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Jaguar V12 engine

An evolution of the 1964 DOHC prototype “XJ13” engine, the Jaguar V12 engine is a family of SOHC internal combustion V12 engines with a common block design, that were mass-produced by Jaguar Cars for a quarter of a century, from 1971 to 1997, mostly as 5.3litres, but later also as 6litres, and 7litre versions that were deployed in racing. Except for a few low-volume exotic sports car makers, Jaguar's V12 engine was the world's first V12 engine in mass-production. For 17 years, Jaguar was the only company in the world consistently producing luxury four-door saloons with a V12 engine. The V12 powered all three series of the original Jaguar XJ luxury saloons, as well as its second generation XJ40 and X305 successors.

Originally fitted with carburettors, the SOHC V12s received electronic fuel injection in 1975. In 1981, the engines were improved with higher efficiency (HE) cylinder heads. After two decades, the enlarged 6litre V12 was offered in production in the XJS and Daimler Double Six, from 1991 and 1993 respectively. Including the V12 E-Type mark3 models, and in the XJS (from 1975 to 1996), Jaguar made a total of 161,583 SOHC V12-engined cars. The Jaguar V12 was regarded as one of the premier power plants of the 1970s and 1980s. After launching the second generation XJseries in 1986, Jaguar developed their V12 into the racing engines that brought two overall victories at the 24hours of LeMans endurance races of 1988 and 1990.

Remarkably, three decades earlier, the engine was initiated in 1951 by Claude Baily as a prototype design for an intended LeMans racecar: the Jaguar XJ13 - as well as for planned use in Jaguar’s range of luxury and sports cars. After building six DOHC engines, 3 of which were extensively tested in cars, the XJ13 project was terminated in 1967, before the car ever entered into competition. Under the direction of Jaguar Chief Engineer William Heynes, the DOHC V12 engine design was reworked by engineers Walter Hassan and Harry Mundy into a road-going SOHC production-vehicle version, first installed in the Jaguar E-Type mark 3 of 1971. The SOHC V12 was just the second production engine design in Jaguar's history, after the 1949 straight-six XK engine, built through 1992. It uses an all-aluminium block and cylinder heads with removable wet steel liners, and single overhead camshafts with two valves per cylinder.

Development
Initial designs for a V12 engine were produced by engineer Claude Bailey as early as 1951, with a view to using it in a LeMans race-car. Baily's original 8.0 L design used double overhead camshafts heads sharing the same basic layout as the inline 6-cylinder XK engine, in order to allow for a relatively high redline. Even after Jaguar withdrew from racing in 1957, the V12 design continued to be refined, and Bailey proposed a range of displacements from 7.6 L (sharing 87 mm bore and 106 mm stroke measurements with the 3.8 L XK) down to 5.0 L (sharing the 2.4 L XK's 83 mm bore and 76.5 mm stroke). In 1962 Bailey was instructed to begin prototype tooling and bench testing of a 5.0 L design, having settled on an 87 mm bore and 70 mm stroke.

By 1964 several incarnations of the V12 engine were being tested, including versions meant for racing and others for installation into production cars. An all-aluminium quad-cam design with fuel injection was created for the XJ13, while cast iron blocks and heads, and other double and single overhead cam head designs were created for use in a production road car version. These production versions of the engine were tested in Mark X saloons.

After the XJ13 project was cancelled the team of Hassan and Mundy designed a new single overhead cam head, with the camshaft lobes acting directly on vertically-inclined valves through bucket tappets. This was similar to the cylinder head design of the contemporary Rover 2000, with which the Jaguar V12 also shared the use of dished 'Heron' pistons. These changes reduced complexity, weight, size and noise, and were anticipated to help the engine meet future emissions standards.

The revised head design by Hassan and Mundy also had longer, more restrictive inlet ports sacrificing top-end power but which—along with an increase in displacement to 5344 cc (90 mm bore x 70 mm stroke)—greatly improved performance at lower and mid-range engine speeds, which was more desirable in heavier luxury cars. The chain-driven SOHC heads and the softer valve springs fitted to reduce valve train noise resulted in the red line being lowered to 6,500 rpm from the 8,000 rpm of the original DOHC design. The engine was continuously refined with various carburettor and fuel injection arrangements before finally seeing production in the Series III E-Type in 1971.

5.3 Litre
The 5344 cc production engine had an oversquare 90 mm bore x 70 mm stroke, producing 242 hp to 295 hp (depending on emission controls and compression ratio), and up to 400 Nm of torque in fuel-injected form. Right from the start of production in 1971 the V12 engine had Lucas OPUS (Oscillating Pick-Up System) electronic ignition. Initially the OPUS ignition amplifier unit was secured directly to the engine between the cylinder heads and had problems due to overheating. In later cars the ignition amplifier had been moved away from the engine where it could get air flow for cooling. Originally the V12 was supposed to use an advanced fuel injection system under development by AE Brico but this plan was cancelled at a late stage, possibly due to concerns that the design was too similar to Bosch products. The V12 as used in the Series 3 E-Types, Series 1 XJ12 and early Series 2 XJ12s (1973-April 1975) had four side draft Zenith-Stromberg carburettors. After April 1975, the V12 engine used in the Series 2 XJ12 and the new XJ-S had a licensed copy of the Bosch D-Jetronic system adapted by Lucas for use on the V12.

This version was used in the following cars:
 * 1971-1974 Jaguar E-Type
 * 1975–1981 Jaguar XJS
 * 1972–1981 Jaguar XJ12 (Series 1 and 2)
 * 1973–1981 Daimler Double-Six (Series 1 and 2)
 * 1972-1981 Panther J.72
 * 1974-1985 Panther De Ville

5.3 Litre HE
A "high-efficiency" (HE) version of the engine debuted in 1981, using special high-swirl design cylinder heads designed by Swiss racing driver Michael May. May's design consisted of a swirl chamber at the exhaust valve with a channel around the intake valve. The use of conventional flat-topped pistons in lieu of the original design's dished type allowed squish from the compression stroke to push the air through the channel around the intake valve to the chamber below the exhaust valve, causing turbulent swirling flow around the spark plug (which had been relocated near the exhaust valve at the top of the chamber). This design created a stratified charge, allowing the engine to run at an unusually high compression ratio for the time (10.5:1 to 12.5:1, depending on market and year) while running a relatively lean fuel mixture. In any given market power levels remained similar to the previous model, but fuel economy was improved by nearly 50%. A new fuel injection system called "Digital P" featuring a digital ECU with integrated manifold air pressure transducer was installed, replacing the older analogue control unit and remote pressure sensor from Bosch's original D-Jetronic design. (However, cars sold in Australia, Sweden and Switzerland continued to use the D-Jetronic system until at least 1985. )

The OPUS ignition was replaced by Lucas's Constant Energy Ignition (CEI) in 1982, to deliver a more reliable spark. Series 3 XJ12 and Daimler Double Six cars used the CEI system until the end of their production in 1992, but it was superseded in the XJ-S in mid-1989 by another from Magneti Marelli. The Marelli ignition system was used until the end of XJ-S production, and on the 5993 cc version used in the XJ81 four-door saloons made in 1993 and 1994.

The 5.3 HE was used in the following applications:
 * 1981–1992 Jaguar XJ12 (Series 3)
 * 1981–1992 Jaguar XJ-S
 * 1981–1992 Daimler Double-Six (Series 3)

6.0 Litre HE
The engine was stroked to 78.5 mm in 1992 for a displacement of 5993 cc to make this one of the most powerful Jaguar production engines to date at 318 bhp at 5,400 rpm and 336 lbft at 3,750 rpm. The XJR-S stayed in the line until 1993 with power raised at 333 bhp at 5250 rpm and 365 lbft at 3650 rpm of torque. The 5993 cc engine on X305 used a new Nippondenso distributorless crank-fired ignition system with coil packs very similar to Ford EDIS-6 units. The last Jaguar V12 engine was produced on 17 April 1997.

The 6.0 HE was used in the following cars:
 * 1989–1993 Jaguar XJR-S 6.0 (from september 1989)
 * 1992–1995 Jaguar XJS
 * 1993–1994 Jaguar XJ-12 / Daimler Double-Six (XJ40/XJ81)
 * 1994–1997 Jaguar XJ-12 / Daimler Double-Six (X300)

TWR
In 1985, Tom Walkinshaw Racing became Jaguar's official team in World Endurance Championship, taking over the project from American team Group 44. Their first car, XJR6, used the 5993 cc engine, but in the following year the engine was upgraded to 6.9 L and in 1988 the XJR9 used the engine's most famous displacement of 6995 cc. By 1991, the V12 was good for 7.4 L inside the XJR12, developing an impressive 750 bhp

TWR also upgraded production Jaguar cars (usually XJRSes), with a variety of styling, handling and performance modifications. Most of the cars thus modified were straight from the Jaguar factory and sold through Jaguar dealerships.

By 1989, TWR were selling moderate numbers of XJRSes fitted with a 5993 cc version of the V12, which pre-dated the Jaguar production version by some 3 years.

Lister
Lister Cars, a well-known Jaguar tuner with a long history of technical collaboration with the British automaker, made frequent use of this powerplant. The first Jaguar Lister XJRSes were built by the company BLE Automotive in Erdington, Birmingham in the early 1980s until the Lister brand was passed on to WP Automotive of Leatherhead. In 1991, they fitted the 6995 cc version of the engine, with a 94x84 mm bore and stroke, into a modified Jaguar XJS, which was rebadged Lister Le Mans. This engine officially produced 546 hp and 580 lbft. From 1993, Lister Cars owner Laurence Pearce produced the company's first in house design the Lister Storm, which, naturally, continued using the V12 engine, both on the road and on the track, the car becoming a mainstay of the FIA GT Championship and several national championships for the following decade.

title: Jaguar V12 engine


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User:Rgarvage

This is my wikipedia page

I am a masters computer science student at University of California, Santa Barbara. My interests include:
 * Self-Organizing Systems
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 * watchlist
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license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Rgarvage


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Pozole

Pozole (from pozolli, meaning cacahuazintle, a variety of corn or maize) is a traditional soup or stew from Mexican cuisine. It is made from hominy with meat (typically chicken or pork), and can be seasoned and garnished with shredded lettuce or cabbage, chili peppers, onion, garlic, radishes, avocado, salsa or limes. Known in Mesoamerica since the pre-Columbian era, the stew is common across Mexico and neighboring countries, served both as a day-to-day meal and as a festive dish.

Description
Pozole can be prepared in many ways, but all variations include a base of cooked hominy in broth. The broth is most commonly made with chicken or pork, but vegetarian preparations exist. When the broth is meat-based, pieces of the meat used to make the broth are usually served in the final dish; vegetarian versions substitute beans for the meat.

The three main types of pozole are blanco (white), verde (green), and rojo (red). Pozole blanco—"white pozole"—is the preparation without any additional green or red sauce. Pozole verde—"green pozole"—adds a rich salsa verde based on green ingredients, possibly including tomatillos, epazote, cilantro, green chiles (typically jalapeños or serranos), or pepitas. Pozole rojo—"red pozole"—is similar, but using a salsa roja made from one or more dried or smoked red chiles, such as guajillo, piquin, or ancho, and usually tomato.

Pozole is commonly served accompanied by a wide variety of toppings, particularly raw vegetables. Common toppings include chopped onion, shredded cabbage, sliced radish, avocado, limes, oregano, tostadas, chicharrón, and chiles.

Regional customs
Pozole is also considered a festive dish. In Mexico and in New Mexico, pozole is typically served on New Year's Eve to celebrate the new year. Pozole is frequently served as a celebratory dish throughout Mexico and in Hispanic communities outside Mexico. Other occasions for serving pozole include Mexican Independence Day, birthdays, Christmas, and other holidays.

Pozole is a typical dish in various states, such as Nayarit, Sinaloa, Michoacán, Guerrero, Zacatecas, Jalisco, and Morelos. Pozole is served in Mexican restaurants worldwide. It is also popular in the cuisine of New Mexico where it is known as posole, and is a common dish among the Puebloan Indigenous peoples residing along the Rio Grande.

In the Southwestern United States, a type of field corn (posole corn) is used that differs from hominy. It is considered to be more flavorful and has a firmer texture than hominy which tends to be softer and mushier than posole. The Hopi people make a variety called noquivi (Hopi: nöqkwivi), using lamb or mutton rather than the traditional pork. It is often made from dried blue corn posole kernels; green chiles and juniper berries (instead of bay leaves) are added to the stew. This variety of posole is also prepared by the Puebloan people of New Mexico.

History

Pozole was mentioned in the 16th century Florentine Codex by Bernardino de Sahagún. Since maize was a sacred plant for the Aztecs and other inhabitants of Mesoamerica, pozole was made to be consumed on special occasions.

According to research by the Instituto Nacional de Antropología e Historia (National Institute of Anthropology and History) and the Universidad Nacional Autónoma de México, on these special occasions, the meat used in the pozole may have been human. Possible archeological evidence of mass cannibalism may support this theory, and there is widespread scholarly agreement that the Aztecs practiced cannibalism in the context of human sacrifice and warfare, though the social and dietary significance of such acts is disputed. While some authors such as Marvin Harris suggest that human flesh was a significant part of an aristocratic diet, others argue that there was not sufficient human flesh available to be a major source of proteins and that its consumption was chiefly a status symbol.

title: Pozole


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House of Obrenović

The House of Obrenović or Obrenović Dynasty (Династија Обрeновић, pl. Обрeновићи / Obrenovići, ) was a Serbian dynasty that ruled Serbia from 1815 to 1842, and again from 1858 to 1903.

They came to power through the leadership of their progenitor Miloš Obrenović I in the Serbian Uprising of 1815–1817 against the Ottoman Empire, which led to the formation of the Principality of Serbia in 1817. The Obrenović dynasty were traditionally allied with Austria-Hungary and opposed the Russian-supported House of Karađorđević.

The family's rule came to an end in a coup d’état by the military conspirators, often known today as the Black Hand, who invaded the royal palace and murdered King Alexander I, who died without an heir. The National Assembly of Serbia invited Peter Karađorđević to become king of Serbia.

Unlike other Balkan states such as Greece, Bulgaria, or Romania, Serbia did not import a member of an existing European royal family (mostly German dynasties) to take its throne; the Obrenović dynasty, like its Karađorđević rival, was an indigenous Serbian family.

List of monarchs
Unlike most other dynasties in Europe, where a regnal number is used to distinguish different monarchs who shared the same given name, the Obrenović dynasty assigned subsequent regnal numbers to each ruling prince. Thus, there was never a Milan I, Milan III, a Michael I or a Michael II. Milan II and Michael III were simply the second and third ruling prince from the Obrenović dynasty. This practice was discontinued when prince Milan IV proclaimed himself king and declared the principality of Serbia a kingdom (1882).

Male descendants of Baba Višnja

 * Baba Višnja (1737–1817)
 * Jakov Obrenović (1767–1811)
 * From whom are descended the Jakovljevićs, among whom some self-proclaimed themselves as princes in the 2010s.
 * General Milan Obrenović (c. 1770–1810)
 * Hristifor Obrenović (N/a–1825)
 * [[Image:Princely crown.svg|25px]] Prince Miloš I (1783–1860)
 * [[Image:Princely crown.svg|25px]] Prince Milan II (1819–1839)
 * [[Image:Princely crown.svg|25px]] Prince Mihailo III (1823–1868)
 * (illegit.) Velimir Mihailo Teodorović (1849–1898)
 * Prince Todor (N/a)
 * General Jovan Obrenović (1786–1850)
 * Obren Obrenović (1818–1826)
 * Prince Jevrem (1790–1856)
 * Miloš Obrenović (1829–1861)
 * [[Image:Crown of Petar I.svg|25px]] King Milan I (1854–1901)
 * [[Image:Crown of Petar I.svg|25px]] King Alexander I (1876–1903)
 * Prince Sergei (1878–1878)
 * (illegit.) George Obrenović (1890–1925)
 * Stefan Obrenović (N/a)
 * Panta Obrenović (1945–2002)
 * Stefan Obrenović (N/a)
 * Panta Obrenović (1945–2002)

Other family members

 * Ljubica Vukomanović, wife of Prince Miloš I and mother of Prince Milan II and Prince Michael III
 * Princess Anka Obrenović, daughter of Prince Jevrem Obrenović
 * Katarina Konstantinović, daughter of Princess Anka Obrenović and mistress of her cousin, Prince Michael III
 * Júlia Hunyady de Kéthely, wife of Prince Michael III
 * Natalia Konstantinović, granddaughter of Princess Anka Obrenović and wife of Prince Mirko of Montenegro
 * Elena Maria Catargiu-Obrenović, mother of King Milan I
 * Queen Natalie of Serbia, wife of King Milan I and mother of King Alexander I
 * Queen Draga of Serbia, wife of King Alexander I and former lady-in-waiting to his mother

title: House of Obrenović


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Birmingham Hodge Hill (UK Parliament constituency)

Birmingham Hodge Hill was a constituency of part of the city of Birmingham represented in the House of Commons by a member of the Labour Party since its creation and until its abolition.

Further to the completion of the 2023 Periodic Review of Westminster constituencies, the seat was abolished and replaced with new Birmingham Hodge Hill and Solihull North, first contested at the 2024 general election.

Constituency profile
The constituency covers a diverse area of east Birmingham, including the predominantly Asian inner-city area of Washwood Heath and the mostly white area of Shard End on the city's eastern boundary, as well as Hodge Hill itself. There is roughly a three-way split of social housing, privately rented and privately owned homes. The area has a high proportion of low-income households, with the constituency having one of the highest Indices of Multiple Deprivation in the West Midlands for its central area.

Boundaries
1983–2010: The City of Birmingham wards of Hodge Hill, Shard End, and Washwood Heath.

2010–2024: The City of Birmingham wards of Bordesley Green, Hodge Hill, Shard End, and Washwood Heath.

When the Hodge Hill area committee district of Birmingham was created in 2004, its boundaries were those of the constituency.

For the 2024 general election, Boundary Commission for England abolished the constituency in the 2023 Periodic Review of Westminster constituencies. Birmingham Hodge Hill and Solihull North was created as a primary successor of the constituency with bulk of abolished constituency's boundaries and minor parts transferred to Birmingham Ladywood and Birmingham Yardley.

History
The constituency was created in 1983, taking much of abolished Birmingham Stechford, the remainder of which bolstered Birmingham Yardley (principally Stechford itself). The predecessor seat was won by the Labour candidate in all but one election since its 1950 creation.

In 2004, the appointment of the sitting Member of Parliament (MP), Terry Davis, as secretary general of the Council of Europe resulted in a fiercely contested by-election. The seat saw a strong result by the Liberal Democrat candidate, who hoped to build on her party's previous by-election gain at Brent East, as well as vote splitting by the similarly aligned-to-Labour, anti-war RESPECT The Unity Coalition candidate. On a low turnout, the incumbent held the seat by a margin of 460 votes over the Liberal Democrats. The 2015 result made the seat the ninth safest of Labour's 232 seats by percentage of majority.

Members of Parliament
The current Member of Parliament is Liam Byrne of the Labour Party, who was elected in the 2004 by-election. He succeeded Terry Davis, who had held the seat since its creation in the 1983 general election. For the four years from the 1979 general election Davis held the largely predecessor constituency to the area, Birmingham Stechford.

Elections in the 2000s
Note: percentage changes are from the figures at the 2001 general election, not the 2004 by-election.

Elections in the 2010s
1: The Liberal Democrats suspended Waheed Rafiq from the party over numerous antisemitic and other offensive social media posts. It was too late to prevent him standing in the election and his name remained on the ballot paper as a Liberal Democrat. Rafiq polled the lowest percentage for any Liberal Democrat candidate in the 2019 election.


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Cayley transform

In mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things. As originally described by, the Cayley transform is a mapping between skew-symmetric matrices and special orthogonal matrices. The transform is a homography used in real analysis, complex analysis, and quaternionic analysis. In the theory of Hilbert spaces, the Cayley transform is a mapping between linear operators.

Real homography
A simple example of a Cayley transform can be done on the real projective line. The Cayley transform here will permute the elements of {1, 0, −1, ∞} in sequence. For example, it maps the positive real numbers to the interval [−1, 1]. Thus the Cayley transform is used to adapt Legendre polynomials for use with functions on the positive real numbers with Legendre rational functions.

As a real homography, points are described with projective coordinates, and the mapping is
 * $$[y,\ 1] = \left[\frac {x - 1}{x +1},\ 1\right] \thicksim [x - 1, \ x + 1] = [x,\ 1]\begin{pmatrix}1 & 1 \\ -1 & 1 \end{pmatrix} .$$

Complex homography
On the upper half of the complex plane, the Cayley transform is:
 * $$f(z) = \frac {z - i}{z + i} .$$

Since $$\{\infty, 1, -1\}$$ is mapped to $$\{1, -i, i\}$$, and Möbius transformations permute the generalised circles in the complex plane, $$f$$ maps the real line to the unit circle. Furthermore, since $$f$$ is a homeomorphism and $$i$$ is taken to 0 by $$f$$, the upper half-plane is mapped to the unit disk.

In terms of the models of hyperbolic geometry, this Cayley transform relates the Poincaré half-plane model to the Poincaré disk model.

In electrical engineering the Cayley transform has been used to map a reactance half-plane to the Smith chart used for impedance matching of transmission lines.

Quaternion homography
In the four-dimensional space of quaternions $$a+b\vec{i}+c\vec{j}+d\vec{k}$$, the versors
 * $$u(\theta, r) = \cos \theta + r \sin \theta $$ form the unit 3-sphere.

Since quaternions are non-commutative, elements of its projective line have homogeneous coordinates written $$U[a,b]$$ to indicate that the homogeneous factor multiplies on the left. The quaternion transform is
 * $$f(u,q) = U[q,1]\begin{pmatrix}1 & 1 \\ -u & u \end{pmatrix} = U[q - u,\ q + u] \sim U[(q + u)^{-1}(q - u),\ 1].$$

The real and complex homographies described above are instances of the quaternion homography where $$\theta$$ is zero or $$\pi/2$$, respectively. Evidently the transform takes $$u\to 0\to -1$$ and takes $$-u \to \infty \to 1$$.

Evaluating this homography at $$q=1$$ maps the versor $$u$$ into its axis:
 * $$f(u,1) =(1+u)^{-1}(1-u) = (1+u)^*(1-u)/ |1+u|^2.$$

But $$|1+u|^2 = (1+u)(1+u^*) = 2 + 2 \cos \theta ,\quad \text{and}\quad (1+u^*)(1-u) = -2 r \sin \theta .$$

Thus $$f(u,1) = -r \frac {\sin \theta}{1 + \cos \theta} = -r \tan \frac{\theta}{2} .$$

In this form the Cayley transform has been described as a rational parametrization of rotation: Let $$t=\tan\phi/2$$ in the complex number identity
 * $$e^{-i \varphi} = \frac{1 - ti}{1 + ti} $$

where the right hand side is the transform of $$ti$$ and the left hand side represents the rotation of the plane by negative $$\phi$$ radians.

Inverse
Let $$u^* = \cos \theta - r \sin \theta = u^{-1} .$$ Since
 * $$\begin{pmatrix} 1 & 1 \\ -u & u \end{pmatrix}\ \begin{pmatrix} 1 & -u^* \\ 1 & u^* \end{pmatrix} \ = \ \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix} \ \sim \  \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \ ,$$

where the equivalence is in the projective linear group over quaternions, the inverse of $$f(u,1)$$ is
 * $$U[p,1] \begin{pmatrix} 1 & -u^* \\ 1 & u^* \end{pmatrix} \ = \ U[p+1,\ (1-p)u^*] \sim U[u(1-p)^{-1} (p+1), \ 1] .$$

Since homographies are bijections, $$f^{-1} (u,1)$$ maps the vector quaternions to the 3-sphere of versors. As versors represent rotations in 3-space, the homography $$f^{-1}$$ produces rotations from the ball in $$\R^3$$.

Matrix map
Among n×n square matrices over the reals, with I the identity matrix, let A be any skew-symmetric matrix (so that AT = −A).

Then I + A is invertible, and the Cayley transform
 * $$ Q = (I - A)(I + A)^{-1} \,\!$$

produces an orthogonal matrix, Q (so that QTQ = I). The matrix multiplication in the definition of Q above is commutative, so Q can be alternatively defined as $$ Q = (I + A)^{-1}(I - A)$$. In fact, Q must have determinant +1, so is special orthogonal.

Conversely, let Q be any orthogonal matrix which does not have −1 as an eigenvalue; then
 * $$ A = (I - Q)(I + Q)^{-1} \,\!$$

is a skew-symmetric matrix. (See also: Involution.) The condition on Q automatically excludes matrices with determinant −1, but also excludes certain special orthogonal matrices.

However, any rotation (special orthogonal) matrix Q can be written as

 * $$Q = \bigl((I - A)(I + A)^{-1}\bigr)^2$$

for some skew-symmetric matrix A; more generally any orthogonal matrix Q can be written as

 * $$Q = E(I - A)(I + A)^{-1}$$

for some skew-symmetric matrix A and some diagonal matrix E with ±1 as entries.

A slightly different form is also seen, requiring different mappings in each direction,
 * $$\begin{align}

Q &= (I - A)^{-1}(I + A), \\[5mu] A &= (Q - I)(Q + I)^{-1}. \end{align}$$

The mappings may also be written with the order of the factors reversed; however, A always commutes with (μI ± A)−1, so the reordering does not affect the definition.

Examples
In the 2×2 case, we have

\begin{bmatrix} 0 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 0 \end{bmatrix} \leftrightarrow \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}. $$ The 180° rotation matrix, −I, is excluded, though it is the limit as tan θ⁄2 goes to infinity.

In the 3×3 case, we have

\begin{bmatrix} 0 & z & -y \\ -z & 0 & x \\ y & -x & 0 \end{bmatrix} \leftrightarrow \frac{1}{K} \begin{bmatrix} w^2+x^2-y^2-z^2 & 2 (x y-w z) & 2 (w y+x z) \\ 2 (x y+w z) & w^2-x^2+y^2-z^2 & 2 (y z-w x) \\ 2 (x z-w y) & 2 (w x+y z) & w^2-x^2-y^2+z^2 \end{bmatrix} , $$

where K = w2 + x2 + y2 + z2, and where w = 1. This we recognize as the rotation matrix corresponding to quaternion

 * $$ w + \mathbf{i} x + \mathbf{j} y + \mathbf{k} z \,\!$$

(by a formula Cayley had published the year before), except scaled so that w = 1 instead of the usual scaling so that w2 + x2 + y2 + z2 = 1. Thus vector (x,y,z) is the unit axis of rotation scaled by tan θ⁄2. Again excluded are 180° rotations, which in this case are all Q which are symmetric (so that QT = Q).

Other matrices
One can extend the mapping to complex matrices by substituting "unitary" for "orthogonal" and "skew-Hermitian" for "skew-symmetric", the difference being that the transpose (·T) is replaced by the conjugate transpose (·H). This is consistent with replacing the standard real inner product with the standard complex inner product. In fact, one may extend the definition further with choices of adjoint other than transpose or conjugate transpose.

Formally, the definition only requires some invertibility, so one can substitute for Q any matrix M whose eigenvalues do not include −1. For example,

\begin{bmatrix} 0 & -a & ab - c \\ 0 & 0 & -b \\ 0 & 0 & 0 \end{bmatrix} \leftrightarrow \begin{bmatrix} 1 & 2a & 2c \\ 0 & 1 & 2b \\ 0 & 0 & 1 \end{bmatrix}. $$ Note that A is skew-symmetric (respectively, skew-Hermitian) if and only if Q is orthogonal (respectively, unitary) with no eigenvalue −1.

Operator map
An infinite-dimensional version of an inner product space is a Hilbert space, and one can no longer speak of matrices. However, matrices are merely representations of linear operators, and these can be used. So, generalizing both the matrix mapping and the complex plane mapping, one may define a Cayley transform of operators.
 * $$\begin{align}

U &{}= (A - \mathbf{i}I) (A + \mathbf{i}I)^{-1} \\ A &{}= \mathbf{i}(I + U) (I - U)^{-1} \end{align}$$ Here the domain of U, dom U, is (A+iI) dom A. See self-adjoint operator for further details.

title: Cayley transform


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User talk:VivaRose

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title: User talk:VivaRose


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Proofs and Refutations

Proofs and Refutations: The Logic of Mathematical Discovery is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron. A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs. This gives mathematics a somewhat experimental flavour. At the end of the Introduction, Lakatos explains that his purpose is to challenge formalism in mathematics, and to show that informal mathematics grows by a logic of "proofs and refutations".

Background
The 1976 book Proofs and Refutations is based on the first three chapters of his 1961 four-chapter doctoral thesis Essays in the Logic of Mathematical Discovery. But its first chapter is Lakatos's own revision of its chapter 1 that was first published as Proofs and Refutations in four parts in 1963–4 in the British Journal for the Philosophy of Science.

Synopsis
Many important logical ideas are explained in the book. For example, the difference between a counterexample to a lemma (a so-called 'local counterexample') and a counterexample to the specific conjecture under attack (a 'global counterexample' to the Euler characteristic, in this case) is discussed.

Lakatos argues for a different kind of textbook, one that uses heuristic style. To the critics that say such a textbook would be too long, he replies: 'The answer to this pedestrian argument is: let us try.'

The book includes two appendices. In the first, Lakatos gives examples of the heuristic process in mathematical discovery. In the second, he contrasts the deductivist and heuristic approaches and provides heuristic analysis of some 'proof generated' concepts, including uniform convergence, bounded variation, and the Carathéodory definition of a measurable set.

The pupils in the book are named after letters of the Greek alphabet.

Method
Though the book is written as a narrative, it aims to develop an actual method of investigation based upon "proofs and refutations". In Appendix I, Lakatos summarizes this method by the following list of stages:

 * 1) Primitive conjecture.
 * 2) Proof (a rough thought-experiment or argument, decomposing the primitive conjecture into subconjectures).
 * 3) "Global" counterexamples (counterexamples to the primitive conjecture) emerge.
 * 4) Proof re-examined: the "guilty lemma" to which the global counter-example is a "local" counterexample is spotted. This guilty lemma may have previously remained "hidden" or may have been misidentified. Now it is made explicit, and built into the primitive conjecture as a condition. The theorem - the improved conjecture - supersedes the primitive conjecture with the new proof-generated concept as its paramount new feature.

He goes on and gives further stages that might sometimes take place:

Proofs of other theorems are examined to see if the newly found lemma or the new proof-generated concept occurs in them: this concept may be found lying at cross-roads of different proofs, and thus emerge as of basic importance. The hitherto accepted consequences of the original and now refuted conjecture are checked. Counterexamples are turned into new examples - new fields of inquiry open up.

Publication history
The 1976 book has been translated into more than 15 languages worldwide, including Chinese, Korean, Serbo-Croat and Turkish, and went into its second Chinese edition in 2007.

Impact on teaching
A number of mathematics teachers have implemented Lakatos' method of proofs and refutations in the classroom, when teaching other mathematical topics. The method has been applied to the analysis and presentation of problem  solving in mechanics by high school to college level students.

The Mathematical Association of America has included this book on a list of books that they consider to be "essential for undergraduate mathematics libraries".

title: Proofs and Refutations


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Frank Tanana

Frank Daryl Tanana (born July 3, 1953) is an American former professional baseball left-handed pitcher. In a Major League Baseball career that stretched from 1973 to 1993, he pitched for the California Angels, Boston Red Sox, Texas Rangers, Detroit Tigers, New York Mets, and New York Yankees. He struck out 2,773 batters in his career and twice won playoff-clinching games for the teams he was on, the 1979 Angels and the 1987 Tigers.

Raised in northwest Detroit, Tanana was a first-round draft pick by the Angels in 1971. He made his debut with the team in 1973 and won 14 games his rookie year. Tanana and fellow starter Nolan Ryan formed one of the toughest pairs of starting pitchers to hit against in baseball. Tanana led the American League (AL) in strikeouts in 1975, then made the AL All-Star team three years in a row. He won 19 games in 1976 and led the AL with a 2.54 earned run average (ERA) in 1977. In 1979, he won the game that clinched the Angels' first-ever playoff appearance. Injuries began to take their toll on him by the end of his tenure with the Angels, and he changed his style from relying on a hard fastball to throwing a repertoire of slower pitches, using deception to get hitters out instead.

Tanana was traded to Boston for the 1981 season; he went 4–10 with the Red Sox before becoming a free agent and signing with the Rangers. He tied for the AL lead in losses his first year with Texas, then failed to make their starting rotation at the beginning of the 1983 season, though he returned to it in June. In 1984, he had a 15–15 record for the team, his most wins since 1978. After getting off to a poor start with Texas in 1985, he was traded to Detroit, the team he rooted for growing up. Tanana would stay with the Tigers through 1992, pitching eight seasons with the club. He threw a shutout in the final game of the 1987 season to clinch a playoff spot for the team, winning 15 games that year. In 1988, he won 14 games; in 1989, he posted a 3.58 ERA. He was removed from the rotation for a time in 1990, only winning nine games that year, but the next season, he became the Tigers' first pitcher besides Jack Morris to start on Opening Day since 1979. This was the fifth Opening Day start of Tanana's career, as he had made four for the Angels in the 1970s. He won 13 games apiece in 1991 and 1992 before pitching one more season with the Mets and the Yankees in 1993.

After becoming a born-again Christian in November 1983, Tanana became a leader among baseball's Christian community. He has continued to serve in the ministry following his retirement, serving as an elder in his church, assisting the Tigers' chaplain, and performing Bible studies and marriage counselling. He lives in Farmington Hills, Michigan.

Early life
Tanana grew up in the northwest part of Detroit, Michigan. His father, also named Frank, had played professional baseball in the 1950s and was on the 1955 Eastern League championship team, the Reading Indians, before he left baseball and joined the Detroit Police Department to support his family. After young Frank got done with homework, he and his friends would spend the rest of the afternoon playing various sports. He rooted for the hometown Detroit Tigers growing up, listing Al Kaline, Mickey Lolich, Willie Horton, and Mickey Stanley among his favorite players.

Tanana attended Detroit Catholic Central High School, an all-boys school; though it was seven miles from his home, he was attracted to it after seeing their basketball team featured on the front page of a newspaper sports section. He made all-state twice in basketball, but it was in baseball he excelled, as he had a 32–1 record in his high school career. In a cocky moment his senior year, he threw sidearm to a hitter and injured his shoulder. He pitched through the injury for the rest of the year until leaving the mound after the fourth inning of the championship game, when the pain got to be too much for him. Thinking the injury would hurt his baseball chances, he had just about decided to attend Duke University on a basketball scholarship when the California Angels made him their first-round draft pick in 1971.

Minor league career
Tanana was assigned to the Idaho Falls Angels of the rookie-level Pioneer League in 1971, but tendinitis in his shoulder prevented him from pitching. Instead, he received cortisone treatments. "I tell you, I didn't have many friends on that team," Tanana said. "Here were guys being cut off the team, and I, who couldn't throw, was staying because I had this bonus." Arm feeling better in 1972, he pitched for the Single-A Quad Cities Angels, posting a 7–2 record. In 1973, he spent most of the season with the Double-A El Paso Sun Kings. "He struck out 14 in his first game for us," El Paso (and later Angel) manager Norm Sherry said. "Right then, I knew he could pitch." Tanana also pitched a couple games for the Triple-A Salt Lake City Angels before getting called up in September and added to the Angels starting rotation.

California Angels
Along with Nolan Ryan, Tanana anchored the pitching staff of the California Angels from 1973 to 1979. This led to the saying, "Tanana and Ryan and two days of cryin'", an indication of just how much the two meant to the rotation. (This was a variation on "Spahn and Sain, then pray for rain," referring to the pitchers of the Boston Braves of the late 1940s.) The duo were considered two of the toughest pitching teammates in history, drawing comparisons to Sandy Koufax and Don Drysdale of the Los Angeles Dodgers. Tanana described pitching with Ryan as "exciting," saying, "He was just an amazing athlete, and you know we both wanted to be the best pitcher on the team, so it was good for both of us—that good, healthy competition. We had a wonderful staff."

Tanana made four starts with the Angels in September 1973. His major league debut was September 9, in the second game of a doubleheader against the Kansas City Royals. Tanana only lasted four innings, giving up four runs and taking the loss. His next start, on September 14, also was against Kansas City—Tanana threw a complete game this time, only allowing two runs (one earned) to earn his first major league victory. He threw a complete game shutout in the Angels' last game of the year on September 30, allowing just two hits in a 3–0 win over the Minnesota Twins.

In his first full season, Tanana was named the Angels' number two starter, behind Ryan. An elbow injury during the season caused Tanana to lose seven games in a row at one point; Tanana could not remember losing more than two games in a row before in his career. "My confidence was taking a beating, but I knew it wouldn't last forever," he said. After losing his 19th game September 22, Tanana was in danger of losing 20 games his rookie season, as there were still seven games to go. In his next start, September 27, he gave up two runs and was losing until pinch-hitter Doug Howard drove in two runs in the seventh inning to give him and the Angels a 3–2 victory over the Minnesota Twins. Then, in the last game of the year against the Oakland Athletics, he threw a shutout in a 2–0 victory. In 39 games (35 starts) his rookie year, Tanana had a 14–19 record, a 3.12 earned run average (ERA), 12 complete games (four shutouts), and 180 strikeouts in $268 2/3$ innings pitched. The 180 strikeouts were seventh in the American League (AL) (teammate Ryan led the league with 367), the four shutouts were tied for sixth (with five other pitchers), and Tanana did not lead the league in losses, as four other pitchers tied him for third behind Lolich (21) and Clyde Wright (20).

In the first game of a doubleheader on June 21, 1975, Tanana struck out 17 batters in a 4–2 victory over the Texas Rangers, becoming the first left-hander in AL history to have that many strikeouts in a game. "Everybody stood up and applauded for me in the ninth inning," he remembered. "I felt invincible." He threw 13 shutout innings on September 22 against the Chicago White Sox, yet left with a no decision because neither Jim Kaat nor Rich Gossage had allowed a run thus far—the game would go to 16 innings before the Angels eventually won 3–0. Tanana struck out 13. At season's end, Tanana's 269 strikeouts led the American League; it would be the only time from 1972 to 1979 that anyone other than teammate Ryan, injured, led the AL in strikeouts. Tanana placed fourth in ERA (2.62), tied for third with three others with five shutouts, and had a 16–9 record on the season. He and Kaat tied for fourth in AL Cy Young Award voting after the season.

With Ryan coming off a year in which he had missed time with injury, Tanana was named the Angels' Opening Day starter for 1976. As it turned out, 1976 would be the first of four straight Opening Day starts for Tanana. He was named an All-Star for the first time in 1976. The Angels' offense did not always score a lot for him; on August 27, 1976, he and Catfish Hunter of the New York Yankees each pitched 13 scoreless innings in a game where both men received a no-decision. It was the second year in a row Tanana had thrown 13 scoreless innings without getting a decision, but the Angels would lose this one in 15, 5–0. At season's end, he was among the league leaders once again in wins (19, tied with Mark Fidrych and Ed Figueroa for fourth), ERA (2.43, behind Fidrych's 2.34 and Vida Blue's 2.35), strikeouts (261, second to a healthy Ryan's 327), and complete games (23, tied with Jim Palmer for second behind Fidrych's 24). With a 19–10 record, he came close to winning twenty games, missing the mark because of a midseason injury and also an August 22 outing against the Yankees where, having allowed only two hits going into the ninth, he started taking it easy, gave up six runs and was removed, and received a no decision, though the Angels eventually won 11–8 in eleven. As it turned out, 19 wins would be his career high. He came in third in Cy Young voting behind Palmer and Fidrych and also got votes for the AL Most Valuable Player (MVP) award.

For the second year in a row, Tanana made the All-Star Game in 1977. In July, Sports Illustrated forecasted that he might reach 25 wins on the season. From April 29 through July 3, he threw 14 straight complete games. Shortly after the streak, though, he got an inflamed tendon in his left arm and had to be shut down for almost two weeks. After he returned, his arm was still tired, and the Angels had to shut him down for the rest of the year after September 5. Still, United Press International called the 1977 season his best year. He led the AL in earned run average (ERA) (2.54) and shutouts (7) while posting a 15–9 record. His 205 strikeouts were good for third in the league, behind Ryan's 341 and Dennis Leonard's 244. He finished ninth in Cy Young voting after the season.

Tanana started the 1978 season strong, with a 1–0 shutout of Oakland on Opening Day. He was named to the All-Star Game for the third year in a row. Through the end of July, he had a 14–6 record and a 2.99 ERA. However, his numbers were not as good in his final 11 starts; though his record was 4–6, his ERA hopped up to 5.22. Still, Tanana finished the year with an 18–12 record, tying with Lary Sorensen and Fergie Jenkins for ninth in the AL in wins. He threw ten complete games and tied with four others for fifth in the league in shutouts, with four. His 3.65 ERA was the highest of his career at the time, though, and his strikeout total dropped to 137, even though he threw 239 innings.

By the end of 1978, Tanana had stopped throwing as hard, relying on changing speeds of his pitches to get hitters out instead of a devastating fastball. Though he had recovered from the tendinitis that had plagued him in 1977, fear of the pain coming back caused him to alter his delivery and go with a slower approach. After giving up six runs in two innings on June 10, 1979, against the Detroit Tigers, Tanana was shut down for a couple months with shoulder tendinitis. The injury kept him out two months of the 1979 season with a shoulder injury, but through intensive therapy, he was able to pitch in September. Limited to 18 games (17 starts), he had a 7–5 record, a 3.89 ERA, and 46 strikeouts in $90 1/3$ innings.

For the first time in Tanana's career, as well as in California's history, the Angels made the playoffs, winning the AL West, with Tanana allowing one run in a complete game against the Royals on September 25 to clinch the division for the team. Tanana started Game 3 of the AL Championship Series (ALCS) against the Baltimore Orioles, limiting them to one run through five innings. He was taken out in the sixth, though, after giving up two straight singles and a walk to open the frame. Don Aase came in and got three straight outs, but the first was a sacrifice fly off the bat of Doug DeCinces that scored a run, tying the game for the Orioles and making Tanana ineligible for the win. The Angels ultimately prevailed 4–3, but that would be their only win of the series, as Baltimore beat them in four games.

Tanana slipped to fifth in the Angels' starting rotation in 1980. After going 2–6 through the month of May, he had his turn in the rotation skipped at the beginning of June. Through June 4, he had a 7.93 ERA. After that, he pitched better for the rest of the year, with his ERA going down to 3.33 in his last 23 starts. In 32 games (31 starts), Tanana had an 11–12 record, a 4.15 ERA, and 113 strikeouts in 204 innings pitched.

Boston Red Sox
On January 23, 1981, the Angels traded Tanana to the Boston Red Sox along with Jim Dorsey and Joe Rudi for Steve Renko and Fred Lynn (who the Red Sox worried they would lose to free agency because of paperwork errors). "I stunk," Tanana summarized his performance for Boston. He pitched for the Red Sox for a single season, earning only 4 victories against 10 losses (the 10 losses tied with five others for 8th in the AL in a strike-shortened season). While his 4.01 ERA was better than the previous season, he struggled to pitch at Fenway Park, where he had a 5.36 ERA. "Anything can happen in this ballpark, like in a pinball game," he later described Fenway. He would have finished 3–10, but he threw a shutout against the Cleveland Indians on October 3 in his last start of the year (at Cleveland Stadium, not Fenway). Despite the finish, he was granted free agency by the Red Sox on November 13, 1981.

Texas Rangers
Tanana signed as a free agent with Texas Rangers on January 6, 1982. His contract was for $375,000 a year for two years, plus a $75,000 signing bonus. His first season with the Rangers, his ERA went up to 4.21, only 0.20 higher than his previous season with the Red Sox. However, the Rangers lost 98 games, and Tanana was responsible for 18 of those, tying with Matt Keough for the AL lead in losses while only earning seven wins.

For the first time in his career in 1983, Tanana was not a part of his team's starting rotation, opening the season as a long reliever for the Rangers. He had a 1.57 ERA in eight games, though, and returned to the rotation June 10, allowing one run and three hits in six innings in a 4–2 victory over the Twins. Through August 22, he had a 7–4 record, but he went on a five-game losing streak to end the year, finishing up 7–9. He appeared in 29 games (22 starts), had a 3.16 ERA, and struck out 108 in $159 1/3$ innings.

Back in the rotation for good in 1984, Tanana had his best season since 1978 for a Rangers team that finished in last place in its division. He threw eight shutout innings April 21 in a 1–0 victory over the Yankees, then threw his first shutout since 1981 on June 13 in a 3–0 victory over the Twins. He finished the season with a 15–15 record, a 3.25 ERA, and 141 strikeouts in $246 1/3$ innings pitched.

1985 did not start well for Tanana, as he posted a 2–7 record with a 5.91 ERA through his first 13 starts. Teammates were sympathetic—"He hasn't pitched the way he's capable of pitching, and we haven't played as well as we're capable of playing behind him," assessed fellow starter Charlie Hough. Tanana himself was more critical of his performance: "Awful. Absolutely awful." He was traded by the Rangers to the Detroit Tigers for minor-league pitcher Duane James on June 20, 1985.

While with the Rangers, Tanana served as the team's player representative.

Detroit Tigers
"It was a wonderful gift from the Lord," Tanana said of getting to come play with the Tigers. "I was raised here and to have the opportunity to play for the Tigers was a dream come true."

Tanana threw seven shutout innings in his debut with the Tigers June 23, 1985, helping Detroit beat the Yankees 3–1. His ERA went down with Detroit, and he won each of his last five starts. In 20 starts for Detroit, Tanana had a 10–7 record, a 3.34 ERA, and 107 strikeouts in $130 1/3$ innings pitched. In a combined 33 starts between Texas and Detroit, he had a 12–14 record, a 4.27 ERA, and 159 strikeouts in 215 innings.

On May 29, 1986, Tanana allowed one run against the Twins, coming within one out of a complete game before getting pulled in favor of Willie Hernández after allowing a double and a walk with two outs in the ninth. Twice that year, he had ten-strikeout games—the first in a 14–0 shutout of the Seattle Mariners on August 23, and the second in only seven innings on September 25, though Tanana allowed four runs and took the loss to the Toronto Blue Jays that day. In 32 games (31 starts), he had a 12–9 record, a 4.16 ERA, and 119 strikeouts in $188 1/3$ innings.

In the last year of his contract in 1987, Tanana made $662,500. He picked up his 2,000th strikeout July 12 against the Angels, though the milestone came in a 5–4 loss. Through August 6, he had a 3.40 ERA, but he struggled after that, posting a 9.00 ERA in his next eight starts and prompting manager Sparky Anderson to take him out of the rotation in September. However, Tanana only missed one start before rejoining the rotation with the Tigers in the middle of a pennant race. On the final day of the 1987 season, Tanana pitched a 1–0 complete-game shutout over second-place Toronto to clinch the American League East title for the Tigers. As the final out was recorded, a jubilant Anderson rushed to the mound, embracing and kissing his pitcher. "That game was probably the highlight of my career,” Tanana said. He went 15–7 in 34 starts as he helped the Tigers win the division, posting a 3.91 ERA and striking out 146 in $218 2/3$ innings pitched.

The Tigers faced the Twins in the ALCS; in Game 4, Tanana was matched up against Frank Viola. He allowed six hits over $5 1/3$ innings, walking four batters and giving up four runs (three earned) in a 4–3 defeat. The Twins won the series in five games.

After the 1987 season, Tanana went to arbitration with the Tigers. Seeking a two-year contract initially, Tanana ultimately received a one-year, $1.1 million deal, $300,000 more than the Tigers had wanted to pay him. Tanana won eight of his first ten decisions in 1988, matching the best start of his career (he also won eight of his first ten decisions in 1977 and 1978). His only two complete games of the year came in back-to-back starts, a win against Texas on July 29 and a loss to Kansas City August 3 when he only went eight innings due to it being a road game. In 32 starts, Tanana had a 14–11 record, a 4.21 ERA, and 127 strikeouts in 203 innings.

On June 9, 1989, Tanana struck out 10 in his first complete game of the year, but the two runs he allowed were the only runs of the game in a loss to Toronto. After Tanana beat the White Sox on August 6, 1989, Anderson praised his pitcher: "Tanana should have at least 15 wins this year. He is pitching the best for me this year since he came over here. He's a real pitcher. He knows what he's doing even when he makes a mistake." He struck out 10 in a two-hit shutout of the Orioles on August 16. Tanana's 3.58 ERA would be his lowest ever for the Tigers, save for the 20 starts he made for them in 1985. He had a 10–14 record, striking out 147 batters in $223 2/3$ innings. He became a free agent after the season but re-signed with the club a week later.

Entering his 18th major league season in 1990, Tanana had won 198 games. He gave up five runs in seven innings on April 28, against the Milwaukee Brewers, but still picked up the win, the 200th of his career. The season saw him struggle, though—he had a 6.47 ERA through July 28, prompting the Tigers to re-sign Walt Terrell to replace him in the rotation. It was during this time that Tanana got the only save of his career, inducing Oscar Azócar to hit a foul pop-up and stranding a runner on second in the 14th inning of a 6–5 triumph over the Yankees August 2. He rejoined the rotation August 25 and posted a 2.44 ERA for the remainder of the year. In 34 games (29 starts), he had a 9–8 record, a 5.31 ERA, and 114 strikeouts in $176 1/3$ innings pitched.

Following Jack Morris's departure via free agency in 1991, Tanana became the first pitcher besides him to make an Opening Day start for the Tigers since 1979, also the last year Tanana had made an Opening Day start. He gave up four runs in five innings against the Yankees, leaving with the game tied, but the Tigers beat New York 6–4. He threw a shutout against the White Sox April 18, then threw another shutout against the Angels June 7. Also, June 18, he came within one out of throwing another shutout but left after giving up two straight singles in the ninth; Mike Henneman finished a 2–0 victory over Oakland. On September 27, he became the last player to throw a pitch in the history of Memorial Stadium, allowing one run in a complete game, 7–1 victory over the Orioles. He made 33 starts for the Tigers in 1991, posting a 13–12 record, a 3.77 ERA, and 107 strikeouts in $217 1/3$ innings pitched.

Tanana posted a 7.07 ERA in his first six starts of the 1992 season, then had a start skipped after May 7. Used in relief May 12, he picked up the win against California, pitching two scoreless innings. He rejoined the rotation after that and posted a 3.96 ERA the rest of the way. There were no shutouts for Tanana in 1992, but he did throw eight scoreless innings for the win in a 6–0 victory over Texas on August 16. In 31 starts, he had a 13–11 record, a 4.39 ERA, and 91 strikeouts in $186 2/3$ innings pitched. After the 1992 season, he became a free agent.

New York Mets and New York Yankees
Tanana signed as a free agent with the New York Mets for the 1993 season. The Mets were interested in him partly as a mentor for left-handed prospect Pete Schourek. Tanana's manager with the team, Jeff Torborg, was his catcher in his MLB debut in 1973. He won seven games for the last-place team but lost 15 (tied for 6th in the National League (NL)) before being traded to the New York Yankees for Kenny Greer on September 17, as the Yankees sought pitching help in an attempt to capture the AL East pennant. Tanana lost two of his three starts for the Yankees, and they did not reach the post-season. In his last start of the season (and ultimately, his final major league appearance) on October 1, he held the Tigers to four runs (three earned) over $6 1/3$ innings and left with the Yankees leading 5–4. Bobby Muñoz blew the lead, costing Tanana the chance for the win, but the Yankees prevailed 9–6. Tanana's combined totals for the season were a 7–17 record, a 4.35 ERA, and 116 strikeouts in $202 2/3$ innings pitched. Following the year, he again became a free agent.

On February 15, 1994, Tanana signed a minor league contract with the Angels, hoping to pitch another year. He competed for a starting spot in their rotation but was released in favor of Mark Leiter after going 0–3 with a 13.50 ERA in spring training, marking the end of his professional career. In 21 seasons in the major leagues, Tanana had a 3.66 lifetime ERA.

Pitching style
In his prime, Tanana was known for a hard fastball in the mid-to-upper nineties, to go along with a devastating curveball. Arm injuries in 1977 and 1979 made him realize that he would not be able to stick around the big leagues very long if he kept throwing so hard. As a result, he altered his style, throwing less hard and developing a mixture of off-speed pitches, such as the forkball and the screwball. He mixed his repertoire of off-speed pitches very effectively, using deception rather than speed to get hitters out. "I have to change speeds and try to get ahead of the hitters in any ballpark," he summarized his style. He and others quipped that he was "the guy who threw 90 in the 70s and 70 in the 90s." The new style extended his career, and he accumulated 34 shutouts, $4,188 1/3$ innings pitched, and 2,773 strikeouts. He is one of only 26 major league pitchers to have struck out at least 2,700 batters in his career.

In a 21-year career, Tanana never had any sort of surgery on his arm. "I had sore arms, of course, that just goes right along with pitching. You're going to have sore arms on occasion." When his arm did get sore, Tanana treated it with physical therapy and strengthening exercises. In a 2019 interview, he speculated that young pitchers were having arm surgery more often because they threw too much when they were young, and they focused too much on baseball when they were young, instead of playing other sports as well during the year.

Legacy
As a result of his 21-year career, Tanana is among the career leaders in baseball history in a number of categories. His 240 wins are 58th all-time, and the second-most by a pitcher who never won 20 games in a season (Dennis Martínez won 245). His 236 losses rank 17th all-time, and he holds the AL record for most home runs allowed (422). Tanana's $4,188 1/3$ innings pitched are the 35th most in baseball history, his 1,704 earned runs allowed are 21st, and his 17,641 batters faced rank 37th.

In 1999, Tanana appeared on the Hall of Fame ballot for the first time but received no votes and thus, he was removed from future Baseball Writers' Association of America (BBWAA) consideration for election (though he could still be elected by the Veterans Committee). He has the most career WAR (57.1 according to Baseball Reference) of any player to appear on the BBWAA ballot and not receive any votes. Tanana is one of five Hall of Fame-eligible pitchers who rank in the top 25 all-time in career strikeouts and who have not been elected to the Hall. Tanana's 2,773 strikeouts rank him at number 23 all-time. Also not in the Hall of Fame are Roger Clemens (#3 with 4,672 strikeouts), Curt Schilling (#15 with 3,116), Lolich (#20 with 2,832), and David Cone (#25 with 2,668).

Tanana is in the top 10 among Angels in several categories. His 102 wins with the team are tied for fifth with John Lackey, his 3.08 ERA ranks fifth, and his 1,233 strikeouts rank fifth in franchise history. His 269 strikeouts in 1975 are still the most by a left-handed pitcher for the Angels. Tanana is one of only two pitchers in MLB history (along with Rick Reuschel) to give up a home run to both Hank Aaron and Barry Bonds, the top two players on MLB's all-time home run leaderboard.

Personal life
When Tanana first reached the major leagues, he quickly earned a reputation as a partier and drinker. He told reporters his idol was himself, that he was already one of the greatest pitchers of all-time, and that "Nothing I do awes me." After his injury in 1979, though, Tanana realized his career could be over any day. He also found himself struggling for answers following the 1978 murder of his Angel teammate Lyman Bostock. On November 6, 1983, while at an Arizona hotel room, Tanana became a born again Christian. "I understood that I was dead in my sins," Tanana said. "I realized I had no chance of having a relationship with my Holy God. But His Son, Jesus, had lived a perfect life and paid the penalty for my sin. If I trusted my life in Him and asked Him for forgiveness and asked Him to come into my life, that I would be a brand new creature. I would be a brand new person. My sins would all be forgiven. On November 6, 1983, I made that commitment of trusting in Jesus. I have walked with Him ever since."

Since then, Tanana has been a leader in the Christian community within professional baseball. He credits God for the success of his marriage and the longevity of his career. While he was still playing, he joined the Fellowship of Christian Athletes. Since retiring, he has ministered to professional athletes in a number of ways. He and his wife, Cathy, serve on the Pro Athletes Outreach Board of Directors. As of 2002, Tanana was assisting Detroit Tiger chaplain Jeff Totten, and he would also participate in Home Plate events, where Tiger players would speak about their faith in Christ at Tiger Stadium before games. Tanana has spoken about his faith at different churches. He has participated in Bible studies and performed marriage counselling since retiring. Says Tanana, "I've been fortunate and blessed the way my life has turned out."

Tanana met his wife, Cathy Mull, at a Newport Beach disco in 1977, while she was a dance major at Long Beach State University. Five hundred guests showed up at their wedding in 1978. They have four daughters—Lauren, Jill and Kari (twins), and Erin—and several grandchildren. The couple now reside in Farmington Hills, Michigan, and he is an Elder at Highland Park Baptist Church in Southfield. Frank has coached young athletes at Southfield Christian School. In 1996, Tanana was inducted into the National Polish-American Sports Hall of Fame, and in 2006, Tanana was inducted into the Michigan Sports Hall of Fame.

title: Frank Tanana


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-- Hi ! Welcome to Wikipedia! I encourage you to continue your contributions, specially on E.C..--Jondel 11:25, 7 Aug 2004 (UTC)

I'll do the best I can and thanks for the info. Say Yang 17:09, 10 Aug 2004 (UTC)

Hey look, i'm talking to myself. haha, i must really be new. testing Say Yang

title: User talk:Say Yang


text:
J. Gordon Edwards (entomologist)

J. Gordon Edwards (August 24, 1919 – July 19, 2004) was an American entomologist and proponent of the use and safety of the pesticide DDT. He was professor of entomology at San Jose State University for 40 years, and namesake to the university's entomology museum. He was an outspoken critic of Rachel Carson and efforts to ban DDT, famously eating the substance to demonstrate its safety to humans. He was also a noted mountain climber, spending nine seasons as a ranger-naturalist in Glacier National Park during the 1940s and '50s, and returning often to collect insects and map routes. His 1961 book A Climber's Guide to Glacier National Park, republished several times since, made him known as the "patron saint of climbing" in the park, where he died while hiking, aged 84.

Early life and education
J. Gordon Edwards was born on August 24, 1919, in Wilmington, Ohio, to parents Gus and Evadne Edwards (née Spears). He was named after the silent film director J. Gordon Edwards. He grew up in Indianapolis, Indiana, and joined the Boy Scouts at age 12. He studied botany at Butler University, Indiana, graduating in 1942, then enlisted in the United States Army during World War II, serving as a combat medic with the 95th Infantry Division in Europe. He wrote about eradicating bed bugs in the barracks, and dusting personnel with DDT to control body lice and prevent typhus. He was discharged from the military after the 1945 bombings of Hiroshima and Nagasaki, having spent nearly four years with the army.

His graduate education was at Ohio State University, where he earned his MS degree in 1946 and his PhD in Entomology in 1949. He also worked as an ornithological assistant to Donald J. Borror. At Ohio State he met Alice Althaus and they were married on October 13, 1946.

Entomology
In 1949 Edwards joined the faculty of San Jose State University (then San Jose State College), where he was professor of entomology until his retirement in 1990, after which he continued research and teaching as professor emeritus. He specialized in beetles, and published several articles on the insects of Glacier National Park. He was elected a life fellow of the California Academy of Sciences in 1977, and served as president of the Pacific Coast Entomological Society in 1948 and 1953, elected as honorary member in 1993. During his career he supervised 90 master's students in entomology, including scientists such as Terry L. Erwin, who credits Edwards with inspiring his interest in entomology. To students and friends he was widely called "Doc". In 1991 the university's entomology museum was dedicated to him and renamed the J. Gordon Edwards Entomology Museum. He is commemorated in the scientific names of the beetles Bembidion edwardsi and Nebria arkansana edwardsi. Dr. Michael Ivie, past president of the Entomological Society of America, calls Edwards an "unsung mentor", writing that despite his influence he is little-known among entomologists beyond his students, a trait Ivie attributes to his teaching at a non-PhD granting university. In 2007 The Coleopterists Society established the annual J. Gordon Edwards Prize for the best published paper based on a Master's Thesis dealing with beetles.

DDT and environmental issues
Edwards was a prominent supporter of the use of DDT and critic of Rachel Carson. He claimed that bans of DDT were not based on good science, and accused environmentalists of politicizing issues regarding pesticides. He was active as a member of, or consultant for, a wide range of lobby groups opposed to environmental regulation, including the American Council on Science and Health. According to Edwards, he was also active as a member of several environmental groups, such as the Sierra Club (which published one of his books), and the Audubon Society. Edwards was a fellow of the California Academy of Sciences. He published his ideas in 21st Century Science and Technology, a publication of the Lyndon LaRouche Movement. Edwards last work, titled DDT: A Case Study in Scientific Fraud was published in 2004 after his death in the fringe partizan Journal of American Physicians and Surgeons, in which he makes the impassioned plea "The ban on DDT, founded on erroneous or fraudulent reports and imposed by one powerful bureaucrat, has caused millions of deaths, while sapping the strength and productivity of countless human beings in underdeveloped countries. It is time for an honest appraisal and for immediate deployment of the best currently available means to control insect-borne diseases. This means DDT."

In 1971 he gave testimony before the Congressional House Committee on Agriculture which was widely cited and circulated, despite having published no scientific papers on DDT or birds at the time.

In the 1970s Edwards was involved in a libel suit against the New York Times and the National Audubon Society. In April 1972, Robert Arbib Jr., the editor of the Society's American Birds journal, wrote in an editorial that representatives of pesticide industries and "paid 'scientist-spokesmen were misleadingly using data from Christmas Bird Count to claim that bird populations were increasing despite the usage of DDT, and that apparent increases in songbirds were the result of more birdwatchers rather than more birds. Arbib did not name any individuals in his article, but when contacted by the Times, said they included Edwards, Thomas H. Jukes, and Robert H. White-Stevens, among others. Edwards, Jukes, and White-Stevens sued the Times for libel, and in 1976 were awarded $61,000, a ruling that was overturned the following year by a Federal appeals court citing freedom of the press to report on public figures.

Mountaineering
Edwards was a seasonal park ranger-naturalist in Glacier National Park for nine years beginning in 1947, and returned almost every summer in the years afterward for research. He spent much of his free time exploring the rugged terrain of the park, and pioneered many different routes up a variety of its spectacular mountains. In 1961 he produced A Climber's Guide to Glacier National Park, published by the Sierra Club, which quickly became a classic work, the definitive mountain guide to the park. I The book was revised and reprinted in the 1970s, 1990s, and as recently as 2017. In the foreword to its 1995 edition, Rolf Larson gave him the unofficial title of "patron saint of climbing" in the park. Ansel Adams personally gave Edwards permission to use his iconic photographs in the book. Edwards was also a founding member of the Glacier Mountaineering Society, a group that publishes an annual climbing journal and continues to be active in organizing hikes and climbs throughout the park.

On July 19, 2004, Edwards died of a heart attack at the age of 84 while hiking up Divide Mountain on the eastern edge of Glacier National Park with his wife, Alice. A memorial issue of the Glacier Park Foundation's newsletter called him "a legendary mountaineer and one of the most distinguished and famous figures in Glacier's history". He had a daughter, Jane who died in 2005, followed by his wife in 2015.

Books

 * Coleoptera or Beetles East of the Great Plains (1949) Edwards Bros.
 * A Climber's Guide to Glacier National Park (1961)
 * Insects (with Matthew F. Vessel and Herbert H. Wong) (1971) Fearon. Western Environmental Science Series

title: J. Gordon Edwards (entomologist)


text:
Luis Brandoni

Adalberto Luis Brandoni (born 18 April 1940) is an Argentine actor and politician.

Biography
Brandoni was born in Dock Sud, a port community east of Avellaneda. He debuted on the stage in 1962, television in 1963, and on film in 1966. He joined the National Comedy Theater in 1964 under the direction of Luisa Vehil.

Politically active in the centrist Radical Civic Union (UCR) party, he also served as cultural policy adviser for President Raúl Alfonsín (1983–89), and was elected to the Argentine Chamber of Deputies in 1993, where he served until 2001. He was an unsuccessful Argentine Senate candidate for the UCR in 2005, and for Vice Governor of Buenos Aires Province, with nominee Ricardo Alfonsín, in 2007.

An actor with extensive film, television and theatre credits, he portrayed leading roles in acclaimed pictures such as La tregua (1974), Juan que reía (1976), Darse cuenta (1984), Esperando la carroza (1985), Made in Argentina (1986), Cien veces no debo (1990), Convivencia (1993), Una sombra ya pronto serás (1994), De mi barrio con amor (1995), and Los pasos perdidos (2001).

His career remained strong during 2011: among his notable theatre credits was his portrayal of former President Arturo Illia; and his notable television credits included a costarring role in Telefé's sitcom El hombre de tu vida, together with Guillermo Francella and directed by Juan José Campanella. He also starred in Gastón Duprat & Mariano Cohn's comedy film Mi obra maestra (2018), together again with Guillermo Francella. He is currently set to star in the Star+ TV series Nada, which will be released in 2023. Cohn & Duprat wrote and directed the series, which features a supporting cast that includes Robert De Niro.

Brandoni also served in numerous actors' guilds, including the International Federation of Actors (IFA) as its Vice President, between 1974 and 2004.

Awards
Brandoni has won several awards, including four Martín Fierro Awards (1970, 1993, 1995 and 2017); and two Argentine Film Critics Association Silver Condor awards for Best Actor for his roles in Seré cualquier cosa pero te quiero and Convivencia.

Personal life
Brandoni was married to actress Marta Bianchi, and in 2007 married Mónica López.

Controversies
In July 2017, the Argentine Association of Actors issued a harsh statement criticizing Brandoni for some statements made at the time on the television program Intratables, where he described as "verse" (meaning "false") the current denomination of "civil-military" regarding Argentina's last dictatorship, while denying there was any important civilian participation or decision-making in the military government of the dictatorship.

title: Luis Brandoni


text:
Jaguar AJ6 engine

The AJ6 (Advanced Jaguar 6-cylinder), and the similar AJ16, are inline-6 piston engines used by Jaguar cars in the 1980s and 1990s. The AJ6 was designed to replace the successful and long-used Jaguar XK6 engine, and was introduced in 1984. It was only the third all-new engine ever designed by the company. The AJ16 evolution was replaced in 1996 with the Jaguar developed AJ-V8 engine.

Jaguar had considered cutting their existing V12 in half to build a V6, or possibly a V8, but chose instead to develop a new inline six. The cylinders are inclined, as in a slant-6, by 22 degrees. It uses an aluminium block to reduce weight, and has an optional DOHC head for higher efficiency and power.

AJ6
The original engines were the DOHC 3.6 and the SOHC 2.9. The DOHC 3.6 was revised and enlarged to 4.0 in 1990. It is still essentially an "AJ6", however. This was, as per usual, offered for the XJ-S before it was built into the XJ40 saloon.

3.6
The 3590 cc was the first AJ6 engine, debuting in 1983 on the XJ-S. It had DOHC 4-valve heads with a 91x92 mm bore and stroke. Power was 165 kW with 325 Nm of torque. Power was reduced to 201 hp for versions having catalytic exhaust system. Early versions of the 3590 cc AJ6 as used in the 1984 - 1987 XJ-S cars had a conventional distributor type of ignition system with electronics within the distributor body. This early AJ6 ignition system is nearly identical to the system used on the XK engine in the Series III XJ6 cars. The Lucas fuel injection system on the 3590 cc AJ6 engines in these early XJ-S cars sensed engine load using a Manifold Absolute Pressure (MAP) sensor just like the V12 cars from the same era. Later 3590 cc AJ6 engines as used in the 1986–1989 XJ40 cars had a crank-sensor type of ignition system with a bare distributor that only carried the spinning ignition rotor inside the distributor cap. The fuel-injection system used on the later 3590 cc AJ6 engines used a hot-wire Mass Air Flow sensor to determine engine load.

Vehicles using the 3.6 were:
 * 1984–1989 Jaguar XJ-S
 * 1986–1989 Jaguar XJ6
 * 1986–1989 Jaguar XJ6 Sovereign
 * 1986–1989 Daimler

2.9
The 2919 cc used a SOHC head from the Jaguar V12 engine, and was prone to failure. The block is the same as the 3.6, with the crankshaft and pistons lowering the stroke to 74.8 mm. Only the 1986–1989 Jaguar XJ6 used the 2.9. It was used for the entry-level XJ6 in Britain and Europe but rarely, if ever, seen in models exported to the US. The SOHC 2.9, which was generally considered somewhat underpowered for such a large car, was discontinued in late 1990 and replaced with a DOHC 3.2 (essentially identical to the DOHC 4.0).

The 2.9 Engine was, as in earlier years the 2.8 XK-engine, sized to match road-tax regulations in some European Countries like Italy or France. In France cars with more than 3 litres of engine size had to pay a luxury tax.

Unlike all other AJ6's, the 2.9l used Bosch LH Jetronic fuel injection and EZ-K ignition (rather than Lucas 9 or 15CU EMS)

4.0 (1989–1994)
The 24-valve DOHC 3980 cc version replaced the 3590 cc AJ6 in 1989. It featured a longer 102 mm stroke, and generated 183 kW power at 4,750 rpm and 392 Nm of torque at 3,650 rpm. The 3980 cc engines as used in the 1990–1994 XJ40 cars continued with the crank sensor and empty distributor type of ignition system and the hot-wire Mass Air Flow sensor type of fuel injection control system as the 1988–1989 3590 cc XJ40 cars.

TWR modified XJ40s resulting in the XJR. Jaguarsport was also formed as a partnership between TWR and Jaguar. The first XJR, the XJR 3590 cc, had extensive appearance changes coupled with stiffer suspension, anti-roll bar/links, power steering valve that reduced efficiency by 40% and an LSD but no performance enhancements. Interior-wise it included special stitching, "sport" or "XJR" embossed front headrests, and Jaguarsport speedometer labels and tread-plates.

1990 XJRs had the upgraded 3L engine with the old style body-kits, and appearance changers.

XJR 1.0Ls from 1990 on had all of the XJR 3.6 handling upgrades and benefits from engine enhancements such as high lift cams, improved double plenum inlet manifold, and a compression ratio of 9.75:1. They were sent to TWR in Coventry to be modified directly after being produced.

The exterior changed again for the last generation of the XJ40 XJR (from H-registration year onwards). Bodykit was re-sculptured and the boot spoiler was deleted. Side mouldings were added, with the smaller "XJR" badge embedded in them. Engine had a plaque saying "Jaguarsport XJR 4L" on the rocker cover. XJR badge size was decreased on the boot (had previously ranged from XJR-3.6, XJR-4L, 4-litre and "XJR". The later one ("XJR") is most common and the only badge that could be chosen on the boot infill panel models. A "sport" one on the front within its own unique XJR grill. In this unique grill a "sport" badge was installed. Interior even had XJR specific wood (SPB part number).

Total XJ40 cars built was 208,733 and supposedly 500 JaguarSport cars built, 200 of the round headlight versions and then about 300 with the square headlights like the Sovereigns and Daimler's. 1990+ XJR power output is around 250 bhp / 278 lbft.

The prototype Jaguar XJ41/42 sports car used a twin-turbo version of the AJ6 4.0, developing 330bhp.

3.2 (1990–1994)
A 24-valve DOHC 3239 cc, essentially a shorter-stroke of 83 mm 3980 cc, replaced the 12-valve SOHC 2.9 in 1990. It produced 149 kW of power at 5,250 rpm and 298 Nm of torque at 4,000 rpm, and proved a popular engine in Europe (sales outnumbered 3980 cc saloons roughly 4:1) but was not exported to America.

Following the launch of the Aston Martin DB7, the Jaguar AJ6 was used by Aston Martin as well (both companies being owned by Ford at the time). This version featured an Eaton supercharger.

Cars using the 4.0 and 3.2 included:
 * Jaguar XJS (4.0 only)
 * Aston Martin DB7 (modified, supercharged 3.2)
 * Jaguar XJ6
 * Jaguar Sovereign
 * Jaguar XJR (4.0 only)
 * Daimler Six

AJ16
Both the 3.2 and 4.0 were substantially revised for the 1995 launch of the renewed Jaguar XJ (X300) saloon. These are the "AJ16" engines, both featuring coil-on-plug distributorless ignition, new engine management systems, magnesium alloy valve covers, revised pistons and other detail changes. The AJ16 was discontinued with the launch of the AJ-V8 (XK8 and XJ8 in 1996/7).

4.0 / 3.2 (1994–1997)
For the launch of the new X300 saloon for 1995, substantial revisions were made to the 3980 cc and 3239 cc AJ6 engines. The new design was called the AJ16 to reflect the major differences between it and the original AJ6.

Cars using the 4.0 and 3.2 included:
 * Jaguar XJS (4.0 only)
 * Jaguar XJ6
 * Jaguar XJ6 Sovereign
 * Jaguar XJ6 Sport
 * Daimler

AJ16S
A supercharged version of the 3980 cc AJ16 was released in 1994 in the Jaguar XJR which used an Eaton M90 blower to boost output to 240 kW and 512 Nm

title: Jaguar AJ6 engine


text:
Category:Jaguar engines

This category is for engines designed by Jaguar Cars.

title: Category:Jaguar engines


text:
User talk:Rgarvage

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title: User talk:Rgarvage


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Patricio Contreras

Patricio Contreras (born December 15, 1947) is a Chilean-Argentine television, film and stage actor.

Biography
Contreras was born in Santiago, Chile in 1947 and emigrated to neighboring Argentina following the 1973 coup d'état against left-wing President Salvador Allende, of whom Contreras was a vocal supporter. He was shortly afterwards cast in a number of minor Argentine cinema roles, notable among them a part in Adolfo Aristarain's 1978 crime thriller, La parte del león (The Lion's Share).

He married an up-and-coming Argentine actress, Leonor Manso, in 1981, and in 1983, he was given his first significant film role as the treacherous Sergeant Comini in Aristarain's Funny Dirty Little War. Contreras then gave what became perhaps his best-known performance as the targeted Professor Benítez in the Oscar-winning The Official Story (1985), for which he was awarded a Silver Condor. This was followed a leading role in Juan José Jusid's emotional look at exile, Made in Argentina (1986), which earned Contreras a Havana Film Festival Best Actor Award.

He appeared next to Gregory Peck and Jane Fonda in the 1989 movie Old Gringo. He starred in fellow Chilean exile Miguel Littín's Sandino (1990), and the end of General Augusto Pinochet's dictatorship in 1990 allowed Contreras to return to Chile itself, where he starred as the lead in Ricardo Larraín's La Frontera (1991). Continuing to live and work in Argentina, he starred in Betty Kaplan's adaptation of Chilean writer Isabel Allende's Of Love and Shadows (1995), and to his film credits were added those in the local theatre, notably his work in a local, 1996-98 production of Samuel Beckett's Waiting for Godot (directed by his wife). His marriage suffered, however, and the couple were divorced in 2001. Among Contreras' later film roles some of the best-known are as writer Rodolfo Walsh's version of Hercule Poirot in Santiago Carlos Oves' Asesinato a Distancia (Murder at a Distance, 1998), and as the merciless detective in Eduardo Mignogna's fact-based La fuga (The Escape, 2001). He was reunited with his ex-wife for the stage in 2007 in her production of Sarah Kane's Blasted.

Contreras continues to live in Buenos Aires and remains a prolific film and stage actor.

title: Patricio Contreras