are public employees, are also part of the citizenry.


title: Public sector

text: Public roads, bridges, tunnels, water supply, sewers, electrical grids and telecommunication networks are among the public infrastructure.


title: Public sector

text: Right-libertarian and Austrian School economists have criticized the idea of public sector provision of goods and services as inherently inefficient. In 1961, Murray Rothbard wrote: "Any reduction of the public sector, any shift of activities from the public to the private sphere, is a net moral and economic gain."


title: Public sector

text: American libertarians and anarcho-capitalists have also argued that the system by which the public sector is funded, namely taxation, is itself coercive and unjust. However, even notable small-government proponents have pushed back on this point of view, citing the ultimate necessity of a public sector for provision of certain services, such as national defense, public works and utilities, and pollution controls.


title: Gabriel Agbonlahor

text: Gabriel Imuetinyan Agbonlahor (born 13 October 1986) is an English former professional footballer who played as a forward; he mostly played as a central striker, but he was also capable of playing on the wing. He spent his entire professional career with Aston Villa in the Premier League and later the Championship, with loans at Watford and Sheffield Wednesday at the start of his career.


title: Gabriel Agbonlahor

text: He is a product of Aston Villa's Academy, and made his first-team debut in 2006 following loans to Football League clubs Watford and Sheffield Wednesday. He made 391 total appearances for Aston Villa, including 322 in the Premier League. He scored 87 goals for the club, and is their all-time leading Premier League goalscorer, with 74 across 11 consecutive league seasons. Formerly a regular with the England under-21s, Agbonlahor made his senior international debut for England in 2008 and earned three caps.


title: Gabriel Agbonlahor

text: Before being scouted by Aston Villa, Agbonlahor was playing for Great Barr Falcons and his district. It was at a district game where he was scouted by Aston Villa. During this time he had also been scouted by Wolverhampton Wanderers and played a few games for them, but chose to join his boyhood football team Aston Villa. Agbonlahor came through the youth ranks at local club Aston Villa. He signed a two-year professional contract at the club in June 2005. On 22 September 2005, he was loaned to Championship club Watford, where he made his senior debut six days later, replacing Trevor Benjamin at half time in a 3–1 defeat away to Coventry City. He made his first start in his only other match for Watford, a goalless draw against Leeds United at Vicarage Road on 1 October, in which he made way for Francino Francis after 65 minutes. Agbonlahor was loaned to another team from the division on 28 October, Sheffield Wednesday, where he made eight appearances without scoring.


title: Gabriel Agbonlahor

text: Agbonlahor's Premier League debut for Villa came on 18 March 2006 at the age of 19, under manager David O'Leary, against Everton at Goodison Park. O'Leary was forced to delve into the youth academy because of a lack of senior strikers due to injury, thus earning Agbonlahor a rare start. He scored after 63 minutes, although Villa went on to lose the match 4–1.


title: Gabriel Agbonlahor

text: In five pre-season matches of the 2006–07 season, Agbonlahor netted three goals for Aston Villa; a quick double salvo against Walsall (the first a near-post header, the latter a close range finish) in a 5–0 victory, and a consolation strike in a 2–1 defeat at NEC. Agbonlahor started the season on the right wing in Martin O'Neill's new-look Villa team, and would be part of the team that managed to get a point from the first Premier League match at Arsenal's new Emirates Stadium. Agbonlahor's first goal of the season came at home against Charlton Athletic in a 2–0 win. On 30 September, Agbonlahor scored a crucial equaliser against Premiership champions Chelsea just before half-time, heading in Liam Ridgewell's cross with a glancing header to earn Villa a 1–1 draw.


title: Gabriel Agbonlahor

text: Agbonlahor also provided cup heroics in 2006, scoring an injury-time winner to beat Leicester City 3–2 at the Walkers Stadium. The following match, he scored a consolation effort in Villa's first loss of the season, on 28 October, ten matches in. Agbonlahor completed his run of scoring against the so-called "Big Four", when he scored against Manchester United. Aston Villa were beaten 3–1 in the match at Old Trafford. Agbonlahor then scored deep into injury time in the following match, against Watford on 20 January 2007, to end a Villa winless run that stretched back to 11 November.


title: Gabriel Agbonlahor

text: Agbonlahor had played every minute of Aston Villa's campaign in 2006–07, until he was replaced by Patrik Berger in the 2–0 away fixture against Reading on 10 February 2007. The following match was the first of the season that Agbonlahor did not start—he instead appeared from the bench, replacing new Villa signing Shaun Maloney. Manager Martin O'Neill suggested that Agbonlahor, who had been playing out of position on the right wing for much of the season, had done superbly, and being dropped from the first 11 was in order to rest him, and alleviate growing crowd pressure. Following this break, Agbonlahor went on a scoring spree. He scored from the right-wing against Everton on 2 April to gain Villa a valuable point. Following this match, Agbonlahor signed a new-four-year contract at Villa. The following Saturday, in the absence of John Carew, he was moved back to his natural position at centre forward and again found his name on the scoresheet. Agbonlahor made it three in a row on Easter Monday, again scoring an equaliser, adjudged to have crossed the line by assistant referee Dave Richardson.


title: Gabriel Agbonlahor

text: Agbonlahor also scored the vital second goal in the match between Aston Villa and Chelsea on 2 September, in which Villa won 2–0. Agbonlahor headed the winning goal in the 86th minute of the Second City derby away to Birmingham on 11 November, shortly after saving the ball on the line from a Liam Ridgewell shot. Agbonlahor won the Premier League Player of the Month award for November and manager Martin O'Neill won the equivalent award for the same month. On 12 April 2008, Agbonlahor scored the fourth goal against Derby County in a 6–0 victory at Pride Park Stadium in the Premier League. In the Second City derby against Birmingham City on 20 April 2008, he scored the fifth and final goal in the 5–1 victory.


title: Gabriel Agbonlahor

text: On 15 August 2008, Agbonlahor signed a new four-year contract with Villa, tying him to the club until 2012. Following his contract extension, on 17 August 2008, Agbonlahor scored a "perfect" hat-trick (scoring goals with his head, right foot and left foot) against Manchester City in Villa's opening match of the 2008–09 Premier League season at Villa Park. The three goals were netted in the space of seven minutes, making it the third-fastest hat-trick in the history of the Premier League after Robbie Fowler and Sadio Mané. He was later named man of the match for this performance, which led to a 4–2 victory.


title: Gabriel Agbonlahor

text: Early in the season, he began to form a successful strike partnership with teammate John Carew, this demonstrated in the Premier League away matches against West Bromwich Albion and Wigan Athletic where both players scored in both matches and provided assists. On 3 November 2008, Agbonlahor was at the centre of a controversy with Newcastle United's Joey Barton when, during the match, Barton appeared to brush his fingers on Agbonlahor's face. It later emerged that Barton's attack might have been race-orientated but, after careful consideration by both Aston Villa and The Football Association, no further action was taken. On 8 November, it emerged in some national newspapers that the reason Agbonlahor decided not to pursue legal action against Barton was because he "felt sorry" for him. On 15 November, he scored once and played a part in the other goal, when Aston Villa beat Arsenal 2–0 at Emirates Stadium. He scored a brace against Bolton Wanderers on 13 December. Agbonlahor notched his tenth league goal of the season in the 90th minute in a 2–0 win against Blackburn Rovers on 7 February.


title: Gabriel Agbonlahor

text: However, this was a high point in a dismal run of form in which he scored just one goal in 12 league matches. Some fans began to get frustrated with Agbonlahor, and in Villa's home defeat against Tottenham Hotspur, there were some sarcastic cheers as he was substituted off by Martin O'Neill. He was subsequently dropped to the bench for Villa's next match away to Liverpool, which Villa lost 5–0. After the heavy defeat to Liverpool and despite his lack of form, Agbonlahor was recalled to the starting 11 and went on to score a goal against Manchester United on 5 April in a 3–2 defeat for Villa. Agbonlahor was nominated for the PFA Young Player of the Year, with teammate ultimately Ashley Young winning the honour.


title: Gabriel Agbonlahor

text: Agbonlahor's first goal of the 2009–10 season came in a 2–0 home victory over Fulham on 30 August 2009, scoring from 25 yards. The striker scored the only goal in the season's opening Birmingham derby against Birmingham City, netting an open header past Joe Hart as a result of a free kick taken by Ashley Young. Agbonlahor scored his third goal of the season scoring in a 2–0 win against Portsmouth. He scored his fourth and fifth consecutive goals of the season against Cardiff City in the League Cup and Blackburn in the Premier League. His next goal came on 24 October 2009 against Wolverhampton Wanderers at Molineux in the Premier League. Fellow Villa forward Emile Heskey played the ball into the penalty area where Agbonlahor turned a defender and placed a low shot past Wolves goalkeeper Wayne Hennessey. The match finished 1–1.


title: Gabriel Agbonlahor

text: He scored the only goal in the 1–0 win against Manchester United at Old Trafford, heading in a cross from Ashley Young after 21 minutes, providing Villa's first league win at Old Trafford since 1983. Agbonlahor also scored in the second leg of the League Cup semi-final against Blackburn, helping Villa to get to the final where they lost to Manchester United, 2–1. He scored twice in 2–0 win at Fulham on 30 January 2010. On 21 February 2010, Agbonlahor provided an assist for Emile Heskey before adding Villa's final goal in a 5–2 victory over Burnley for his 11th league goal of the season. Agbonlahor finished the season with 13 goals in the Premier League, and 16 in all competitions.


title: Gabriel Agbonlahor

text: Despite Villa suffering some issues on and off the field at the beginning of the season, such as the resignation of manager Martin O'Neill and a humiliating 6–0 defeat at the hands of Newcastle United, Agbonlahor defended the club and stated his intent to remain there for the long term. Agbonlahor signed a new four-and-a-half-year contract on 12 November 2010, keeping him at Villa Park until at least 2015. On 16 January 2011, he made his 200th appearance in an Aston Villa shirt in a 1–1 draw with rivals Birmingham, playing the full 90 minutes at St Andrew's. Agbonlahor scored his first goal in the Premier League since April 2010 in the 2–1 victory over Wigan Athletic on 26 January 2011 at the DW Stadium. On 16 April 2011, he scored an injury-time winner away at West Ham United. Agbonlahor was less prolific in terms of goalscoring during 2010–11 due to Aston Villa manager Gérard Houllier preferring to use him as a winger.


title: Gabriel Agbonlahor

text: Agbonlahor scored his first goal of the 2011–12 season in Aston Villa's 3–1 home win over Blackburn Rovers on 20 August 2011, and followed this up with the leveller in a 2–2 away draw against Everton ten days later. For his positive performances during the opening month of the season, Agbonlahor was named as Aston Villa's Player of the Month for August 2011, beating off competition from Fabian Delph to the top spot. He then made it three goals in three matches when he scored in a 1–1 home draw against Newcastle on 17 September. This meant that Agbonlahor had equalled his Premier League goals tally from the 2010–11 season after just five matches into the new season.


title: Gabriel Agbonlahor

text: After rediscovering his goalscoring form under new boss Alex McLeish, the striker publicly spoke of his discontent at the managerial tenure of Gérard Houllier and his assistant Gary McAllister and said that he even considered quitting the club had the previous regime remained. Meanwhile, on the pitch Agbonlahor continued to impress, scoring the first goal and setting up Darren Bent for the second in a man of the match performance against Wigan on 1 October. He then put in another man of the match performance against Norwich City in a 3–2 win on 5 November, setting up both of Darren Bent's goals and scoring the second himself. On 7 January 2012, he scored the second goal in a 3–1 win against Bristol Rovers in the third round of the FA Cup after Marc Albrighton had given Villa the lead. On 3 April 2012, after Aston Villa captain Stiliyan Petrov's diagnosis with acute leukaemia, Agbonlahor was named team captain upon Petrov's diagnosis.


title: Gabriel Agbonlahor

text: Following the sacking of Alex McLeish in the summer of 2012, Agbonlahor was not chosen as interim captain by McLeish's successor, Paul Lambert. The Scotsman opted firstly for Darren Bent as skipper, before ultimately choosing new signing Ron Vlaar to wear the captain's armband in the absence of Stiliyan Petrov. Agbonlahor began the season injured, and could not make an appearance until the 1–1 away draw with Newcastle United on 2 September 2012. He later returned to full fitness and started the away match at Manchester City on 25 September. Agbonlahor managed to score two goals in the match as Villa secured a memorable 4–2 League Cup win (after extra time) over the Premier League champions at the City of Manchester Stadium. On 3 November 2012, he scored his first Premier League goal in just under a year against Sunderland in a run stretching 29 matches. On 6 April 2013, Agbonlahor scored his 60th Premier League goal for Aston Villa, making him joint top Premier League goalscorer for the club alongside Dwight Yorke. On 29 April, in a 6–1 win over Sunderland, Agbonlahor scored his 61st Premier League goal to overtake Yorke as Villa's highest all-time Premier League goal scorer. He scored two goals in a 2–1 win over Norwich on 4 May, moving Aston Villa up to 13th place in the Premier League.


title: Gabriel Agbonlahor

text: Agbonlahor began the season brightly, winning two penalties in a 3–1 away win over Arsenal on 17 August 2013 and assisting Christian Benteke's goal against Chelsea four days later in a controversial 2–1 defeat at Stamford Bridge. This resulted in strong praise from manager Paul Lambert, and a huge demand from the public for an England call up, which was ignored by Roy Hodgson. In September, Agbonlahor participated in a charity match organised by Stiliyan Petrov, which featured many celebrities and footballers, both former and current. During the match, Agbonlahor tackled and injured One Direction member Louis Tomlinson, who then became ill after being substituted. Despite apologising to Tomlinson, Agbonlahor received many threats after the match from One Direction fans via Twitter.


title: Gabriel Agbonlahor

text: On 10 September 2014, Agbonlahor signed a new four-year contract, saying, "I can still remember making my debut, so to still be able to contribute is a great feeling." Three days later, he scored the only goal as Villa won away at Liverpool, a club he had only scored once against before in the Premier League. Agbonlahor was given a straight red card on 20 December for a challenge on former teammate Ashley Young as Villa drew 1–1 with Manchester United, however his three-match suspension was rescinded on appeal three days later.


title: Gabriel Agbonlahor

text: Agbonlahor made his 300th Premier League appearance for Villa on 14 March 2015 away to Sunderland, scoring twice in the first half in a 4–0 win. On 30 May in the FA Cup Final against Arsenal at Wembley Stadium, manager Tim Sherwood chose to start Charles N'Zogbia instead of Agbonlahor, and then brought him on in place of the Frenchman after 53 minutes, with Villa already 2–0 down; they eventually lost 4–0.


title: Gabriel Agbonlahor

text: Agbonlahor was named club captain at the start of the 2015–16 season, with new signing Micah Richards named team captain. Soon after manager Rémi Garde joined, Agbonlahor was dropped from the starting line-up. During the January transfer window, there was speculation surrounding Agbonlahor and his future at the club; however, though Turkish club Kayserispor were linked, Garde later revealed that no offers had been made for him. Agbonlahor returned to the squad in an FA Cup tie against Manchester City on 30 January 2015, and scored his first goal of the season a week later in a Premier League match in a 2–0 home victory against Norwich. This was his first goal in 11 months.


title: Gabriel Agbonlahor

text: On 1 April 2016, Aston Villa suspended Agbonlahor, pending an investigation into reports that he was pictured appearing to hold a shisha pipe while on holiday in Dubai. On 19 April 2016, he was again suspended after he was allegedly pictured with laughing gas canisters. He was punished with a substantial fine and resigned the captaincy. Agbonlahor failed to impress new manager Roberto Di Matteo in pre-season, and his lack of involvement led to media speculation of a move away from the club. Despite interest from Reading, he turned them down and a move failed to materialise.


title: Gabriel Agbonlahor

text: When manager Steve Bruce arrived, he immediately reinstated Agbonlahor into first-team training, saying that he's "not interested in what has happened in the past" and that it's a "clean slate" for him. Bruce subsequently put him on a six-week fitness regime in a bid to get him fit for the rest of the season. Agbonlahor came on as a substitute in the Second City derby on 23 April 2017 and scored his only goal of the season in a 1–0 win.


title: Gabriel Agbonlahor

text: Agbonlahor made six appearances for Villa during 2017–18 and scored a single goal, during the first game of the season against Hull City. His final game for the club came against Sheffield United on 23 December 2017. He left the club at the end of the season after his contract was not renewed, ending a 17-year association with his hometown club. During his career at Villa, he has scored 86 times in 391 appearances and is the club's record Premier League scorer with 73 goals. He retired from playing on 27 March 2019 at the age of 32.


title: Gabriel Agbonlahor

text: Agbonlahor's ancestry qualified him to play for Scotland or Nigeria at international level, but he chose to play for his homeland of England.


title: Gabriel Agbonlahor

text: On 20 September 2006, Agbonlahor was pencilled in as a player in the Nigeria under-20 team for the match against Rwanda. He turned down the call, whilst not ruling out playing for the country in the future, but subsequently pledged his future to England.


title: Gabriel Agbonlahor

text: On 28 September 2006, Agbonlahor received his first call-up to the England under-21 team, and won his first cap as a substitute for Wayne Routledge against Germany on 6 October. Four days later he started in place of Routledge against the same opponents. Agbonlahor was then omitted from the England's 2007 UEFA European Under-21 Championship squad, by manager Stuart Pearce, as a result of missing the England U21 training camp in Spain.


title: Gabriel Agbonlahor

text: Agbonlahor was later recalled to the team by Pearce, in September 2007, netting his first goal for the under-21s, the second of a 3–0 victory over Montenegro.


title: Gabriel Agbonlahor

text: On 7 March 2007, Agbonlahor one of several surprise names called up as part of a 37-man provisional Nigeria squad by new manager Berti Vogts, alongside fellow English players Victor Anichebe and Carl Ikeme, and full Israel international Toto Tamuz.


title: Gabriel Agbonlahor

text: On 1 February 2008, Agbonlahor was named in Fabio Capello's 23-man England squad to play Switzerland later in the month, although a hamstring injury forced him to withdraw from the match. Agbonlahor was also an unused substitute in England's respective 2–0 and 3–0 friendly victories against the United States and Trinidad & Tobago in May–June 2008.


title: Gabriel Agbonlahor

text: On 15 November 2008, he was called up to Capello's squad for the upcoming match away to Germany, joining three other Aston Villa players in the squad: Ashley Young, Curtis Davies and Gareth Barry. On 19 November 2008, he was named to start against Germany. He played for 76 minutes, had a goal disallowed and received high praise from John Terry, the latter describing him as "a nightmare to play against".


title: Gabriel Agbonlahor

text: On 11 February 2009, he was in the starting line up against Spain, where he played for 75 minutes before being substituted for debutant Carlton Cole. He made his first appearance in a competitive international on 14 October 2009, playing 66 minutes in the 3–0 win over Belarus in the last match of qualification for the 2010 World Cup. He was last called up to the squad in November 2011.


title: Gabriel Agbonlahor

text: Agbonlahor was born in Birmingham, West Midlands. His parents separated while he was still young and he lived with his father, without any contact with his mother, for around 20 years. In 2009, ahead of the striker's 23rd birthday, his mother made a public appeal to him via the city's "Sunday Mercury" newspaper in order to become part of his life once more. Agbonlahor later contacted his mother and the pair reconciled. Following retirement, he has worked as a pundit for both Sky Sports and Talksport and written columns for online magazines such as Football Insider.


title: Z-transform

text: In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representation.


title: Z-transform

text: It can be considered as a discrete-time equivalent of the Laplace transform (s-domain). This similarity is explored in the theory of time-scale calculus.


title: Z-transform

text: Whereas the continuous-time Fourier transform is evaluated on the Laplace s-domain's imaginary line, the discrete-time Fourier transform is evaluated over the unit circle of the z-domain. What is roughly the s-domain's left half-plane, is now the inside of the complex unit circle; what is the z-domain's outside of the unit circle, roughly corresponds to the right half-plane of the s-domain.


title: Z-transform

text: One of the means of designing digital filters is to take analog designs, subject them to a bilinear transform which maps them from the s-domain to the z-domain, and then produce the digital filter by inspection, manipulation, or numerical approximation. Such methods tend not to be accurate except in the vicinity of the complex unity, i.e. at low frequencies.


title: Z-transform

text: The basic idea now known as the Z-transform was known to Laplace, and it was re-introduced in 1947 by W. Hurewicz and others as a way to treat sampled-data control systems used with radar. It gives a tractable way to solve linear, constant-coefficient difference equations. It was later dubbed "the z-transform" by Ragazzini and Zadeh in the sampled-data control group at Columbia University in 1952.


title: Z-transform

text: The idea contained within the Z-transform is also known in mathematical literature as the method of generating functions which can be traced back as early as 1730 when it was introduced by de Moivre in conjunction with probability theory.


title: Z-transform

text: From a mathematical view the Z-transform can also be viewed as a Laurent series where one views the sequence of numbers under consideration as the (Laurent) expansion of an analytic function.


title: Z-transform

text: The Z-transform can be defined as either a "one-sided" or "two-sided" transform. (Just like we have the one-sided Laplace transform and the two-sided Laplace transform.)


title: Z-transform

text: The "bilateral" or "two-sided" Z-transform of a discrete-time signal formula_1 is the formal power series formula_2 defined as


title: Z-transform

text: where formula_6 is the magnitude of formula_4, formula_8 is the imaginary unit, and formula_9 is the "complex argument" (also referred to as "angle" or "phase") in radians.


title: Z-transform

text: Alternatively, in cases where formula_1 is defined only for formula_11, the "single-sided" or "unilateral" Z-transform is defined as


title: Z-transform

text: In signal processing, this definition can be used to evaluate the Z-transform of the unit impulse response of a discrete-time causal system.


title: Z-transform

text: An important example of the unilateral Z-transform is the probability-generating function, where the component formula_1 is the probability that a discrete random variable takes the value formula_3, and the function formula_2 is usually written as formula_15 in terms of formula_16. The properties of Z-transforms (below) have useful interpretations in the context of probability theory.


title: Z-transform

text: where "C" is a counterclockwise closed path encircling the origin and entirely in the region of convergence (ROC). In the case where the ROC is causal (see Example 2), this means the path "C" must encircle all of the poles of formula_2.


title: Z-transform

text: A special case of this contour integral occurs when "C" is the unit circle. This contour can be used when the ROC includes the unit circle, which is always guaranteed when formula_2 is stable, that is, when all the poles are inside the unit circle. With this contour, the inverse Z-transform simplifies to the inverse discrete-time Fourier transform, or Fourier series, of the periodic values of the Z-transform around the unit circle:


title: Z-transform

text: The Z-transform with a finite range of "n" and a finite number of uniformly spaced "z" values can be computed efficiently via Bluestein's FFT algorithm. The discrete-time Fourier transform (DTFT)—not to be confused with the discrete Fourier transform (DFT)—is a special case of such a Z-transform obtained by restricting "z" to lie on the unit circle.


title: Z-transform

text: The region of convergence (ROC) is the set of points in the complex plane for which the Z-transform summation converges.


title: Z-transform

text: Let formula_23 (where "u" is the Heaviside step function). Expanding "x"["n"] on the interval (−∞, ∞) it becomes


title: Z-transform

text: The last equality arises from the infinite geometric series and the equality only holds if |0.5"z"| < 1 which can be rewritten in terms of "z" as |"z"| > 0.5. Thus, the ROC is |"z"| > 0.5. In this case the ROC is the complex plane with a disc of radius 0.5 at the origin "punched out".


title: Z-transform

text: Let formula_26 (where "u" is the Heaviside step function). Expanding "x"["n"] on the interval (−∞, ∞) it becomes


title: Z-transform

text: Using the infinite geometric series, again, the equality only holds if |0.5"z"| < 1 which can be rewritten in terms of "z" as |"z"| < 0.5. Thus, the ROC is |"z"| < 0.5. In this case the ROC is a disc centered at the origin and of radius 0.5.


title: Z-transform

text: What differentiates this example from the previous example is "only" the ROC. This is intentional to demonstrate that the transform result alone is insufficient.


title: Z-transform

text: Examples 2 & 3 clearly show that the Z-transform "X(z)" of "x[n]" is unique when and only when specifying the ROC. Creating the pole–zero plot for the causal and anticausal case show that the ROC for either case does not include the pole that is at 0.5. This extends to cases with multiple poles: the ROC will "never" contain poles.


title: Z-transform

text: In example 2, the causal system yields an ROC that includes |"z"| = ∞ while the anticausal system in example 3 yields an ROC that includes |"z"| = 0.


title: Z-transform

text: In systems with multiple poles it is possible to have a ROC that includes neither |"z"| = ∞ nor |"z"| = 0. The ROC creates a circular band. For example,


title: Z-transform

text: has poles at 0.5 and 0.75. The ROC will be 0.5 < |"z"| < 0.75, which includes neither the origin nor infinity. Such a system is called a mixed-causality system as it contains a causal term (0.5)"u"["n"] and an anticausal term −(0.75)"u"[−"n"−1].


title: Z-transform

text: The stability of a system can also be determined by knowing the ROC alone. If the ROC contains the unit circle (i.e., |"z"| = 1) then the system is stable. In the above systems the causal system (Example 2) is stable because |"z"| > 0.5 contains the unit circle.


title: Z-transform

text: Let us assume we are provided a Z-transform of a system without a ROC (i.e., an ambiguous "x"["n"]). We can determine a unique "x"["n"] provided we desire the following:


title: Z-transform

text: For stability the ROC must contain the unit circle. If we need a causal system then the ROC must contain infinity and the system function will be a right-sided sequence. If we need an anticausal system then the ROC must contain the origin and the system function will be a left-sided sequence. If we need both stability and causality, all the poles of the system function must be inside the unit circle.


title: Z-transform

text: is the discrete-time unit impulse function (cf Dirac delta function which is a continuous-time version). The two functions are chosen together so that the unit step function is the accumulation (running total) of the unit impulse function.


title: Z-transform

text: For values of formula_4 in the region formula_36, known as the unit circle, we can express the transform as a function of a single, real variable, ω, by defining formula_37. And the bi-lateral transform reduces to a Fourier series:


title: Z-transform

text: which is also known as the discrete-time Fourier transform (DTFT) of the formula_1 sequence. This 2-periodic function is the periodic summation of a Fourier transform, which makes it a widely used analysis tool. To understand this, let formula_39 be the Fourier transform of any function, formula_40, whose samples at some interval, "T", equal the x["n"] sequence. Then the DTFT of the "x"["n"] sequence can be written as follows.


title: Z-transform

text: When "T" has units of seconds, formula_41 has units of hertz. Comparison of the two series reveals that  formula_42  is a normalized frequency with units of "radians per sample". The value "ω"=2 corresponds to formula_43.  And now, with the substitution  formula_44  can be expressed in terms of the Fourier transform, X(•):


title: Z-transform

text: As parameter T changes, the individual terms of move farther apart or closer together along the f-axis. In however, the centers remain 2 apart, while their widths expand or contract. When sequence "x"("nT") represents the impulse response of an LTI system, these functions are also known as its frequency response. When the formula_45 sequence is periodic, its DTFT is divergent at one or more harmonic frequencies, and zero at all other frequencies. This is often represented by the use of amplitude-variant Dirac delta functions at the harmonic frequencies. Due to periodicity, there are only a finite number of unique amplitudes, which are readily computed by the much simpler discrete Fourier transform (DFT).  (See .)


title: Z-transform

text: The bilinear transform can be used to convert continuous-time filters (represented in the Laplace domain) into discrete-time filters (represented in the Z-domain), and vice versa. The following substitution is used:


title: Z-transform

text: to convert some function formula_47 in the Laplace domain to a function formula_48 in the Z-domain (Tustin transformation), or


title: Z-transform

text: from the Z-domain to the Laplace domain. Through the bilinear transformation, the complex s-plane (of the Laplace transform) is mapped to the complex z-plane (of the z-transform). While this mapping is (necessarily) nonlinear, it is useful in that it maps the entire formula_50 axis of the s-plane onto the unit circle in the z-plane. As such, the Fourier transform (which is the Laplace transform evaluated on the formula_50 axis) becomes the discrete-time Fourier transform. This assumes that the Fourier transform exists; i.e., that the formula_50 axis is in the region of convergence of the Laplace transform.


title: Z-transform

text: Given a one-sided Z-transform, "X"("z"), of a time-sampled function, the corresponding starred transform produces a Laplace transform and restores the dependence on sampling parameter, "T":


title: Z-transform

text: The linear constant-coefficient difference (LCCD) equation is a representation for a linear system based on the autoregressive moving-average equation.


title: Z-transform

text: Both sides of the above equation can be divided by "α", if it is not zero, normalizing "α" = 1 and the LCCD equation can be written


title: Z-transform

text: This form of the LCCD equation is favorable to make it more explicit that the "current" output "y"["n"] is a function of past outputs "y"["n"−"p"], current input "x"["n"], and previous inputs "x"["n"−"q"].


title: Z-transform

text: From the fundamental theorem of algebra the numerator has "M" roots (corresponding to zeros of "H") and the denominator has N roots (corresponding to poles). Rewriting the transfer function in terms of zeros and poles


title: Z-transform

text: where "q" is the "k"-th zero and "p" is the "k"-th pole. The zeros and poles are commonly complex and when plotted on the complex plane (z-plane) it is called the pole–zero plot.


title: Z-transform

text: In addition, there may also exist zeros and poles at "z" = 0 and "z" = ∞. If we take these poles and zeros as well as multiple-order zeros and poles into consideration, the number of zeros and poles are always equal.


title: Z-transform

text: By factoring the denominator, partial fraction decomposition can be used, which can then be transformed back to the time domain. Doing so would result in the impulse response and the linear constant coefficient difference equation of the system.


title: Z-transform

text: If such a system "H"("z") is driven by a signal "X"("z") then the output is "Y"("z") = "H"("z")"X"("z"). By performing partial fraction decomposition on "Y"("z") and then taking the inverse Z-transform the output "y"["n"] can be found. In practice, it is often useful to fractionally decompose formula_59 before multiplying that quantity by "z" to generate a form of "Y"("z") which has terms with easily computable inverse Z-transforms.


title: Gladiolus

text: Gladiolus (from Latin, the diminutive of "gladius", a sword) is a genus of perennial cormous flowering plants in the iris family (Iridaceae).


title: Gladiolus

text: It is sometimes called the 'sword lily', but is usually called by its generic name (plural "gladioli").


title: Gladiolus

text: The genus occurs in Asia, Mediterranean Europe, South Africa, and tropical Africa. The center of diversity is in the Cape Floristic Region. The genera "Acidanthera", "Anomalesia", "Homoglossum", and "Oenostachys", formerly considered distinct, are now included in "Gladiolus".


title: Gladiolus

text: Gladioli grow from round, symmetrical corms (similar to crocuses) that are enveloped in several layers of brownish, fibrous tunics.


title: Gladiolus

text: Their stems are generally unbranched, producing 1 to 9 narrow, sword-shaped, longitudinal grooved leaves, enclosed in a sheath. The lowest leaf is shortened to a cataphyll. The leaf blades can be plane or cruciform in cross section.


title: Gladiolus

text: The flowers of unmodified wild species vary from very small to perhaps 40 mm across, and inflorescences bearing anything from one to several flowers. The spectacular giant flower spikes in commerce are the products of centuries of hybridisation and selection.


title: Gladiolus

text: The flower spikes are large and one-sided, with secund, bisexual flowers, each subtended by 2 leathery, green bracts. The sepals and the petals are almost identical in appearance, and are termed tepals. They are united at their base into a tube-shaped structure. The dorsal tepal is the largest, arching over the three stamens. The outer three tepals are narrower. The perianth is funnel-shaped, with the stamens attached to its base. The style has three filiform, spoon-shaped branches, each expanding towards the apex.


title: Gladiolus

text: The ovary is 3-locular with oblong or globose capsules, containing many, winged brown, longitudinally dehiscent seeds.


title: Gladiolus

text: These flowers are variously coloured, ranging from pink to reddish or light purple with white, contrasting markings, or white to cream or orange to red.


title: Gladiolus

text: The South African species were originally pollinated by long-tongued anthophorini bees, but some changes in the pollination system have occurred, allowing pollination by sunbirds, noctuid and Hawk-moths, long-tongued flies and several others. In the temperate zones of Europe many of the hybrid large flowering sorts of gladiolus can be pollinated by small well-known wasps. Actually, they are not very good pollinators because of the large flowers of the plants and the small size of the wasps. Another insect in this zone which can try some of the nectar of the gladioli is the best-known European Hawk-moth "Macroglossum stellatarum" which usually pollinates many popular garden flowers like "Petunia", "Zinnia", "Dianthus" and others.


title: Gladiolus

text: Gladioli are used as food plants by the larvae of some Lepidoptera species including the Large Yellow Underwing, and gladiolus thrips.


title: Gladiolus

text: Gladioli have been extensively hybridized and a wide range of ornamental flower colours are available from the many varieties. The main hybrid groups have been obtained by crossing between four or five species, followed by selection: 'Grandiflorus', 'Primulines' and 'Nanus'. They can make very good cut flowers for display.


title: Gladiolus

text: The majority of the species in this genus are diploid with 30 chromosomes (2n=30) but the Grandiflora hybrids are tetraploid and possess 60 chromosomes (2n=4x=60). This is because the main parental species of these hybrids is "Gladiolus dalenii" which is also tetraploid and includes a wide range of varieties (like the Grandiflora hybrids).


title: Gladiolus

text: The genus "Gladiolus" contains about 300 species, the World Checklist of Selected Plant Families had over 276 species in 1988, , it accepted 300 species.


title: Gladiolus

text: The genus "Gladiolus" has been divided into many sections. Most species, however, are only tentatively placed.


title: Gladiolus

text: In temperate zones, the corms of most species and hybrids should be lifted in autumn and stored over winter in a frost-free place, then replanted in spring. Some species from Europe and high altitudes in Africa, as well as the small 'Nanus' hybrids, are much hardier (to at least ) and can be left in the ground in regions with sufficiently dry winters. 'Nanus' is hardy to Zones 5–8. The large-flowered types require moisture during the growing season, and must be individually staked as soon as the sword-shaped flower heads appear. The leaves must be allowed to die down naturally before lifting and storing the corms. Plants are propagated either from small cormlets produced as offsets by the parent corms, or from seed. In either case, they take several years to get to flowering size. Clumps should be dug up and divided every few years to keep them vigorous.


title: Gladiolus

text: They are affected by thrips, (thrip simplex), and wasps "Dasyproctus bipunctatus", which burrow into the flowers causing them to collapse and die.


title: Gladiolus

text: Numerous garden cultivars have been developed, of which ‘Robinetta’ (a "G. recurvus" hybrid), with pink flowers, has gained the Royal Horticultural Society’s Award of Garden Merit.


title: Louvre Pyramid

text: The Louvre Pyramid (Pyramide du Louvre) is a large glass and metal structure designed by the Chinese-American architect I. M. Pei. The pyramid is in the main courtyard (Cour Napoléon) of the Louvre Palace in Paris, surrounded by three smaller pyramids. The large pyramid serves as the main entrance to the Louvre Museum. Completed in 1988 as part of the broader Grand Louvre project, it has become a landmark of the city of Paris.


title: Louvre Pyramid

text: The Grand Louvre project was announced in 1981 by François Mitterrand, then President of France. In 1983 the Chinese-American architect I. M. Pei was selected as its architect. The pyramid structure was initially designed by Pei in late 1983 and presented to the public in early 1984. Constructed entirely with glass segments and metal poles, it reaches a height of . Its square base has sides of and a base surface area of . It consists of 603 rhombus-shaped and 70 triangular glass segments.


title: Louvre Pyramid

text: The pyramid structure was engineered by Nicolet Chartrand Knoll Ltd. of Montreal (Pyramid Structure / Design Consultant) and Rice Francis Ritchie of Paris (Pyramid Structure / Construction Phase).


title: Louvre Pyramid

text: The pyramid and the underground lobby beneath it were created because of deficiencies with the Louvre's earlier layout, which could no longer handle the increasing number of visitors on an everyday basis. Visitors entering through the pyramid descend into the spacious lobby then ascend into the main Louvre buildings.


title: Louvre Pyramid

text: For design historian Mark Pimlott, "I.M. Pei’s plan distributes people effectively from the central concourse to myriad destinations within its vast subterranean network... the architectonic framework evokes, at gigantic scale, an ancient atrium of a Pompeiian villa; the treatment of the opening above, with its tracery of engineered castings and cables, evokes the atria of corporate office buildings; the busy movement of people from all directions suggests the concourses of rail termini or international airports."


title: Louvre Pyramid

text: Several other museums and commercial centers have emulated this concept, most notably the Museum of Science and Industry in Chicago and Pioneer Place in Portland, designed by Kathie Stone Milano with ELS/Elbasani and Logan, Architects from Berkeley, California. The Dolphin Centre, featuring a similar pyramid, was opened in April 1982, by Prince Richard, Duke of Gloucester. The construction work on the pyramid base and underground lobby was carried out by the Vinci construction company.


title: Louvre Pyramid

text: The construction of the pyramid triggered many years of lively aesthetic and political debate. Criticisms tended to fall into four areas: (1) the modernist style of the edifice being inconsistent with the classic French Renaissance style and history of the Louvre; (2) the pyramid being an unsuitable symbol of death from ancient Egypt; (3) the project being megalomaniacal folly imposed by then-President François Mitterrand; and (4) Chinese-American architect I.M. Pei being insufficiently familiar with French culture to be entrusted with the task of updating the treasured Parisian landmark.


title: Louvre Pyramid

text: Those criticizing the aesthetics said it was "sacrilegious" to tamper with the Louvre's majestic old French Renaissance architecture, and called the pyramid an anachronistic intrusion of an Egyptian death symbol in the middle of Paris. Meanwhile, political critics referred to the structure as "Pharaoh François' Pyramid". Writing in "The Nation", Alexander Cockburn ridiculed Pei's rationale that the structure would help visitors locate the entrance: "What Pei really meant was that in our unfolding "fin de siècle", public institutions need an area (...) where rich people can assemble for cocktail parties, banquets and kindred functions, to which the word 'charity' is attached to satisfy bodies such as the IRS." Some still feel the modernism of the edifice is out of place.


title: Louvre Pyramid

text: The pyramid has a total of 673 panes, as confirmed by the Louvre, 603 rhombi and 70 triangles. Three sides have 171 panes each: 18 triangular ones on the edges and 153 rhombic ones arranged in a triangle; the fourth side, with the entrance, has 9 fewer rhombic and 2 fewer triangular ones, giving 160. Some commentators report that Pei's office counts 689.


title: Louvre Pyramid

text: However, a longstanding rumor claims that the pyramid includes exactly 666 panes, "the number of the beast", often associated with Satan. The story of the 666 panes originated in the 1980s, when the official brochure published during construction cited this number twice. The number 666 was also mentioned in various newspapers. One writer on esoteric architecture asserted that "the pyramid is dedicated to a power described as the Beast in the Book of Revelation... The entire structure is based on the number 6."


title: Louvre Pyramid

text: The myth resurfaced in 2003, with the protagonist of the best-selling novel "The Da Vinci Code" saying: "this pyramid, at President Mitterrand's explicit demand, had been constructed of exactly 666 panes of glass — a bizarre request that had always been a hot topic among conspiracy buffs who claimed 666 was the number of Satan." In fact, according to Pei's office, Mitterrand never specified the number of panes.


title: Louvre Pyramid

text: The Inverted Pyramid (Pyramide Inversée) is a skylight in the Carrousel du Louvre shopping mall in front of the Louvre Museum. It looks like an upside-down and smaller version of the Louvre Pyramid.


title: Louvre Pyramid

text: Designed for a museum that attracted 4.5 million visitors a year, the pyramid proved inadequate by the time the Louvre's attendance had doubled in 2014. Between 2014 and 2017, the layout of the foyer area in the Cour Napoleon beneath the glass pyramid underwent a thorough redesign, including better access to the pyramid and the Passage Richelieu.


title: Louvre Pyramid

text: Prior to designing the Louvre Pyramid, Pei had included smaller glass pyramids in his design for the National Gallery of Art's East Building in Washington, D.C., completed in 1978. Multiple small glass pyramids, along with a fountain, were built in the plaza between the East Building and the pre-existing West Building, acting as a unifying element between the two properties and serving as skylights for the underground atrium that connected the buildings. The same year the Louvre Pyramid opened, Pei included large glass pyramids on the roofs of the IBM Somers Office Complex he designed in Westchester County, New York. Pei returned again to the glass pyramid concept at the Rock and Roll Hall of Fame in Cleveland, Ohio, opened in 1995.


title: Louvre Pyramid

text: In 1839, according to one newspaper account, in ceremonies commemorating the "glorious revolution" of 1830, "The tombs of the Louvre were covered with black hangings and adorned with tricolored flags. In front and in the middle was erected an expiatory monument of a pyramidal shape, and surmounted by a funeral vase."


title: Josh Hamilton

text: Joshua Holt Hamilton (born May 21, 1981) is an American former professional baseball player. He played in Major League Baseball as an outfielder from to , most prominently as a member of the Texas Rangers teams that won two consecutive American League pennants in 2010 and 2011. A five-time All-Star player, Hamilton won three Silver Slugger Awards and was named the American League (AL) Most Valuable Player (MVP) in 2010. He also won an AL batting championship along with an AL RBI title. During his major league tenure, he also played for the Cincinnati Reds and the Los Angeles Angels of Anaheim.


title: Josh Hamilton

text: Hamilton was the first overall pick in the 1999 MLB draft by the Tampa Bay Devil Rays. He was considered a blue chip prospect until injuries and a drug addiction derailed his career beginning in 2001. Prior to the 2007 season, Hamilton was selected by the Chicago Cubs in the Rule 5 draft, but was traded to the Cincinnati Reds. Prior to the 2008 season, he was traded to the Rangers. In 2012, Hamilton received more votes than any other player on the All-Star Game ballot, besting by approximately 3.5 million votes the vote count set in 2011 by José Bautista. On May 8, 2012, Hamilton became the 16th player in MLB history to hit four home runs in a game. All four home runs were two-run home runs, and he set an AL record for total bases in a game with 18. Regarded as one of the best Rangers players of all time and pivotal to their back-to-back World Series appearances, the only ones in Rangers history, Hamilton was inducted into the Texas Rangers Hall of Fame in 2019.


title: Josh Hamilton

text: Hamilton's career was marked by persistent drug and alcohol abuse, largely stemming from trauma from a 2001 automobile accident that caused his career to be delayed by several years. In 2019, four years following his retirement, Hamilton was charged with physically assaulting his daughter.


title: Josh Hamilton

text: Hamilton, of majority Scottish heritage, was born and raised in Raleigh, North Carolina, playing little league baseball alongside former South Carolina and Oakland Athletics catcher Landon Powell. Hamilton attended Athens Drive High School in Raleigh where he starred as both a pitcher and outfielder. As a high school senior, Hamilton ran the 60-yard dash in 6.7 seconds and was clocked at on the mound. After hitting .529 in 25 games with 13 home runs, 20 stolen bases, 35 runs batted in (RBIs), and 34 runs scored, Hamilton was widely considered one of the top two prospects for the 1999 MLB draft, along with Josh Beckett, a Texas high school athlete. Hamilton initially signed a letter of intent to play college baseball for North Carolina State.


title: Josh Hamilton

text: The Tampa Bay Devil Rays owned the number one pick and selected Hamilton with the first overall selection. Hamilton signed with Tampa Bay, receiving a $3.96 million signing bonus, and joined their minor league system. His first stop in the minors was the rookie level Princeton Devil Rays of the Appalachian League, where he played 56 games. Hamilton later joined the Short Season Single-A club, the Hudson Valley Renegades, and helped lead them to their first New York–Penn League championship. He spent the season with the Charleston RiverDogs in the South Atlantic League. Hamilton enjoyed a breakout season during which he hit .301 in 96 games, with 13 home runs and 61 RBIs. He was also selected to the South Atlantic League All Star game and took home MVP honors after going 2–6 with two triples and two runs scored. In addition, Hamilton was named to the 2000 All-Star Futures Game, a game designed to showcase minor league prospects. Hamilton was also voted Minor League Player of the Year by "USA Today". At the start of his pro career, Hamilton's parents quit their jobs so they could travel with their son.


title: Josh Hamilton

text: Prior to the season, Hamilton was involved in an automobile accident. His mother and father were also injured but recovered. The 2001 season marked the beginning of Hamilton's drug and alcohol use, and he made his first attempt at rehabilitation. Hamilton only played 45 games in the 2001 season, split between the Charleston (Single-A) and the Orlando Rays, a Double-A team in the Southern League. Hamilton began the season with the Bakersfield Blaze, batting .303 with nine home runs and 44 RBIs in 56 games before his season came to an end due to lingering toe and neck injuries. The Devil Rays noticed a change in Hamilton and reacted by sending him to the Betty Ford Center for drug rehabilitation.


title: Josh Hamilton

text: During spring training of the 2003 season, Hamilton failed his first drug test. At the start of the season, Hamilton showed up late several times during spring training and was reassigned to the team's minor league camp. He left the team and resurfaced several times, but eventually took the rest of the season off for personal reasons. Hamilton was hoping to return to spring training with the Devil Rays in , though was suspended 30 days and fined for violating the drug policy put in place by MLB. A "failed" test is one in which there is a positive result for a drug more severe than marijuana. A month later, MLB suspended him for the entire season after he failed two more tests.


title: Josh Hamilton

text: Hamilton was out of baseball for almost three years. He made several attempts at rehabilitation, and started off the season with hopes of being a star major league outfielder. However, he was arrested before the season for smashing the windshield of a friend's truck. The Rays placed Hamilton on the restricted list, moving him off the 40-man roster. After another relapse, MLB suspended him for the entire 2006 season.


title: Josh Hamilton

text: During the days of his most prolific abuse, Hamilton met a businessman named Michael Chadwick, who made an attempt to steer him in the right direction. It was through this relationship Hamilton ended up meeting his wife, Katie, who was Chadwick's daughter. Hamilton's return to baseball was helped along by former minor league outfielder and manager Roy Silver, who owned a baseball academy in Florida. After hearing about Hamilton's desire to return to baseball, Silver offered the use of his facility if Hamilton agreed to work there. Hamilton first started working at Silver's Academy in January 2006. His duties included cleaning the bathrooms and raking the infield. Hamilton spent his nights sleeping on an air mattress in one of the facility's offices. After several months there, Hamilton attempted to play with an independent minor league team, but MLB stepped in and disallowed it.


title: Josh Hamilton

text: Hamilton was allowed to work out with the Devil Rays' minor league players starting on June 2, 2006. By the end of the month, he was allowed to participate in minor league games. In order for this to happen, the Rays had to run Hamilton through waivers, making him available for any team for $20,000. No team put a claim in for him. Hamilton played in 15 games with the Hudson Valley Renegades at the end of the 2006 season, his second stint with the minor league ball club.


title: Josh Hamilton

text: Left off the Rays' 40-man roster, Hamilton was selected third overall in the 2006 Rule 5 draft by the Chicago Cubs, who immediately traded him to the Reds for $100,000 ($50,000 for his rights, and $50,000 to cover the cost of the Rule 5 selection). In their coverage of the draft, Chris Kline and John Manuel of "Baseball America" called Hamilton "the biggest name in the Rule 5 in many years".


title: Josh Hamilton

text: Hamilton was one of the Reds' best hitters in spring training in 2007, leaving camp with a .403 batting average. In order to retain the rights to Hamilton, though, the Reds would have to keep him on their Major League 25-man roster for the entire 2007 season, so they planned to use him as a fourth outfielder.


title: Josh Hamilton

text: Hamilton made his Major League debut at the age of 26 on April 2 against the Chicago Cubs in a pinch-hit appearance, receiving a 22-second standing ovation. As he was waiting to bat, Cubs catcher Michael Barrett said, "You deserve it, Josh. Take it all in, brother. I'm happy for you." After he lined out, Hamilton stayed in the game to play left field. He made his first start on April 10 against the Arizona Diamondbacks, batting leadoff. In that game, he recorded his first Major League hit, a home run off Édgar González. The next night, he hit another. Hamilton was named the National League Rookie of the Month for April.


title: Josh Hamilton

text: On May 22, the Reds placed Hamilton on the 15-day disabled list with gastroenteritis; they activated him on June 5 after he batted .333 (8-for-24) with four home runs and six RBIs in a six-game Minor League rehabilitation assignment. Hamilton went back on the DL on July 12 with a sprained wrist.


title: Josh Hamilton

text: Hamilton ended up starting most of the season in center field after an injury to Ryan Freel, but was shut out in the voting for the Rookie of the Year, which was won by Ryan Braun. On December 21, 2007, the Reds traded Hamilton to the Texas Rangers for Edinson Vólquez and Danny Herrera.


title: Josh Hamilton

text: In , Hamilton locked up the Rangers' starting center fielder job with a stellar spring training. His spring training performance continued into the regular season. Hamilton, usually slotted fourth in the Texas batting order, led all major league players in RBIs for the month of April. He was named AL Player of the Month after hitting .330 with 32 RBIs during the month. Hamilton then went on to win player of the month for the second straight month in May, becoming the first AL player in baseball history to be awarded Player of the Month for the first two months of the season. Hamilton was featured on the cover of the June 2, 2008, issue of "Sports Illustrated", in a story chronicling his comeback. On July 9, Hamilton hit the first walk-off home run of his career, against Francisco Rodríguez.


title: Josh Hamilton

text: Fans selected Hamilton as one of the starting outfielders for the AL at the 2008 Major League Baseball All-Star Game at Yankee Stadium. He finished first in voting among outfielders. He was one of seven first-time starters in the game. Along with Kosuke Fukudome, Geovany Soto, and Ryan Braun, Hamilton was one of four who had made their MLB debut in 2007 or 2008. He was selected to participate in the 2008 Major League Baseball Home Run Derby the evening before the game. Hamilton selected 71-year-old Clay Council to throw to him during the Derby. Council was a volunteer who threw batting practice for him as a child in Raleigh, North Carolina. In the first round of the event Hamilton hit 28 home runs, breaking the single-round record of 24 set by Bobby Abreu in 2005. Hamilton ended up hitting the most total home runs in the contest with 35, but lost in the final round to Justin Morneau, as the scores were reset. His record-setting first round included 13 straight home runs at one point, and seven that went further than . His longest home run was 518 feet. In 2006, when Hamilton was trying to get back into baseball, he had a dream in which he participated in a Home Run Derby at Yankee Stadium, but he could not remember how many home runs he had hit. After the Derby, Hamilton said: "This was like living the dream out, because like I've said, I didn't know the ending to that dream."


title: Josh Hamilton

text: On August 17, Hamilton was intentionally walked with the bases loaded against the Rays in the bottom of the ninth, with the Rays leading 7–3, to bring Marlon Byrd to the plate. The Rays went on to win the game 7–4. Hamilton thus became the sixth player in history, and the first American League player in 107 years, to receive an intentional walk with the bases loaded. Joe Maddon said after the game, "We didn't want Hamilton to hit a home run. He's got 28, and Marlon Byrd's got 8." Hamilton finished seventh in the balloting for AL MVP, behind Dustin Pedroia, Justin Morneau, Kevin Youkilis, Joe Mauer, Carlos Quentin, and Francisco Rodríguez.


title: Josh Hamilton

text: In spring training, Hamilton led all players in RBIs, with 27, and total bases, with 59, in 81 at-bats. He hit a home run into the right field home run porch off Angels reliever Shane Loux in the bottom of the eighth inning on May 15 in Arlington. Then, in the same series against the Angels, Hamilton leaped at the wall in center field and slammed into it, robbing Howie Kendrick of a possible home run.


title: Josh Hamilton

text: Hamilton spent a portion of 2009 on the disabled list, with a bruised rib cage and an abdominal strain. After visiting doctors in Philadelphia on June 8, 2009, they found a slight abdominal tear, and he underwent a successful surgical operation to repair it the next day. He was expected to be out 4–6 weeks.


title: Josh Hamilton

text: Though injured, he was selected by fan voting to play in the 2009 All-Star game, where he was joined by teammates Michael Young and Nelson Cruz. Hamilton finished batting .268 with 10 home runs and 54 RBIs in 2009.


title: Josh Hamilton

text: A story that brought some controversy emerged when it was revealed Hamilton had gotten drunk in an Arizona bar earlier in the year. Hamilton subsequently apologized about the lapse.


title: Josh Hamilton

text: In 2010, Hamilton was moved to left field to put young outfielder Julio Borbon in center field. As in his prior two seasons with the Rangers, Hamilton was again selected to start in the 2010 All-Star Game, as one of six members of the Rangers to represent the franchise at the All-Star Game. Hamilton entered the All-Star Break with a .346 batting average, tied for first in the AL with Miguel Cabrera.


title: Josh Hamilton

text: On August 27, he set a Rangers record with his 24th three-hit game of the season. On September 4, Hamilton bruised his rib cage after making a leaping catch into the outfield wall. He was sidelined for almost a month and returned to play with only three games left in the regular season, hitting a home run the next day.


title: Josh Hamilton

text: Hamilton's talent and popularity earned him a litany of nicknames including "The Hammer"; "Hambino", referencing the great Babe Ruth; "The Natural"; and "Hambone", his high school nickname tattooed on his arm.


title: Josh Hamilton

text: Hamilton hit for a league-leading .359 average in 2010, winning his first batting title. This was the fourth-highest batting average since the end of the 2004 season. He also finished fourth in Major League Baseball in OBP (.411), first in slugging percentage (.633) and OPS (1.044), and tied for 10th in home runs (32), despite missing 29 games due to an injury. Hamilton was also one of 25 players to have 100 RBIs. His performance in 2010 made him a front-runner for the AL MVP Award. Hamilton won the AL Players Choice Award for Outstanding Player in 2010.


title: Josh Hamilton

text: On October 22, Hamilton and the Rangers won the 2010 ALCS. It was the first time in Rangers' history they had gone to a World Series. With four home runs, seven RBIs, and the recipient of several (5) intentional walks in the ALCS win against the Yankees, he won the ALCS MVP Award. On November 23, 2010, Hamilton was voted the AL MVP.


title: Josh Hamilton

text: Hamilton avoided arbitration by signing a contract for two years and $24 million on February 10, 2011, with the Texas Rangers. On April 12, in Detroit, he suffered a fracture to his right humerus on a play at home plate. On May 18, Hamilton began a rehab assignment with the Double-A Frisco RoughRiders. He returned to the Rangers' lineup on May 23, and went 2–4 against Chicago White Sox pitcher John Danks, hitting his first home run of the season on the second pitch he saw during his first at-bat. He was an All-Star in 2011.


title: Josh Hamilton

text: On July 7, during a home game at Rangers Ballpark, a 39-year-old firefighter died while catching a foul ball tossed into the stands by Hamilton. The fan, Shannon Stone, leaned over the rail to catch the ball and fell 20 feet behind the scoreboard. He was transported to a hospital, but died on the way. After learning the news after the game, Hamilton was said to be distraught. It was the third incident in which a fan fell out of the stands at Rangers Ballpark. On September 30, the son of the fallen firefighter and his mother returned to Rangers Ballpark for the first time after the incident. The son, eight-year-old Cooper Stone, threw out the ceremonial first pitch to Hamilton to start the American League Division Series. Hamilton proceeded to exchange multiple hugs with the family.


title: Josh Hamilton

text: In 2011, Hamilton batted .298 with 25 home runs. He was third in the American League in sacrifice flies (10), sixth in intentional walks (13), and eighth in slugging percentage (.536).


title: Josh Hamilton

text: Hamilton hit .395 with nine home runs and 25 RBI during the month of April and was named the league's AL Player of the Month. His home run total for the month tied a franchise record for April with four other Rangers. Hamilton was considered to be in a breakout season, batting for the Triple Crown and MVP.


title: Josh Hamilton

text: On May 8, in a 10–3 win over the Baltimore Orioles at Camden Yards, Hamilton registered multiple career-highs; he had five hits in five at-bats, hitting four two-run home runs and a double for a total of eight runs batted in. Incidentally, the only runner on base each time was Elvis Andrus. In doing this, he not only became just the 16th player in MLB history to hit four home runs in one game and the first to do so since Carlos Delgado in , but also now holds the American League record for most total bases in a single game with 18. Hamilton was one base shy of tying the Major League record.


title: Josh Hamilton

text: Hamilton was selected to appear in his fifth All-Star Game after accumulating the most fan votes by any player in the history of the All-Star Game selection process. José Bautista held the previous record with 7,454,753 votes in 2011 until Hamilton received 11,073,744 in 2012. The record stood until 2015, when Josh Donaldson received 14,090,188 votes.


title: Josh Hamilton

text: Manager Ron Washington moved Hamilton to fifth in the batting order and designated hitter before a game with the White Sox on July 29. Since June 1, Hamilton had been hitting .190 with a slugging percentage of .374. Washington said he moved Hamilton in hopes of taking some of the pressure off him and also gave Hamilton the day off on July 28. Hamilton responded quickly—in a game on July 29, he recorded multiple walks for the first time in the month of July and did not record a strikeout for the first time in seven games. On July 30 he went 3–for–4 with a home run, his first game recording greater than two hits since May 11.


title: Josh Hamilton

text: On December 13, 2012, Hamilton agreed in principle to a five-year contract, worth $125 million with the Los Angeles Angels of Anaheim. This deal became official on December 15.


title: Josh Hamilton

text: During his first year with the Angels, Hamilton played in 151 games, batting .250 with 32 doubles, 21 home runs, and 79 RBI.


title: Josh Hamilton

text: During 2014, Hamilton batted .263 with 10 home runs and 44 RBIs. In the ALDS against Kansas City, Hamilton went hitless (going 0–13 overall).


title: Josh Hamilton

text: During February 2015, Hamilton underwent shoulder surgery to repair the AC joint. While he was recovering, it was revealed he had a relapse into his drug addiction, which he voluntarily reported to MLB. An outside arbitrator ruled Hamilton's voluntary admission did not violate baseball's drug policy, and he could not be suspended. Despite the ruling, team owner Arte Moreno made comments to the media, implying he did not want Hamilton back on the team. Furthermore, all Hamilton-related merchandise items were removed and recalled from all stores as well as an exchange program being set up. The Players Association and several Angels players spoke up in Hamilton's defense. The Angels began to lay out a rehab plan for him, but shortly afterwards, reports surfaced where the Angels were looking to trade Hamilton.


title: Josh Hamilton

text: Hamilton was traded back to the Rangers on April 27, 2015, for cash or a player to be named later. After a short rehab stint to rehabilitate his injured shoulder between the Rangers AA and AAA Minor League affiliates, Hamilton was called up to the MLB team on May 24, and was inserted into the starting lineup on May 25 in a Memorial Day matchup in Cleveland against the Indians. He recorded his first hit back with the Rangers on May 35. On May 28 of the same year, Hamilton returned to Texas for the first time in a Rangers uniform since leaving the team after the 2012 season. He received a standing ovation from the crowd and proceeded to hit a double on the first pitch he saw. Hamilton went 2–4 in the game, driving in the only run for his own team in a 5–1 loss. On May 29, Hamilton hit two home runs in his first multi-homer game with the Rangers since 2012, leading the team to a 7–4 victory. Two days later, he hit a pinch-hit two RBI double vs. the Red Sox to win the game in walk-off fashion, 4–3. On July 30, 2015, Hamilton recorded four RBI, a home run and walk off base hit in a 7–6 Rangers' win over the New York Yankees.


title: Josh Hamilton

text: In the ALDS, Hamilton's first hit was a single in Game 3. This ended his postseason hitless streak at 31 at-bats, which tied for second all time.


title: Josh Hamilton

text: Hamilton began the 2016 season on the 15-day disabled list. On May 25, 2016, it was announced Hamilton would not participate for the entire 2016 season after undergoing knee surgery for the third time in nine months. The Rangers activated Hamilton from the disabled list and released him on August 23, as releasing Hamilton before September 1 would allow them to play Hamilton in the major leagues before May 15, 2017, if they chose to re-sign him.


title: Josh Hamilton

text: On January 16, Texas re-signed Hamilton to a minor-league deal, with intentions of him trying out at first base.


title: Josh Hamilton

text: On February 26, it was revealed Hamilton was experiencing discomfort in his left knee again, the same knee which had underwent surgery on June 8 of the previous season. Seeking an opinion with Dr. Walt Lowe, an orthopedic surgeon in Houston, it was acknowledged Hamilton would have to undergo another surgery, therefore putting his career in jeopardy. On February 27, Hamilton underwent surgery on the knee to repair torn cartilage that was causing discomfort. Recovery time required up to three months. On April 21, the Rangers released Hamilton after revealing he suffered a right knee injury while in rehabilitation for the injury of the left knee.


title: Josh Hamilton

text: In 1,027 games over nine seasons, Hamilton posted a .290 batting average (1,134-for-3,909) with 609 runs, 234 doubles, 24 triples, 200 home runs, 701 RBI, 50 stolen bases, 352 bases on balls, .349 on-base percentage and .516 slugging percentage. Defensively, he recorded a .980 fielding percentage playing at all three outfield positions. In 42 postseason games, he hit .202 (33-for-163) with 18 runs, 9 doubles, 6 home runs, 23 RBI, 4 stolen bases and 15 walks for a .633 OPS overall.


title: Josh Hamilton

text: Hamilton was married to Katie (née Chadwick), the daughter of Michael Chadwick who helped guide him in his recovery from drugs and alcohol abuse for several years. They started dating in 2002 when he returned to Raleigh, and married in 2004. In early 2015, shortly after another substance-abuse relapse, Hamilton filed for divorce from Katie after 11 years of marriage. The couple had three daughters together, along with Katie's daughter from a previous relationship.


title: Josh Hamilton

text: Hamilton's struggles with drugs and alcohol are well documented. He finally stopped using drugs and alcohol after being confronted by his grandmother, Mary Holt. In May 2008, Hamilton said he had not used drugs or alcohol since October 6, 2005.


title: Josh Hamilton

text: When giving a brief summary of his recovery, Hamilton says simply: "It's a God thing." He does not shy away from telling his story, speaking to community groups and fans at many functions. He frequently tells stories publicly of how he believes that Jesus brought him back from the brink and that faith is what keeps him going. Hamilton also wrote an autobiography called "Beyond Belief" which explains how he quit drugs and alcohol and found a relationship with God. His ex-wife Katie sometimes accompanied him, offering her perspective on his struggles as well.


title: Josh Hamilton

text: To comply with the provisions of MLB's drug policy, Hamilton provided urine samples for drug testing at least three times per week. Rangers' coach Johnny Narron said of the frequent testing: "I think he looks forward to the tests. He knows he's an addict. He knows he has to be accountable. He looks at those tests as a way to reassure people around him who had faith."


title: Josh Hamilton

text: In late 2008 Hamilton, among other celebrities such as Brian Welch and Greg Ellis, appeared in testimonial videos called "I Am Second", in which he shares his story of recovering from drug use with the help of his Christian faith.


title: Josh Hamilton

text: A portion of his return to sobriety was shown on The Learning Channel's reality show "The Real Deal". "A Home Run for Trademark" aired March 31, 2007, and chronicled the renovation of Shoeless Joe Jackson's house during 2006. Richard C. Davis, the owner of Trademark Properties, hired Hamilton as the construction foreman. Davis was negotiating the purchase of a minor league baseball team and entertaining the idea of giving Hamilton a chance to join the team.


title: Josh Hamilton

text: Hamilton's teammates—mindful of his past struggles—chose to celebrate major events (such as winning the 2010 American League Division Series and 2010 American League Championship Series) with ginger ale instead of champagne. The Rangers repeated the celebrations with ginger ale the following postseason when they won their second consecutive pennant and reached the 2011 World Series.


title: Josh Hamilton

text: Hamilton confirmed he suffered a relapse in early 2009 after photos were released in August 2009. Sports website Deadspin posted photos of Hamilton shirtless in a bar in Tempe, Arizona with several women. According to reports, witnesses saw Hamilton drinking, heard him asking where he could obtain cocaine, and heard him reveal his plans to go to a strip club later that evening. The photos do not show Hamilton drinking or taking any illegal drugs.


title: Josh Hamilton

text: Prior to Hamilton's public admission, Johnny Narron said he doubted the validity of the photos, telling Deadspin, "I'm sure, in the depths of his drug addiction, he was in a lot of bars. He was in and out of bars, 'crackhouses', everything. There are probably photographs of him in all kinds of places." When responding, Narron had not seen the photos and was told they were taken during March 2009, not two months prior when the incident took place.


title: Josh Hamilton

text: Although this news did not break until August 2009, Hamilton revealed he had informed his wife, the Texas Rangers, and MLB the day after the incident occurred. Hamilton called a press conference on August 8 to discuss the photos. Regarding the incident Hamilton said:


title: Josh Hamilton

text: Obviously it was one of those things that reinforce that I can't have alcohol. I got away from the one thing that kept me on the straight and narrow and that was my relationship with the Lord. That should always come first. Hopefully some good will come out of this. It just crossed my mind that night, 'Can I have a drink?' Obviously I can't and this reinforces that. Since that night, I have not had another thought like that. I know it's something I shouldn't do because it leads to other things.


title: Josh Hamilton

text: Hamilton also admitted he had very little memory of the night after getting drunk, and did not know about the contents of the photos. Hamilton did not see the photos after their release, but listened on the phone as his wife described them to him. After the press conference Rangers general manager Jon Daniels said, "My first reaction in January was one of concern. Since then I've talked to a lot of people and they say it was significant that he came forward immediately and was honest about it." MLB tested Hamilton for illegal drugs two days after the incident and he passed that test.


title: Josh Hamilton

text: On February 2, 2012, it was reported Hamilton had suffered a second relapse with alcohol. He claims to have had two or three drinks before inviting his friend and then-teammate, Ian Kinsler, to talk at the bar. Hamilton held a press conference on February 3, 2012, to apologize for his actions.


title: Josh Hamilton

text: Hamilton was arrested on October 30, 2019, and charged with injury to a child, a third-degree felony, after being accused of physically assaulting his oldest daughter. On April 8, 2020, Hamilton was indicted on a felony charge for beating his daughter. If convicted, he could face up to 10 years in prison. On February 22, 2022, Hamilton was found guilty of an unlawful restraint under a plea deal, regarding a misdemeanor case that stemmed from the incident with his daughter dating back to October 2019. In the aftermath, Hamilton received a year of probation, was fined $500, and ordered to undergo 20 hours of community service along with anger management counseling and parenting rehabilitation classes. In addition, Hamilton was prohibited from possessing any weapons or substances that relate to drugs and alcohol. He was also prevented from making any contact or communication with the daughter he attacked before during the time of his probation. If he satisfies the probation requirements, the charge will be dismissed.


title: Bovril

text: Bovril is the trademarked name of a thick and salty meat extract paste similar to a yeast extract, developed in the 1870s by John Lawson Johnston. It is sold in a distinctive bulbous jar, and as cubes and granules. Bovril is owned and distributed by Unilever UK. Its appearance is similar to the British Marmite and its Australian equivalent Vegemite.


title: Bovril

text: Bovril can be made into a drink (referred to in the UK as a "beef tea") by diluting with hot water or, less commonly, with milk. It can be used as a flavouring for soups, broth, stews or porridge, or as a spread, especially on toast in a similar fashion to Marmite and Vegemite.


title: Bovril

text: The first part of the product's name comes from Latin "bovīnus", meaning "ox". Johnston took the "-vril" suffix from Edward Bulwer-Lytton's then-popular novel, "The Coming Race" (1871), the plot of which revolves around a superior race of people, the Vril-ya, who derive their powers from an electromagnetic substance named "Vril". Therefore, Bovril indicates great strength obtained from an ox.


title: Bovril

text: In 1870, in the Franco-Prussian War, Napoleon III ordered one million cans of beef to feed his troops. The task of providing this went to John Lawson Johnston, a Scottish butcher living in Canada. Large quantities of beef were available across the British Dominions and South America, but transport and storage were problematic. Therefore, Johnston created a product known as 'Johnston's Fluid Beef', later called Bovril, to meet Napoleon's needs. By 1888, over 3,000 UK public houses, grocers and dispensing chemists were selling Bovril. In 1889, Bovril Ltd was formed to develop Johnston's business further.


title: Bovril

text: During the 1900 Siege of Ladysmith in the Second Boer War, a Bovril-like paste was produced from horsemeat within the garrison. Nicknamed "Chevril" (a portmanteau of Bovril and "cheval", French for "horse") it was made by boiling down horse or mule meat to a jelly and serving it as a beef tea-like mixture. Bovril also produced concentrated, pemmican-like dried beef as part of the British Army emergency field ration during the war. The ration came in the form of a pocket-sized tin can that contained the beef on one half alongside a dried cocoa drink on another half. The dried beef could be eaten alone, or mixed with water to create a beef tea.


title: Bovril

text: Bovril continued to function as a "war food" in World War I and was frequently mentioned in the 1930 account "" by Helen Zenna Smith. It describes the drink being prepared for the casualties at Mons where "the orderlies were just beginning to make Bovril for the wounded, when the bearers and ambulance wagons were shelled as they were bringing the wounded into the hospital".


title: Bovril

text: Bovril beef tea was the only hot drink that Ernest Shackleton's team had when they were marooned on Elephant Island during the 1914–17 Endurance Expedition.


title: Bovril

text: When John Lawson Johnston died, his son George Lawson Johnston inherited and took over the Bovril business. In 1929, George Lawson Johnston was made Baron Luke, of Pavenham, in the county of Bedford.


title: Bovril

text: Bovril's instant beef stock was launched in 1966 and its "King of Beef" range of instant flavours for stews, casseroles and gravy in 1971. In 1971, James Goldsmith's Cavenham Foods acquired the Bovril Company but then sold most of its dairies and South American operations to finance further take-overs. The brand is now owned by the Anglo-Dutch multinational Unilever, which bought Bovril in 2001.


title: Bovril

text: Bovril holds the unusual distinction of having been advertised with a Pope. An advertising campaign of the early 20th century in Britain depicted Pope Leo XIII seated on his throne, bearing a mug of Bovril. The campaign slogan read: "The Two Infallible Powers – The Pope & Bovril."


title: Bovril

text: In 2004, Unilever removed beef ingredients from the Bovril formula, rendering it vegetarian. This was mainly due to concerns about decreasing sales, particularly from exports due to an export ban on British beef, as a result of the growing popularity of vegetarianism, religious dietary requirements, and public concerns about bovine spongiform encephalopathy. In 2006, Unilever reversed that decision and reintroduced beef ingredients to their Bovril formula once sales increased and the beef export bans were lifted. Unilever now produces Bovril using beef extract and a chicken variety using chicken extract.


title: Bovril

text: In November 2020, Forest Green Rovers Football Club announced a collaboration with the makers of Bovril to create a beet-based version of Bovril to be sold at their New Lawn stadium, where meat-based products had been removed from sale some years prior.


title: Bovril

text: Bovril was promoted as a superfood in the early 20th century. Advertisements recommended people to dilute it into a tea or spread it on their morning toast. Some adverts even claimed that Bovril could protect one from influenza.


title: Bovril

text: Bovril jars are commonly excavated as part of archaeological assemblages, such as at Knowles Mill in Worcestershire.


title: Bovril

text: Since its invention, Bovril has become an icon of British culture. It is associated with football culture. During the winter British football fans in stadium terraces drink it as a tea from Thermos flasks – or from disposable cups in Scotland, where thermoses are from football stadiums.


title: Bovril

text: In the film "In Which We Serve", the officers on the bridge are served "Bovril rather heavily laced with sherry" to warm them up, after being rescued during the Dunkirk evacuation of the British Expeditionary Force.


title: Bovril

text: British mountaineer Chris Bonington appeared in TV commercials for Bovril in the 1970s and 1980s in which he recalled melting snow and ice on Everest to make hot drinks.


title: Big Three (automobile manufacturers)

text: In the automotive industry, the term Big Three is used for a country's three largest motor vehicle manufacturers, especially indicating companies that sell under multiple brand names.


title: Big Three (automobile manufacturers)

text: The term originated in the United States, where General Motors was the first to form a large, multi-brand, motor-vehicle corporation (in the 1910s), followed by Ford Motor Company, and the Chrysler Corporation, all before World War II.


title: Big Three (automobile manufacturers)

text: General Motors, Ford Motor Company, and Chrysler Stellantis North America are often referred to as the "Big Three", being the largest automakers in the United States. They were for a while the three largest in the world, with GM and Ford remaining as mainstays in the top five. The Big Three are also distinguished not just by their size and geography, but also by their business model. All three have their headquarters in the Detroit area; the majority of their operations are unionized with the United Auto Workers and Unifor.


title: Big Three (automobile manufacturers)

text: Ford has held the position of second-ranked automaker for the past 56 years, being relegated to third in North American sales after being overtaken by Toyota in 2007. That year, Toyota produced more vehicles than GM although GM still outsold Toyota. At that time, GM had 77 consecutive calendar years of top sales. For the first quarter of 2008, Toyota finally overtook GM in sales.


title: Big Three (automobile manufacturers)

text: In their domestic American market, the major Detroit automakers have consistently retained the top three spots. Honda passed Chrysler for the fourth spot in 2008 US sales. Since then, because of Toyota's controversy surrounding their recent unintended acceleration recall, Toyota has fallen back to fourth place in sales , with Honda trailing in fifth place , allowing the Detroit Three to reclaim their Big Three title. Toyota overtook GM as the best selling automaker in the United States in 2021, marking the first time an American automaker has not led U.S. auto sales for a full year.


title: Big Three (automobile manufacturers)

text: Union labor can result in higher labor costs than other multinational automakers, including those with plants in North America. The 2005 Harbour Report estimated that Toyota's lead in labor productivity amounted to a cost advantage of $350 US to $500 US per vehicle over American manufacturers. The UAW agreed to a two-tier wage in recent 2007 negotiations, something which the CAW has so far refused. Delphi, which was spun off from GM in 1999, filed for Chapter 11 bankruptcy after the UAW refused to cut their wages and GM is expected to be liable for a $7 billion shortfall.


title: Big Three (automobile manufacturers)

text: In order to improve profits, the Detroit automakers made deals with unions to reduce wages while making pension and health care commitments. GM, for instance, at one time picked up the entire cost of funding health insurance premiums of its employees, their survivors and GM retirees, as the US did not have a universal health care system. With most of these plans underfunded in the late 1990s, the companies offered and provided retirement packages to its elder senior workers, and made agreements with the UAW to transfer pension obligations to an independent trust. In 2009, the CBC reported that the non-unionized Japanese automakers, with their younger American workforces, lower wages and fewer retirees would continue to enjoy a cost advantage over the Big Three.


title: Big Three (automobile manufacturers)

text: Despite the history of their marques, several long-running cars have been discontinued or relegated to fleet sales, as the Big Three shifted away resources from midsize and compact cars to lead the "SUV Craze". Since the late 1990s, over half of their profits have come from Sport utility vehicles, while they often could not break even on compact cars unless the buyer chose options.


title: Big Three (automobile manufacturers)

text: Ron Harbour, in releasing the Oliver Wyman’s 2008 Harbour Report, stated that many small “econoboxes” of the past acted as loss leaders, but were designed to bring customers to the brand in the hopes they would stay loyal and move up to more profitable models. The report estimated that an automaker needed to sell ten small cars to make the same profit as one big vehicle, and that they had to produce small and mid-size cars profitably to succeed, something that the Detroit three had trouble doing.


title: Big Three (automobile manufacturers)

text: Falling sales and market share at times have resulted in the Big Three's plants operating below capacity leading to production cuts, plant reductions, closures and layoffs. Market incentives and subsidized leases were implemented to help sales which was crucial to keeping the plants operating at capacity, which in turn drove a significant portion of the Michigan economy. These promotional strategies, including rebates, employee pricing and 0% financing, have boosted sales but have also cut into profits. More importantly such promotions drain the automaker's cash reserves in the near term while in the long run the company suffers the stigma of selling vehicles because of low price instead of technical merit. Automakers have since been reduced and scaled back on incentives and raise prices, while cutting production. The subprime mortgage crisis and inflated higher crude prices in 2008 resulted in the plummeting popularity of best-selling trucks and SUVs, led automakers to continue offering heavy incentives to help clear excess inventory.


title: Big Three (automobile manufacturers)

text: The Big Three filed a lawsuit against California Governor Arnold Schwarzenegger because of earmarked impending tailpipe emissions requirement. In response, Governor Schwarzenegger told the Big Three to "get off [their] butt".


title: Big Three (automobile manufacturers)

text: In 2008, with relatively high energy prices, a stagnant and declining economy and an overall tense market situation due to the subprime mortgage crisis, the Big Three were re-strategizing and adapting their operations idling or converting light truck plants to passenger vehicle cars. Due to the declining residual value of its vehicles, Chrysler has stopped offering leases on its vehicles.


title: Big Three (automobile manufacturers)

text: In 2009, General Motors and Chrysler filed for and eventually successfully emerged from Chapter 11 restructuring in order to restructure and liquidate burdensome corporate assets in the same year. General Motors of Canada did not file for bankruptcy. The United States and Canadian government control are reported as temporary.


title: Big Three (automobile manufacturers)

text: On June 10, 2009, Chrysler Group LLC emerged from a Chapter 11 reorganization bankruptcy and its stake was subsequently bought by the Italian automaker Fiat. On June 3, 2011, Fiat bought out the remaining U.S. Treasury’s stake in Chrysler for $500 million, increasing its ownership of the automaker to 53%. On January 21, 2014, Fiat bought out the remaining stake in Chrysler Group that it did not already hold from the United Auto Workers' employee medical benefit retirement trust.


title: Big Three (automobile manufacturers)

text: Due to the corporate structure of Fiat Chrysler Automobiles, which is headquartered in the United Kingdom for taxation purposes and the Italian Agnelli family as the major shareholders, some media sources now list Detroit as having a "Big Two" (GM and Ford) as opposed to a "Big Three". Chrysler has become part of multinational auto giant Stellantis after FCA Group merged with the largely pan-European PSA Group) in 2021.


title: Big Three (automobile manufacturers)

text: Japanese automakers Toyota, Nissan, and Honda, among many others, have long been considered the leaders in the segment of small fuel-efficient cars. A major contributing factor to their success was when their vehicles benefitted from the 1973 oil crisis which at the time drastically changed market situations and had a major impact on the automotive industry. For instance, the Honda Civic was the best-selling car in its segment in Canada for 22 years in a row.


title: Big Three (automobile manufacturers)

text: As well, the Nissan 240Z was introduced at a relatively low price compared to other foreign sports cars of the time (Jaguar, BMW, Porsche, etc.), while providing performance, reliability, and good looks. This broadened the image of Japanese car-makers beyond their econobox successes, as well as being credited as a catalyst for the import performance parts industry.


title: Big Three (automobile manufacturers)

text: Before Honda unveiled Acura in 1986, Japanese automobiles exports were primarily economical in design and largely targeted at low-cost consumers. The Japanese big three created their luxury marques to challenge the established brands. Following Honda's lead, Toyota launched the Lexus name with the LS 400 which debuted at $38,000 in the U.S. (in some markets being priced against mid-sized six cylinder Mercedes-Benz and BMW models), and was rated by "Car and Driver" magazine as better than both the $63,000 Mercedes-Benz W126 and the $55,000 BMW E32 in terms of ride, handling and performance. It was generally regarded as a major shock to the European marques; BMW and Mercedes-Benz's U.S. sales figures dropped 29% and 19%, respectively, with the then-BMW chairman Eberhard von Kuenheim accusing Lexus of dumping in that market. Nissan's Infiniti became a player on the luxury market mostly thanks to its popular Q45. The vehicle included a class-leading (at the time) 278 hp (207 kW) V8 engine, four wheel steering, the first active suspension system offered on a motor vehicle, and numerous interior luxury appointments. These made it competitive against the German imports like Audi, BMW and Mercedes-Benz, which by the time of Infiniti's release had overtaken Cadillac and Lincoln in dominating the luxury segment of the American market. In 1990, four years after the debut of the Legend and Integra, Acura introduced the NSX, a midship V6 powered, rear-wheel-drive sports car. The NSX, an acronym for "New Sports eXperimental", was billed as the first Japanese car capable of competing with Ferrari and Porsche. This vehicle served as a halo car for the Acura brand. The NSX was the world's first all-aluminum production car, and was also marketed and viewed by some as the "Everyday Supercar" thanks in part to its ease of use, quality and reliability, traits that were unheard of in the supercar segment at the time.


title: Big Three (automobile manufacturers)

text: The success of the Japanese automakers contributed to their American counterparts falling into a recession in the late 1970s. Unions and lobbyists in both North America and Europe put pressure on their government to restrict imports. In 1981, Japan agreed to Voluntary Export Restraints in order to preempt protectionism measures that the US may have taken, where it be tariffs or import quotas. Consequently, Japanese companies responded by investing heavily in US production facilities, as they were not subject to the VER. Unlike the plants of domestic automakers, Japanese plants are non-unionized (save for NUMMI), so they have lower wage expenses and do not face the risk of strikes. The VER was lifted in 1994 upon agreement of all members of General Agreement on Tariffs and Trade (GATT). Establishing US production facilities was also a significant step in improving public relations, along with philanthropy, lobbying efforts, and sharing technology. Europe has still largely maintained its protectionism policies against Japanese cars, though theirs varies considerably.


title: Big Three (automobile manufacturers)

text: Toyota has always been by far Japan's largest automaker, and it recently overtook perennial world leader GM in both production and sales by early 2008. As the most aggressive of Japan's companies when it came to expanding into light trucks and luxury vehicles, this proved largely successful. Their high-end brand Lexus became the top-selling luxury marque worldwide in 2000, despite being only started up in 1989. Consequently, Toyota's stock price has traded at a much higher premium than other automakers. Nissan regained its position on second place, financial difficulties in the late 1990s caused it to lose its place to Honda before. Nissan is Japan’s second largest automaker and ranks sixth in the world, behind Toyota, GM, Volkswagen, Ford, and Hyundai. Suzuki, Mazda, and Mitsubishi are in a distant fourth, fifth, and sixth place compared to the Japanese Big Three.