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Household responsibility system

The household responsibility system, or contract responsibility system, was a practice in China, first adopted in agriculture in 1979 and officially established in 1982, by which households are held responsible for the profits and losses of an enterprise. This system, which came to replace collective farming, maintained public ownership of land and some of the means of production, but made production the responsibility of households. Households still had to contribute to state quotas but could make their own decisions about what to plant on contracted land and could sell via a multi-tier price system that included the lowest price for payment to the state up until the quota, a higher rate for above-quota sales to the state, and market price for crops allowed to be sold at fairs.

Overview
The household responsibility system replaced collective farming. In the household responsibility systems, households contributed to state quotas but could also make their own decisions about what to plant on contracted land and could sell via a multi-tier price system that included the lowest price for payment to the state up until the quota, a higher rate for above-quota sales to the state, and market price for crops allowed to be sold at fairs. This was enabled by three policy changes: (1) the state increased the price it paid to purchase staple crops, as well as some other agricultural products, (2) the state reduced the number of agricultural products which were subject to state monopsony and monopoly, and (3) the state reestablished rural markets for produce and other commodities.

Agricultural production increased under the household responsibility system, which in Chinese Marxist discourse was described as liberating the productive forces.

1977–1978: Preparation period
By the late 1970s, China's collectivization and centralization of agricultural production faced several challenges, of which the shortage of agricultural products was the most urgent and serious. Droughts in rural areas resulted in serious food supply crises in urban regions. Many farmers and members of the People's Commune began thinking about new ways of agricultural production. In 1978, 18 households in Xiaogang, Anhui came up with a new arrangement where each household was responsible for their profit and losses of production, which was known as the first trial of the household responsibility system.

In December 1978, the Third Plenary Session of the 11th Central Committee of the Chinese Communist Party was held in Beijing. During the meeting, the Decision of the Central Committee of the Communist Party of China on Accelerating Agricultural Development was passed, which proposed "devolving production responsibility to production units" (包产到组). However, the policy still prohibited delegating production responsibility to households (包产到户).

Initially, these policies were only allowed as an exception applicable to poor and remote areas where peasants struggled for subsistence. A political disagreement developed over whether household contracting should also be permitted in places where collective farming had performed well. Opponents of household contracting included leaders who believed it would be a backwards step ideologically, as well as provincial leaders who anticipated that household contracting would weaken mechanized agricultural production.

1979–1981: Struggling back and forth
In early 1979, the National Agriculture Council was founded, which started a heated debate over whether China should adopt the household responsibility system within the Chinese central government. In March 1979, the National Agriculture Council held the Seven Provinces and Three Counties Meeting on Agriculture Development, during which the majority of representatives displayed a supportive attitude towards this proposal. However, the opposing voices were also strong. Wang Renchong, the Head of the National Agriculture Council, kept emphasizing the advantages of the collective economy and opposing the idea. In the end, Hua Guofeng, the Chairman of the Chinese Communist Party at the time, concluded that collective production did work, yet a certain amount of flexibility was also needed. Also, Hua Guofeng agreed that "for the impoverished households in remote regions, it is appropriate to delegate to them the responsibility and rights for their production." Hua Guofeng's words were written into the official documents of the Central Committee of the Chinese Communist Party and it was the first time that the idea of household responsibility system appeared in the official document of the Central Committee of the CCP.

In January 1980, the People's Communes Management Meeting was held in Beijing. In the meeting, Zhou Yueli, the Director of the Agricultural Committee of Anhui Province, introduced the system of agriculture development in Anhui. Zhou reported that by the end of 1979, 51% of production teams had adopted the production unit responsibility system, and 10% had adopted the household responsibility system; there was a significant production growth and 25% of the underdeveloped regions asked to adopt the household responsibility system. However, Zhou's idea received severe criticism from many representatives from other regions and provoked a huge debate over whether the household responsibility system was the right approach to take. In the end, Deng Xiaoping concluded the debate with the observation that household responsibility was a highly complicated and critical issue, and that it was unlikely to reach a simple conclusion.

While the central government was still struggling with the idea, going back and forth, more and more villages went ahead and started adopting the household responsibility system. In 1979 the system was only adopted as a trial in a few regions, but in 1980, more and more places learned from these regions and developed their own household responsibility system. The growing trend caught the attention of the central leadership of China and also led the decision-makers to a reconsideration of what agricultural production system should be adopted.

In April 1980, at the Long-term Planning Meeting of the Central Committee of CCP, Deng Xiaoping argued: "In underdeveloped and impoverished regions such as Northwestern China, Guizhou, and Yunnan province, approaches such as household responsibility system should be adopted". During another speech in May, Deng Xiaoping supported the practice of Fengyang County and Feixi County of Anhui province and said that "[s]ome colleagues worried that to practice this kind of system might hamper the development of the collective economy. I think these worries are unnecessary. Our overall direction is developing a collective economy. As long as the productivity increases and the division of labor and commodity economy develop, our collective economy will grow from a low level to a high level."

Besides the positive attitude towards the household responsibility system of Deng Xiaoping, the National Agriculture Council also conducted intense field research in Henan, Hebei, and other provinces to better understand the effectiveness and challenges of adopting the system. From 1980 to 1981, more and more collective agricultural production systems were transformed into household responsibility systems. By 1981, 51% of the households in Southeast provinces and Shandong province had already adopted the household responsibility system.

1982: Official establishment
In December 1981, the National Agricultural Work Meeting was held in Beijing, which emphasized the idea of letting people choose by themselves which systems to use. Soon later in 1982, the Central Committee of the CCP announced its "No.1 document" for the year, Minutes of The National Agricultural Work Meeting, which officially established the household responsibility system for China's agricultural production.

The household responsibility system achieved "total victory" in 1983. The reluctance of the leadership of some provinces to adopt the system was overcome by studies showing that the peasants strongly favored being responsible for their own production, which provided important support for Premier Zhao Ziyang's approach of "letting the masses decide for themselves in which way they want to organize the production."

The system was rapidly adopted nationwide and significant agricultural growth was witnessed. During the 20 years of collective agricultural production, the annual agricultural output was 30-50 billion kilograms, yet by the time of 1984, the number increased to 400 billion kilograms. At the same time, the overall agricultural GDP increased by 68% and the average income of farmers increased by 166%.

Another success of the household responsibility system was its price stabilization effects for peasants. By 1984, the supply of grain had increased so much that the price paid by the state for the grain quote and above-quota procurement were both higher than the market price for grain. Thus, "selling the quota at the planned price was no longer a tax but a subsidy for the peasants, and selling the surplus above the quota to the state protected the peasants from bearing the whole burden of the falling market prices." Peasants were simultaneously encouraged to increase agricultural productivity while being protected from the fall of market prices caused by the production boom. The price stabilization effects of the household responsibility system's multi-track pricing were an intentional design to regulate agricultural output through state participation in the market.

The success of the household responsibility system signified a significant transition in China's economic model and opened a new era of China's agricultural economy and rural development.

Recent analyses
According to a 2021 study, the household responsibility system improved individuals' later-life health, education, and labor market outcomes, but it reduced human capital investment in children, making them less likely to receive education and more likely to remain in agriculture.

title: Household responsibility system


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Briertone

Briertone was a band from the Central Coast of California. They combined indie, Southern rock and bluegrass elements to create a musical style that they referred to as "outlaw rock." The band formed in 2002 and ceased in around 2013.

Their first three of EPs were released on independent label Something Sacred Recordings. Their fourth EP, "Sky's Torn Open" was released independently on October 14, 2011.

Band members

 * Adam Pasion - vocals, guitar, mandolin, fiddle
 * Matt Black - guitar, vocals
 * Elijah Merritt - banjo, keys, guitar, mandolin, vocals
 * Bobby Lucy - drums, vocals
 * Robbie English - bass

Former members

 * Taylor Odenwald - bass, guitar, banjo
 * Lane Biermann - drums
 * Roger Tompkins - bass
 * Gabe Munoz - bass
 * Chris Nielsen - guitar, vocals, mandolin.
 * Caleb Ralph - bass, vocals
 * Kurtis Heck - guitar
 * Mike Newsom - bass
 * Aaron Wick - drums
 * Addison Francisco - guitar, vocals
 * Cory O'Keefe - drums
 * Brandon Gatlin - keys, pedal steel
 * Andrew Redel - bass
 * Emily Wilson - vocals, keys

Discography

 * Tumbleweed EP (2003)
 * Confessions Of The Wicked EP(2004)
 * Sojourners EP (2006)
 * Sky's Torn Open EP (2011)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Briertone


text: Category:User jbo-3

title: Category:User jbo-3


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Halle Open

The Halle Open is a men's tennis tournament held in Halle, North Rhine-Westphalia, Germany. Held since 1993, the event is played on four outdoor grass courts and is a part of the ATP Tour 500 series on the ATP Tour schedule.

Between 1993 and 2018 it was sponsored by Gerry Weber. It was sponsored by Noventi from 2019 to 2021. In December 2021, a change of primary sponsor and name was announced. For the years 2022 and 2023, the tournament will be known as the Terra Wortmann Open.

The Halle Open is held at the same time as the Queens Club Championships, and the two are seen as the primary warm-up tournaments for the Wimbledon Grand Slam tournament, also on grass courts, which begins towards the end of June. The event was upgraded in 2015 from a 250 series to a 500 series tournament.

The Centre Court (the OWL Arena) has 12,300 seats and a retractable roof which can be closed in 88 seconds so that tennis matches can continue with a closed roof when it begins to rain. The stadium is heated and also used for other sport events (handball, basketball, volleyball and boxing) and concerts.

Past finals
In singles, Roger Federer (2003–06, 2008, 2013–15, 2017, 2019) holds the record for most overall titles (ten, out of thirteen finals), and most consecutive titles (four, in 2003–06). In doubles, Raven Klaasen (2015–16, 2019) and Marcelo Melo (2017–18, 2023) co-hold the record for most titles with three each, and co-hold the one for consecutive titles with Aisam-ul-Haq Qureshi (2011–12), Rajeev Ram (2015–16), Łukasz Kubot (2017–18) and Melo (2017–18), at two.

title: Halle Open


text: User talk:65.172.237.171

title: User talk:65.172.237.171


text:
Keratoderma blennorrhagicum

Keratoderma blennorrhagicum etymologically meaning keratinized (kerato-) skin (derma-) mucousy (blenno-) discharge (-rrhagia) (also called keratoderma blennorrhagica) are skin lesions commonly found on the palms and soles but which may spread to the scrotum, scalp and trunk. The lesions may resemble psoriasis.

Keratoderma blennorrhagicum is commonly seen as an additional feature of reactive arthritis in almost 15% of male patients. The appearance is usually of a vesico-pustular waxy lesion with a yellow brown colour. These lesions may join to form larger crusty plaques with desquamating edges.

title: Keratoderma blennorrhagicum


text:
User:Dave Sims

Dave Sims a maverick: Born February 23 and is from Longwell Green in Bristol (United Kingdom) in the South West of England.

title: User:Dave Sims


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Wermelskirchen

Wermelskirchen (Ripuarian: Wärmelßkirrshe) is a town in the Rheinisch-Bergischer Kreis, in North Rhine-Westphalia, Germany, southeast of Remscheid. It is home to one of Europe's biggest live Christmas trees (measuring 26m).

Geography
The distance to Cologne is about 35 kilometers, to Düsseldorf about 45 kilometers. The neighboring municipalities are Remscheid, Hückeswagen, Wipperfürth, Kürten, Odenthal, Burscheid and Solingen. The townscape is characterized by Altberg slate and half-timbered houses.

Coat of arms
The coat-of-arms of the city of Wermelskirchen looks like a silver shield split into thirds. In the left field is an oak tree. In the right field there is a Swan and pictured in the middle field there is a church.

History
From 1822 to 1945, Wermelskirchen was part of the Prussian Rhine Province.

Education
Wermelskirchen has an Evangelical, a Roman Catholic church and a Latin school.

Economy
The city has the head office of OBI and the origin of the caster manufacturer TENTE.

Twin towns – sister cities
Wermelskirchen is twinned with:
 * 🇩🇪 Forst, Germany
 * 🇫🇷 Loches, France

Notable people

 * Carl Leverkus (1804–1889), founder of a German chemical and pharmaceutical company and the namesake of the city of Leverkusen
 * Uwe Boll (born 1965), film director and writer, restaurateur and founder of Bauhaus Restaurant chains in Canada
 * Tim Schrick (born 1976), racecar driver, and television presenter
 * Thomas Kleine (born 1977), footballer
 * Christian Lindner (born 1979), politician and Federal Minister of Finance (2021–present)

Honorary citizens

 * 1876: Ludwig von Bohlen
 * 1889: Carl Leverkus
 * 1895: Otto von Bismarck
 * 1933: Paul von Hindenburg

title: Wermelskirchen


text:
Talk:Robb Nen

Speed of his fastball
I thought I remembered hearing that his fastball has been clocked at 101 before. Is this true? I know he was quite the flamethrower, and I tend to think of him as being similar to pitchers like Kyle Farnsworth... --Idont Havaname 20:10, 4 October 2005 (UTC)

Picture
Can we add a picture of Rob Nen I know we have a picture of him somewhere that we can add —Preceding unsigned comment added by Yoctownyocol1 (talk • contribs) 23:13, 11 October 2010 (UTC)

Assessment comment
Substituted at 01:12, 12 June 2016 (UTC)

title: Talk:Robb Nen


text:
Lewis Nixon III

Lewis Nixon III (September 30, 1918 – January 11, 1995) was a United States Army officer who, during World War II, served at the company, battalion, and regimental level with the 506th Parachute Infantry Regiment, 101st Airborne Division. Nixon was portrayed in the HBO miniseries Band of Brothers by Ron Livingston.

Early life
Lewis Nixon was born to Stanhope Wood Nixon and Doris Ryer Nixon on September 30, 1918, in New York City. He was the grandson of shipbuilder Lewis Nixon I (1861–1940) and Sally Wood Nixon (died 1937). At age seven, Lewis took third place in the model yacht regatta at Conservatory Lake in Central Park on May 22, 1926, earning a gold and bronze medal in the 35 in boat class. As a youth, Nixon lived in New York City and Montecito, California; he traveled the world extensively, visiting Germany, France, and England. Nixon graduated from Cate School in Carpinteria, then attended Yale University for two years.

Military service
Nixon was selected (inducted) into the United States Army on January 14, 1941, in Trenton, New Jersey. After graduating from Army Officer Candidate School in 1941 as an infantry second lieutenant, he volunteered for the parachute infantry, part of the U.S. Army's fledgling airborne forces. He was assigned to E Company, 2nd Battalion, 506th Parachute Infantry Regiment (506th PIR). The regiment was commanded by Colonel Robert Sink. The 506th was an independent regiment until June 1943, when it became part of the 101st Airborne Division. Nixon went through the regimental unit training and pre-airborne training at Camp Toccoa, Georgia, and Airborne School at Fort Benning, eventually training at many locations throughout the United States. In September 1943, he was sent with the 506th to Aldbourne, Wiltshire, England, in preparation for the Allied invasion of Normandy.

Nixon was appointed as the 2nd Battalion intelligence officer (S2). He and the 506th parachuted into Normandy on June 6, 1944. Shortly after Easy Company fought in the Battle of Carentan on June 12, 1944, he was moved up to the regimental level as the 506th S2. He served in the Netherlands, Belgium, and Germany. In the Netherlands, he was hit by a bullet from a German MG 42 machine gun. The bullet went through his helmet, grazed his forehead, and left a small burn mark. He developed a drinking problem, and was eventually removed and assigned back down to the 2nd Battalion as the operations officer (S3), where he continued to display his skill at planning and operations, but did not have to deal with the politics and high visibility at the regimental level. In Berchtesgaden, he had first choice of an extensive captured wine collection originally assembled at Hermann Göring's orders, comprising bottles stolen from wineries across France and other European occupied territories.

Nixon was one of the few men of the 101st Airborne to jump with another division or regiment. On March 24, 1945, Nixon was assigned by Major General Maxwell Taylor, the commanding general of the 101st, to be an observer with Major General William Miley's 17th Airborne Division during Operation Varsity, the airborne crossing of the river Rhine. Nixon's plane took a direct hit and only he and three others got out. He is also one of very few men in the 101st to earn three Combat Jump Stars on his Jump Wings.

Nixon saw the defeat of Germany and ended World War II with the rank of captain. Nixon never fired a shot in combat, though he spent much time on the front lines during intense close fighting. He returned home in September 1945.

Nixon was remembered as always having a source of whisky no matter where the company was, and in particular for his love of the blended whisky Vat 69, as noted in the book Band of Brothers by Stephen E. Ambrose and the miniseries made from it.

Family
On 20 December 1941, Nixon married Katharine Page of Phoenix, Arizona. That marriage failed, as did the next.

In 1956, Nixon married his third wife, Grace Umezawa. She had been a student in California in the spring of 1942 when President Franklin Roosevelt ordered the incarceration of Japanese Americans. Richard Winters served as the best man at the wedding. Nixon got his life back together and overcame his alcoholism during their marriage. They had no children.

Later years
After the war, Nixon worked at his family's Nixon Nitration Works in Edison (then Raritan Township), New Jersey, alongside his father, Stanhope, and longtime friend, Dick Winters.

Lewis Nixon died of complications from diabetes in Los Angeles, California, on January 11, 1995. Winters gave the eulogy at Grace's request. Clarence Hester and Bob Brewer of Easy Company also attended the funeral.

Nixon's widow Grace was a guest at a farewell party for Ron Livingston before he left for England for an actor boot camp ahead of filming the Band of Brothers miniseries, where he plays Nixon. Livingston recorded their meeting in an official HBO video diary.

title: Lewis Nixon III


text:
User talk:TomStike

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title: User talk:TomStike


text:
Talk:Dubai World Trade Centre

This move was completed
Change to the correct spelling of "Centre". The former should also redirect

 * Add *Support or *Oppose followed by an optional one sentence explanation, then sign your vote with ~

 * Support The 'About' page from the offical site spells it as suchRenesis13 20:12, 4 October 2005 (UTC)
 * Support. James F. (talk) 00:20, 5 October 2005 (UTC)

The globe kept front of The World Trade Centre is not rolling since 3months. Take action for that and let it roll. —Preceding unsigned comment added by 86.96.226.15 (talk) 11:42, 28 June 2009 (UTC)

Prepare for arneka gardner honei baby dedo and royal crown prince of Dubai wedding today
I would love to become princess arneka fazza love of dubai as well as his love for his USA fiance arneka gardner keys honei baby dedo is awaiting prince of Dubai to come marry her she has no money no kids just herself he has to care for her kids with her x husband love USA I'm in love with prince fazza 💪 thanks again for understanding everyone prince fazza has arneka best interest at heart 2600:1014:B081:75E6:0:36:4BC5:F01 (talk) 08:05, 7 July 2024 (UTC)

title: Talk:Dubai World Trade Centre


text:
Hamell on Trial

Edward James "Ed" Hamell, performing as Hamell on Trial, is an American punk rock, anti-folk, spoken word musician, described by Righteous Babe Records as "loud, fast music informed by politics, passion, energy and intelligence, played by a guy with a sharp tongue and a wicked sense of humor".

Biography
Born in Syracuse, New York, Hamell spent years as a member of many bands before venturing into the realm of the solo singer-songwriter. He finally got his big break when he moved to Austin, Texas and earned a residency at first the Chicago House and then the Electric Lounge.

Since then, he has released a number of albums on various labels, including Mercury Records, his own DiY label Such-A-Punch Media, and Righteous Babe Records, the label started by his longtime supporter and frequent touring companion, Ani Difranco. Ed has a son named Detroit, born in 2002. Detroit performed on Ed's album The Happiest Man in the World. Hamell was seriously injured in a car accident in May 2000, but recovered from head and spinal injuries to release the album Ed's Not Dead: Hamell Comes Alive the following year. His touring covers the US, Europe, Scandinavia and Australia.

In 2008, with the breakup of his 22-year marriage, Hamell wrote a song a day for a year and posted a video of it on his YouTube channel hamelltv. It is now over 450 songs.

In 2014 Hamell signed to New West Records and released The Happiest Man in the World. He began production on a one-man show with the same title based on the album and the demise of his marriage to be world premiered at The Edinburgh Fringe Festival in August 2014.

In 2017, Hamell released his second album for New West Records, Tackle Box. In August of that year, Hamell streamed a selection of songs performed live at monuments around Washington, DC, in a series collectively called "Hamell Takes DC."

In 2018, Hamell composed the music and lyrics for the Columbus, Ohio based Shadowbox Live's play F#(K Cancer: The Musical.

Style
Hamell addresses poignant and controversial issues, but with a comic edge. Known for rapid and powerful strumming on his heavily amplified 1937 Gibson L-00 acoustic guitar, Hamell's musical styling is as far from traditional folk music as it is from the typical drum-heavy electric guitar ridden sounds of traditional punk music. "Hamell’s signature sound comes from his strumming with maximum aggression, tight to the bridge, which lends a metallic ring to a sustained and percussive low-end rumble," writes Randal Doane, in a profile in Harper's. "Hamell also plays slide guitar lines sweetly drenched with the timbre and phrasing of his musical forebears of the Mississippi Delta. 'I’m a Libra,' he told me last fall, over coffee. 'I need the balance.'"

His sound and composition is comparable to that of the Velvet Underground. Live performances also include extended jokes and comic anecdotes between songs, demonstrating Hamell's respect for the stand-up comedy of Bill Hicks, who is celebrated in the closing tracks of Hamell's album Choochtown.

Discography

 * 1989 – Conviction (Blue Wave)
 * 1992 – Letter to Mike (Self-Published, cassette only)
 * 1996 – Big as Life (Doolittle/Mercury)
 * 1997 – The Chord is Mightier Than the Sword (PolyGram)
 * 1999 – Choochtown (Such-A-Punch Media)
 * 2001 – Ed's Not Dead: Hamell Comes Alive (Such-A-Punch Media)
 * 2003 – Yap (Such-A-Punch Media)
 * 2003 – Tough Love (Righteous Babe Records)
 * 2006 – Songs for Parents Who Enjoy Drugs (Righteous Babe Records)
 * 2008 – Live From Edinburgh: The Terrorism of Everyday Life (Righteous Babe Records)
 * 2008 – Rant and Roll (Righteous Babe Records)
 * 2014 – The Happiest Man in the World (New West Records)
 * 2017 – Tackle Box (New West Records)
 * 2017 – Big Mouth Strikes Again (New West Records)
 * 2018 – The Night Guy at The Apocalypse, Profiles of a Rushing Midnight (Saustex Records)
 * 2020 – The Pandemic Songs (Saustex Records)
 * 2023 - Bring the Kids (Saustex Records)

Awards and honors
May 2007 – inducted into the SAMMY (Syracuse Area Music Awards) Hall of Fame

Aug 2007 – Herald Angel Award at the Edinburgh Fringe Festival

May 2009 – Conveyor Awards of Excellence for Best Story Telling – Non-Theatrical & Best Musical Moments at the Cincinnati Fringe Festival

July 2009 – Directors' Award at the Capital Fringe Festival

title: Hamell on Trial


text:
Sam Champion

Samuel James Champion (born August 13, 1961) is an American weather anchor with WABC-TV and Good Morning America. He formerly co-anchored AMHQ: America's Morning Headquarters and 23.5 Degrees With Sam Champion on The Weather Channel.

After December 4, 2013, his final day with ABC, he became the managing editor of The Weather Channel, beginning on January 1, 2014. Champion also appeared on the Today show on NBC. After leaving NBC and the Weather Channel in 2016, he returned to ABC on a fill-in basis and returned to become the weekday morning weather anchor at WABC-TV in June 2019.

Early life and education
Champion was born on August 13, 1961, in Paducah, Kentucky, to Sylvia and James H. Champion. He has one sibling, sister Teresa. His father, who died October 25, 2010, was a lieutenant colonel in the U.S. Marine Corps who served in Vietnam. He graduated from Fairfax High School in Fairfax, Virginia in 1979. He has a B.A. in broadcast news from Eastern Kentucky University, and interned at WKYT-TV in Lexington, Kentucky.

Career
Champion worked at WPSD-TV in Paducah, Kentucky, and WJKS (later WCWJ) in Jacksonville, Florida. He became a weather presenter for WABC-TV's Eyewitness News in New York City in 1988. He went on Good Morning America at a salary in 2004 of $1.5 million per year. On April 7, 2012, he debuted as host of Sea Rescue, an educational and informational program in Litton's Weekend Adventure that focuses on the rescue, rehabilitation, and in many instances release of animals back into wildlife.

In August 2006, Good Morning America announced Champion would join that show and ABC News, effective September 5, 2006. Champion announced his departure from ABC on December 2, 2013, to become an on-air presence at and managing editor of The Weather Channel. His last day on Good Morning America was December 4, 2013. He was immediately replaced by Ginger Zee.

He had occasionally appeared on Live with Kelly and Ryan, the daily talk show produced by WABC-TV, and CNN's Larry King Live. He often begins his 30-second weathercasts by saying, "Let's get to the boards." His catchphrase when breaking for weather reports from local ABC stations is, "That's the weather around the nation. Here's what you can expect this morning."

Immediately following his departure from GMA, it was announced that Champion would join The Weather Channel to host his own morning show, titled America's Morning Headquarters which debuted on March 17, 2014. In September 2015, it was revealed that Champion would leave AMHQ to serve as a contributor to its primetime programs. In December 2016, Champion and The Weather Channel decided not to renew their contract. As a result, Champion left the company on December 27, 2016.

He returned to ABC as a fill-in weather forecaster on Good Morning America during the maternity leave of Chief Meteorologist Ginger Zee, his replacement. On May 22, 2019, it was announced that Champion would be returning to WABC-TV's morning and noon newscasts and contributing to ABC News, beginning June 3, 2019.

On September 8, 2022, Champion was announced as a contestant on season 31 of Dancing with the Stars. He is partnered with Cheryl Burke.

Personal life
Champion is active in charitable organizations in the New York metropolitan area. He was the Grand Marshal of the Multiple Sclerosis Society Fall Bike Tour, the chairman of the 25th annual March of Dimes NYC WalkAmerica, and master of ceremonies of "Stopping AIDS Together," a part of Sunday by the Bay. He hosted the New York City Anti-Violence Project's 2002 "Courage Awards," along with movie critic Frank DeCaro.

In May 2010, Champion had a basal cell carcinoma removed from his skin while on air, after previous bouts with the disease. He said he wanted to raise awareness about skin cancer during Cancer Awareness Month.

Champion and his partner of several years, Rubem Robierb, were married on December 21, 2012.

title: Sam Champion


text:
Ma Yin

Ma Yin (c. 853 – December 2, 930 ), courtesy name Batu (霸圖), also known by his posthumous name as the King Wumu of Chu (楚武穆王), was a Chinese military general and politician who became the founding ruler of the Chinese Ma Chu dynasty during the Five Dynasties and Ten Kingdoms period. He was the only monarch who carried the title of "king" in his dynasty. He initially took control of the Changsha region in 896 after the death of his predecessor Liu Jianfeng, and subsequently increased his territorial hold to roughly modern Hunan and northeastern Guangxi, which became the territory of Ma Chu.

Background and early career
Ma Yin was born in 853, during the reign of Emperor Xuānzong. He was known to be from Yanling (鄢陵, in modern Xuchang, Henan), but all that is known about his ancestors is that his great-grandfather was named Ma Yun (馬筠), his grandfather was named Ma Zheng (馬正), and his father was named Ma Yuanfeng (馬元豐). His family claimed ancestry from the great Han Dynasty general Ma Yuan. Ma Yin was a carpenter in his youth. He had at least two younger brothers, Ma Cong (馬賨) and Ma Cun (馬存).

At one point, when Zhongwu Circuit (忠武, headquartered in modern Xuchang) stationed an army at Cai Prefecture (蔡州, in modern Zhumadian, Henan) to defend against the major agrarian rebel Huang Chao, Ma Yin served in the Zhongwu army stationed at Cai, under the officers Sun Ru and Liu Jianfeng. By that time, Ma had become known for his abilities and bravery. Later, when Qin Zongquan the military governor of Fengguo Circuit (奉國, headquartered at Cai Prefecture) rebelled against the rule of Emperor Xuānzong's grandson Emperor Xizong, Sun and Liu, as well as their army, came under Qin's rule.

Service under Sun Ru
In 887, Qin Zongquan sent his brother Qin Zongheng (秦宗衡), with Sun as his deputy, to advance into Huainan Circuit (淮南, headquartered in modern Yangzhou, Jiangsu), to contend for control of the circuit, which by that point had fallen into an internecine struggle between Qin Yan and Bi Shiduo on one side, and Yang Xingmi on the other. Liu and Ma were both in this army commanded by Qin Zongheng. When they arrived at Huainan's capital Yang Prefecture (揚州), Yang Xingmi had captured it and forced Qin Yan and Bi to flee. Qin Yan and Bi then joined forces with Qin Zongheng as well. Soon thereafter, when Qin Zongquan, himself facing military pressure from Zhu Quanzhong the military governor of Xuanwu Circuit (宣武, headquartered in modern Kaifeng, Henan), tried to recall Qin Zongheng's army, Sun assassinated Qin Zongheng and took over the army, thereafter executing Qin Yan and Bi. Sun soon defeated Yang Xingmi and took over Yang Prefecture, claiming the title of military governor of Huainan. (Yang subsequently took Ningguo Circuit (寧國, headquartered in modern Xuanzhou, Anhui and became its military governor.)

In spring 891, Sun launched the initial phase of an ambitious plan to first destroy Yang Xingmi and then Zhu. He took all of the army available to him and headed for Xuanshe's capital Xuan Prefecture (宣州). Liu was part of Sun's army. Sun's army was initially victorious, and by spring 892 had put Xuan Prefecture under siege. However, Sun was unable to capture Xuan, and soon got bogged down, with Yang sending raiders to cut off his food supplies. Further, his army was soon troubled by torrential floods and illnesses, and Sun himself was suffering from malaria. He was forced to send Liu and Ma out to raid the nearby regions for food. Meanwhile, Yang, hearing that Sun was suffering from malaria, attacked. He crushed Sun's army and killed Sun. Most of Sun's soldiers surrendered to Yang. Liu and Ma took 7,000 soldiers and headed south, toward Zhennan Circuit (鎮南, headquartered in modern Nanchang, Jiangsi); the soldiers supported Liu as their leader, with Ma as his forward commander and Zhang Ji (張佶) as his strategist. The army's size eventually ballooned to over 100,000.

Service under Liu Jianfeng
Instead of attacking Zhennan Circuit, Liu's army continued to head southwest, toward Wu'an Circuit, which was then ruled by Deng Chuna. When Liu reached Liling (醴陵, in modern Zhuzhou, Hunan) in summer 894, Deng sent his subordinates Jiang Xun (蔣勛) and Deng Jichong (鄧繼崇) to defend Longhui Pass (龍回關, in modern Shaoyang, Hunan) against Liu's advance. Ma Yin advanced to the pass and sent a messenger to Jiang and Deng Jichong. The messenger persuaded Jiang and Deng Jichong that Liu's arrival was foretold by the stars and that their army would be unable to resist his. At the suggestion of the messenger, Jiang and Deng Jichong disbanded their army. Liu then had his soldiers put on the uniforms that Jiang's and Deng Jichong's army wore, and then quickly advanced to Wu'an's capital Tan Prefecture (in modern Changsha, Hunan). When they arrived there, the Tan Prefecture's defenders mistook them for Jiang's and Deng Jichong's army, and therefore took no precautions. Liu's army directly headed for the headquarters, where Deng Chuna was holding a feast. They captured Deng Chuna, and Liu executed him and claimed the title of acting military governor. In summer 895, then-reigning Emperor Zhaozong commissioned Liu as the military governor of Wu'an.

In winter 895, after Jiang's request to be the prefect of Shao Prefecture (邵州, in modern Shaoyang) was rebuffed by Liu, he and Deng Jichong rose to oppose Liu. They quickly captured Shao Prefecture and tried to pressure Tan Prefecture. In spring 896, Liu sent Ma Yin to attack Jiang and Deng, and Ma had initial successes. However, during this campaign, Liu was assassinated by his officer Chen Zhan (陳瞻), whose wife Liu had been having an affair with. The soldiers initially supported Zhang to succeed Liu. However, as Zhang was riding a horse to headquarters, the horse suddenly got spooked and bit Zhang in the left leg. This caused Zhang to believe that his succeeding Liu was not in accordance with divine will. He thus issued an order to Ma to return to Tan Prefecture, offering to support him as Liu's successor. Ma thus left his subordinate Li Qiong (李瓊) at Shao to continue the campaign, while he himself returned to Tan. Once Ma returned to Tan, Zhang turned the governance of the circuit over to him, and Ma accepted; Zhang then left to take over the campaign at Shao. Emperor Zhaozong subsequently confirmed Ma as acting military governor.

As Tang military governor of Wu'an
When Ma Yin took over command of Wu'an, he was apprehensive of the strengths of both Yang Xingmi (who was firmly in control of Huainan by that point) and Cheng Rui the military governor of Jingnan Circuit (荊南, headquartered in modern Jingzhou, Hubei), and he considered giving them gold and silk to appease them. His strategist Gao Yu pointed out that Cheng was not as strong as he looked, while Yang was a sworn enemy who could never be appeased through gifts. At Gao's suggestion, Ma concentrated on comforting the people and training his army, to strengthen his own army without external aid.

In 897, Zhang Ji captured Jiang Xun, allowing Shao Prefecture to come under Ma's control. However, it was said that at that point, while Wu'an Circuit legally consisted of seven prefectures, Ma was in actual control of only Tan and Shao; the other five prefectures were all actually controlled by agrarian rebels — Heng (modern Hengyang in Hunan) by Yang Shiyuan (楊師遠), Yong (永州, in modern Yongzhou, Hunan) by Tang Shimin (唐世旻); Dao (道州, in modern Yongzhou) by Cai Jie (蔡結); Chēn (郴州, in modern Chenzhou, Hunan) by Chen Yanqian (陳彥謙); and Lian (連州, in modern Qingyuan, Guangdong) by Lu Jingren (魯景仁). Under the suggestion of Yao Yanzhang, Ma sent an army commanded by Li Qiong and Qin Zongquan's cousin Qin Yanhui (秦彥暉) to attack Heng and Yong, quickly capturing them; Yang died in flight, while Tang was killed by Ma's army. When Ma sent Li Tang (李唐) in 899 to attack Dao, Cai initially repelled Li Tang's attack, but Li Tang subsequently succeeded in capturing Dao and killing Cai, taking Dao under Ma's control as well. By the end of 899, Li Qiong had captured and executed Chen Yanqian, and when he attacked Lian, Lu committed suicide, allowing Ma to control all seven of Wu'an's prefectures. Emperor Zhaozong formally bestowed on Ma the title of military governor.

When Liu Shizheng (劉士政) the military governor of Jingjiang Circuit (靜江, headquartered in modern Guilin, Guangxi) heard that Ma had pacified all of Wu'an, he became apprehensive, and he sent his deputy Chen Kefan (陳可璠) to defend Quanyi Heights (全義嶺, in modern Guilin) against a possible Ma attack. When Ma sent emissaries to Liu to try to establish peaceful relations, Chen refused. Ma, in 900, sent Qin and Li Qiong to attack Jingjiang. They quickly defeated Liu's army, killing Wang Jianwu (王建武) and capturing Chen. They put Jingjiang's capital Gui Prefecture (桂州) under siege, and after a few days of siege, Liu surrendered, allowing Ma to take Jingjiang's five prefectures under control. Ma commissioned Li Qiong as the military governor of Jingjiang.

In 902, Emperor Zhaozong, who was then under the controls of the eunuch Han Quanhui and the warlord Li Maozhen at Li Maozhen's Fengxiang Circuit (鳳翔, headquartered in modern Baoji, Shaanxi), which was then under siege by Zhu Quanzhong, sent the imperial emissary Li Yan to the southeastern circuits to encourage the warlords there to join under Yang's command and attack Zhu. As part of the edicts that Li Yan promulgated, Ma was given the honorary chancellor title of Tong Zhongshu Menxia Pingzhangshi (同中書門下平章事).

By 903, Zhu had prevailed over Li Maozhen, forcing Li Maozhen to seek peace by killing Han and giving control of the emperor to Zhu. Thereafter, Yang sent emissaries to Ma, accusing Zhu of inappropriate actions, and offering an alliance to Ma if Ma would cut off his relationship with Zhu. Ma's general Xu Dexun pointed out that Zhu controlled the emperor and that it would not be advantageous to Ma to end that relationship. Ma agreed and did not accept Yang's proposal.

Meanwhile, an ally of Zhu's, Du Hong the military governor of Wuchang Circuit (武昌, headquartered in modern Wuhan, Hubei), had been under attack by Yang for several years and was in a desperate situation. Zhu sent his general Han Qing (韓勍) south to try to save Du, while also requesting Cheng, Ma, and Lei Yanwei the military governor of Wuzhen Circuit (武貞, headquartered in modern Changde, Hunan) to launch troops to save Du. Cheng agreed and launched a fleet, which he himself commanded, toward Wuchang. However, after Cheng left his capital Jiangling, Ma sent Xu to join forces with Lei's officer Ouyang Si (歐陽思) to attack Jiangling. They captured it, pillaged it for its population and wealth, and then withdrew. Cheng's army, hearing that their families and wealth had been captured, lost its morale, and was subsequently defeated by Yang's general Li Shenfu; Cheng committed suicide by drowning. On the way back to Tan, Xu met with Deng Jinzhong (鄧進忠) the prefect of Yue Prefecture (岳州, in modern Yueyang, Hunan) and persuaded Deng that he should submit to Ma. Deng agreed, surrendered the prefecture, and moved his entire family to Tan to show submission to Ma. Ma made Xu the prefect of Yue and Deng the prefect of Heng.

In 904, Yang realized that Ma Cong, who remained at Huainan and served in his army for a number of years after Yang defeated Sun Ru, was Ma Yin's brother. He offered to send Ma Cong to Ma Yin. Ma Cong initially declined, indicating that he was grateful for Yang's not killing him at the time of Sun's death and making him a Huainan officer, but Yang insisted. After Ma Cong arrived at Tan, Ma Yin made him the deputy military governor. Ma Cong subsequently advocated an alliance between Ma Yin and Yang, but Ma Yin rejected Ma Cong's proposal.

In 906, Yang's son and successor Yang Wo sent his officer Chen Zhixin (陳知新) to attack Yue Prefecture. Chen was successful, forcing Xu to flee, and Yue fell to Huainan control. During the same year, Peng Gan (彭玕) the prefect of Ji Prefecture (吉州, in modern Ji'an, Jiangxi) surrendered Ji to Ma, after Yang Wo had conquered most of Zhennan Circuit (which Ji Prefecture belonged to) and captured its military governor Zhong Kuangshi.

During Emperor Taizu's reign
In 907, Zhu Quanzhong had Emperor Zhaozong's son and successor Emperor Ai yield the throne to him, ending Tang and establishing a new Later Liang as its Emperor Taizu. Several Tang warlords, including Yang Wo, Li Maozhen, Li Keyong, and Wang Jian, refused to recognize him as emperor, but the rest of the formerly Tang realm did, including Ma Yin's Wu'an Circuit. Shortly thereafter, the new Later Liang emperor created Ma the Prince of Chu. Emperor Taizu also gave him the title of military governor of Wuchang, even though he did not control Wuchang.

Later that year, Yang Wo (whose state became known as Hongnong by that point as he carried the title of Prince of Hongnong) sent his general Liu Cun (劉存) with 30,000 men to attack Chu. Ma sent Qin Yanhui and Huang Fan (黃璠) to resist Liu. Liu's fleet soon ran into difficulties due to torrential rains and was repeatedly defeated by Qin. Liu thus sent letters to Ma, offering to surrender, but Qin, arguing to Ma that Liu's surrender offers were deceitful, continued attacking. Qin thoroughly defeated Liu and captured Liu and his deputy Chen Zhixin (陳知新). Initially, Ma tried to persuade Liu and Chen to submit to him and serve him, but after they refused, he executed them. This battle allowed Ma to regain Yue Prefecture. Ma then joined forces with Peng Gan to try to capture Zhennan's capital Hong Prefecture (洪州), but they could not do so. Subsequently, he and Lei Yanwei's brother and successor Lei Yangong jointly attacked Jingnan, which was then under the control of the Later Liang general Gao Jixing, but they were repelled.

Later in 907, when Lei again made an unsuccessful attempt to capture Jiangling and entered into an alliance with Hongnong, Emperor Taizu stripped him of his titles and ordered Gao and Ma to attack him. Gao sent his general Ni Kefu (倪可福), while Ma sent Qin, to put Wuzhen's capital Lang Prefecture (朗州) under siege. When Lei sought aid from Huainan, Yang sent Ling Ye (泠業) and Li Rao (李饒) to try to save Lei. Ma sent Xu Dexun to resist Ling and Li Rao, and he defeated and captured them; Ma then executed them. In summer 908, without Hongnong aid, Lang Prefecture fell. Lei fled to Hongnong territory, allowing Ma to take over Lang and Li (澧州, in modern Changde) Prefectures.

Meanwhile, Gao Yu pointed out to Ma that one way to enrich his state was to sell tea to territory directly under Later Liang control. Thereafter, Ma requested and received permission from Emperor Taizu to establish tea trade offices at Bian Prefecture (汴州, in modern Kaifeng), Jiangling, Xiang Prefecture (襄州, in modern Xiangyang, Hubei), Tang Prefecture (唐州, in modern Zhumadian), Ying (郢州, in modern Jingmen, Hubei), and Fù Prefecture (復州, in modern Tianmen, Hubei), for the purpose of selling Chu tea and purchasing silk and horses, with part of the tea offered to the Later Liang imperial government as tribute. It was said that Chu began to be enriched after this trade began. Later in the year, when Gao Jixing tried to cut off this trade by stationing forces at Hankou (漢口, in modern Wuhan), Ma sent Xu to attack him, and Gao Jixing, in fear, sought peace. Ma also sent Lü Shizhou (呂師周) to attack the territory of Liu Yin the military governor of Qinghai Circuit (清海, headquartered in modern Guangzhou, Guangdong), capturing Zhao (昭州, in modern Guilin), He (賀州, in modern Hezhou, Guangxi), Wu (梧州, in modern Wuzhou, Guangxi), Meng (蒙州, in modern Wuzhou), Gong (龔州, in modern Guigang, Guangxi), and Fù (富州, in modern Hezhou, note different character than the prefecture in Tianmen) Prefectures from Liu Yin.

In 909, Wei Quanfeng, who had been controlling four Zhennan prefectures centered around Fǔ Prefecture (撫州, in modern Fuzhou, Jiangxi, note different tone than the prefectures in Tianmen and Hezhou) for years, claimed the title of military governor of Zhennan and set out to attack Hong Prefecture. When Wei sought support from Ma, Ma sent Wan Mei (苑玫) and Peng Gan's nephew Peng Yanzhang (彭彥章) to put Gao'an (高安, in modern Yichun, Jiangxi) under siege to divert Hongnong forces. Subsequently, after Wei was defeated and captured by the Hongnong general Zhou Ben, Chu forces withdrew. Further, Peng Gan abandoned Ji Prefecture and fled to Tan, thus allowing Hongnong to take over Ji. Ma made Peng Gan the prefect of Chēn Prefecture, and took one of Peng's daughters as the wife of his son Ma Xifan.

In 910, after Ma requested the title of Tiance Shangjiang (天策上將, literally "Grand General of Heavenly Strategies"), a title that had previously been held by the great Tang emperor Emperor Taizong, Emperor Taizu granted him that title. Ma thereafter established an Tiance Office and made Ma Cong and Ma Cun its directors.

Meanwhile, Song Ye (宋鄴) and Pan Jinsheng (潘金盛), the chieftains of non-Han peoples at Chén Prefecture (辰州, in modern Huaihua, Hunan, note different tone than the prefecture in Chenzhou) and Xu Prefecture (漵州, in modern Huaihua), had been harassing cities under Chu control. In late 910, when Song attacked Xiangxiang (湘鄉, in modern Xiangtan, Hunan), and Pan attacked Wugang (武岡, in modern Shaoyang), Ma sent Lü to attack them. Lü soon killed Pan, and, by 912, Song and another non-Han chieftain, Chang Shiyi (昌師益), had submitted to Ma.

Also in 910, Pang Juzhao (龐巨昭) the military governor of Ningyuan Circuit (寧遠, headquartered in modern Yulin, Guangxi), and Liu Changlu (劉昌魯) the defender of Gao Prefecture (高州, in modern Maoming, Guangdong), who had just recently repelled an attack by Liu Yin but believed that they had no strength to stand against Liu Yin long term, wrote to Ma, offering their territory to him. Ma sent Yao Yanzhang (姚彥章) to their territory to escort them to Chu proper. He had Yao serve as the prefect of Ningyuan's capital Rong Prefecture (容州) to defend the territory, and subsequently had him made the deputy military governor of Ningyuan. However, in 911, when Liu Yin attacked again, Yao judged the situation untenable despite a relief force commanded by Xu. He therefore took the people of Rong Prefecture and returned to Chu proper, allowing Liu Yin to take over Rong and Gao Prefectures. Despite this setback, Emperor Taizu still bestowed on Ma the titles of military governor of Wu'an, Wuchang, Jingjiang, and Ningyuan, as well as the commanders of the forces against Hong and E (鄂州, Wuchang's capital) Prefectures. However, not wanting to see prolonged warfare between Ma and Liu Yin, both of whom were his vassals, he sent a number of emissaries to try to broker peace between them.

After Emperor Taizu's reign
In 912, the Wu (i.e., Hongnong, which was now referred to in historical accounts as Wu, as Yang Wo's brother and successor Yang Longyan, while initially carrying the title of Prince of Hongnong as well, later took on the title of Prince of Wu, which Yang Xingmi had carried at the time of his death) general Chen Zhang (陳璋) attacked Yue Prefecture, capturing Wan, who was then the prefect of Yue. When Ma sent Yang Dingzhen (楊定真) to try to recapture Yue, the Wu forces headed toward Jingnan instead. To prevent Ma from aiding Jingnan, the Wu general Liu Xin (劉信), who governed Wei's old territory of Fǔ Prefecture and its surroundings, stationed himself at Ji Prefecture to pressure Ma. Subsequently, though, after Chen was unable to capture Jiangling, he withdrew. In 913, apparently in response, Yao, who carried the title of military governor of Ningyuan by that point despite Chu's loss of Ningyuan, attacked E Prefecture, but when the Wu general Lü Shizao (呂師造) responded, Yao withdrew.

Also in 913, Liu Yin's brother and successor Liu Yan requested that Ma Yin give a daughter to him in marriage. Ma agreed. (The marriage alliance was eventually concluded in 915, when Ma Yin had Ma Cun escort his daughter to Liu Yan's territory to marry Liu Yan.)

In 914, the Wu prefect of Yuan Prefecture (袁州, in modern Yichun), Liu Chongjing (劉崇景), surrendered the prefecture to Ma. Ma sent Xu Zhen (許貞) to support him. After the Wu generals Chai Zaiyong (柴再用) and Mi Zhicheng (米志誠) attacked, however, Liu and Xu abandoned Yuan Prefecture and returned to Chu territory.

In 916, hearing that Li Keyong's son and successor Li Cunxu the Prince of Jin had conquered all of the territory north of the Yellow River in his continued war with Later Liang (which was then ruled by Emperor Taizu's son Zhu Zhen after Emperor Taizu was assassinated in 912 by another son, Zhu Yougui), Ma, despite his status as a Later Liang vassal, sent emissaries to Jin as a peace overture; Li Cunxu reciprocated.

In 918, Liu Xin put Qian Prefecture (虔州, in modern Ganzhou, Jiangxi), which was then ruled by the warlord Tan Quanbo, whose territory was wedged between Wu, Chu, and the territories of the Later Liang vassals Liu Yan and Wang Shenzhi the Prince of Min, under siege. Tan sought aid from three states which were Later Liang vassals — Wuyue, Min, and Chu. In response, Wuyue's prince Qian Liu sent his son Qian Chuanqiu (錢傳球) to attack Wu's Xin Prefecture (信州, in modern Shangrao, Jiangxi); Ma sent his officer Zhang Keqiu (張可求) to advance to Gutting (古亭, in modern Ganzhou); and Wang sent an army to advance to Yudu (雩都, in modern Ganzhou), all seeking to aid Tan. The Wuyue forces, however, were repelled by Xin's prefect Zhou Ben. Subsequently, Liu sent part of his army to repel the Chu army. When the Wuyue and Min forces heard that the Chu army had been repelled, they withdrew, leaving Tan without external aid.

In 919, Chu forces attacked Jingnan, and Gao Jixing sought aid from Wu. Wu had Liu Xin head directly toward Tan Prefecture, while Li Jian (李簡) attacked Chu's Fù Prefecture (復州). Li Jian captured Fù's prefect Bao Tang (鮑唐), and the Chu forces, hearing of Liu Xin's advances, withdrew from Jingnan.

In 920, Qian sought to have Ma give a daughter to his son Qian Chuansu (錢傳璛) in marriage, and Ma agreed.

During Emperor Zhuangzong's reign
In 923, Li Cunxu claimed himself to be the legitimate successor to Tang, establishing a new Later Tang as its Emperor Zhuangzong. Thereafter, he made a surprise attack on the Later Liang capital Daliang (大梁, i.e., formerly Bian Prefecture), catching it defenseless. Zhu Zhen, not wanting to be captured, committed suicide before the city fell to Later Tang forces, ending Later Liang. The circuits that had previously been controlled by Later Liang came under Later Tang control. Ma Yin, hearing of the Later Tang victory, sent Ma Xifan to Daliang to pay tribute to Emperor Zhuangzong. When Ma Xifan met Emperor Zhuangzong, Emperor Zhuangzong asked him about the events in the Chu realm and was impressed. Wanting to praise Ma Xifan while, at the same time, sow seeds of suspicion by Ma Yin against Gao Yu, he stated to Ma Xifan, "I had often heard that one day Gao Yu would take over the Hunan region. If the Prince of Chu has a son like you, how could Gao do so?" Despite this attempt by Emperor Zhuangzong to cause Ma Yin to suspect Gao, Ma Yin refused to do so and continued to trust Gao. Indeed, it was said that it was Gao's suggestion that Ma, who was enticing merchants to come to Chu by collecting no transactional taxes from them, coined money out of iron and lead — two metals that were not used for money outside of the Chu realm. As a result, the merchants were forced to spend the money by purchasing items from Chu, thus allowing Chu to enrich itself through these commercial activities. Further, also at Gao's suggestion, to encourage sericulture, Ma also allowed the people of his realm to pay taxes with silk in lieu of money, and it was said that after several years of this policy, Chu had become a major producer of silk.

In 924, Emperor Zhuangzong bestowed on Ma Yin the title of Shangshu Ling (尚書令).

In 925, Emperor Zhuangzong sent his son Li Jiji the Prince of Wei and the major general Guo Chongtao to attack Former Shu (which was then ruled by Wang Jian's son and successor Wang Zongyan. Former Shu quickly fell and was absorbed into Later Tang.  Hearing of Former Shu's destruction, Ma, in fear, submitted a report to Emperor Zhuangzong, stating:

"I have started managing a mansion at the foot of Mount Heng to be my place of retirement. I am willing to surrender my seal and commission to preserve my old years."

Emperor Zhuangzong sent Ma a reply comforting him and declining his resignation.

However, despite the apparent Later Tang strength that the destruction of Former Shu showed, Emperor Zhuangzong's rule was actually becoming destabilized due to the soldiers' discontent toward his failure to implement his prior promises of rewards to them for their achievements in destroying Later Liang and Former Shu, and the discontent was further exacerbated by the subsequent executions of Guo and another major general, Li Jilin the Prince of Xiping by Emperor Zhuangzong and his wife Empress Liu. Thereafter, Emperor Zhuangzong's adoptive brother Li Siyuan rebelled at Daming (大名, in modern Handan, Hebei). By summer 926, another mutiny at the capital Luoyang caused Emperor Zhuangzong to die in battle. Li Siyuan subsequently declared himself emperor (as Emperor Mingzong).

During Emperor Mingzong's reign
After Emperor Mingzong took the throne, he confirmed Ma Yin's title of Shangshu Ling. Meanwhile, with Gao Jixing taking an increasingly confrontational attitude with the Later Tang court, including seizure of a major shipment of Former Shu wealth that Li Jiji (prior to Emperor Zhuangzong's death and his own suicide) sent toward Luoyang, as well as the seizure of three prefectures that formerly belonged to Former Shu, Emperor Mingzong sent the general Liu Xun (劉訓) to attack Jingnan. Ma sent Xu Dexun with a fleet toward Jingnan, but stopped Xu's fleet at Yue Prefecture. Meanwhile, Gao defended Jiangling and refused to engage Liu, who soon became bogged down in his attack due to rains and illnesses afflicting his army. Emperor Mingzong sent the chief of staff Kong Xun to the front to examine the situation, and Kong tried to entice Ma to join the battle as well by sending a gift of clothes to the Chu army and horses and jade belts to Ma personally, and requesting that Ma send food supplies to Liu's army — a request that Ma apparently did not openly reject but never carried out. Eventually, Liu was forced to withdraw, and Jingnan became effectively independent of Later Tang after that point.

In 927, Emperor Mingzong bestowed the greater title of King of Chu (楚國王) on Ma. After accepting the title, Ma took on greater royal trappings, including referring to his residence as palace and establishing the various offices for his officials like an imperial regime, only changing the official titles somewhat to show deference to the Later Tang emperor. He made Yao Yanzhang and Xu his chancellors. He assumed all responsibilities for commissioning officials within his reign, except that he would submit reports after commissioning the military governors of Wuping (武平, i.e., formerly Wuzhen) and Jingjiang.

In 928, Ma sent Yuan Quan (袁詮), Wang Huan (王環), and his son Ma Xizhan (馬希瞻), to attack Jingnan. After the Chu forces dealt the Jingnan forces a major defeat at Liulang Ford (劉郎洑, in modern Jingzhou), Gao, in fear, returned the Chu emissary to Later Tang, Shi Guangxian (史光憲) (whom Gao had seized after turning against Later Tang). When Ma subsequently blamed Wang for not further destroying Jingnan, Wang responded:

"Jiangling is between the Central Dynasty [(i.e., Later Tang)], Wu, and Shu, and everyone wants it. It is best that we let it stand so that it can serve as our defense."

Ma understood the point and thereafter did not speak of capturing Jingnan any further.

Meanwhile, also in 928, Ma sent a fleet to attack Feng Prefecture (封州, in modern Zhaoqing, Guangdong), which belonged to Liu Yan — who, by that point, had declared himself emperor of a new state of Southern Han. The fleet, however, was defeated by the Southern Han general Su Zhang (蘇章) and forced to withdraw.

Later in 928, Wu launched a major attack on Yue Prefecture, commanded by Miao Lin (苗璘) and Wang Yanzhang (王彥章). Ma sent Xu to face them. Xu secretly sent Wang Huan with a smaller fleet to get behind the Wu fleet, and then attacked the Wu fleet from both ends. The result was a major Chu victory, and both Miao and Wang Yanzhang were captured. Subsequently, though, to try to make peace with Wu, Ma sent both Miao and Wang Yanzhang back to Wu. When sending them off at a feast, Xu, who had by this point had become concerned that Ma's sons were fighting over succession rights, made what was later viewed as a prophetic statement:

"While Chu is small, its senior officials and generals are still present. I hope that the Wu Dynasty will not again think of it. For you to consider attacking us, you have to wait until the ponies [(i.e., Ma's sons, with Xu employing a double entendre given that 'Ma' meant 'horse')] are fighting over the stable."

Meanwhile, Gao, after breaking with Emperor Mingzong, submitted to Wu, and the Wu emperor Yang Pu (Yang Longyan's brother and successor) created Gao the Prince of Qin. Emperor Mingzong ordered Ma to attack Jingnan. Ma sent Xu and Ma Xifan to attack Jingnan. When the two armies met, Gao Jixing's nephew Gao Congsi (高從嗣) challenged Ma Xifan to single combat, but the Chu officer Liao Kuangqi (廖匡齊) came out and engaged Gao Congsi instead, killing him. Gao Jixing then sued for peace, and Xu and Ma Xifan withdrew. However, for some time, there continued to be border skirmishes between Chu and Jingnan.

Meanwhile, as Xu perceived, there was a struggle over succession rights. Ma Yin's oldest son, Ma Xizhen (馬希振), was born of his wife (whose name was not recorded in history), but his favorite son was his second son Ma Xisheng, who was born of his favorite concubine Consort Yuan. Ma Xizhen, not wanting to fight over the succession with Ma Xisheng, became a Taoist monk and retired from politics. In 929, Ma formally put Ma Xisheng, who then carried the title of deputy military governor of Wu'an and acting mayor of the capital Changsha, in charge of the Chu administration. From this point on, all matters of state were to be reported to Ma Xisheng first, before being reported to Ma Yin, and this effectively designated Ma Xisheng as Ma Yin's heir. However, Ma Xifan, who was born on the same day as (but apparently later in the day than) Ma Xisheng, resented Ma Xisheng for not even showing any sign of deferring to him. He hated Ma Xisheng and Consort Yuan from this point on.

In late 928, Gao Jixing died and was succeeded by his son Gao Conghui. Gao Conghui, believing that his small state could not withstand Later Tang military pressure if it continued to confront Later Tang, resubmitted to Emperor Mingzong through Ma Yin and the Later Tang military governor of Shannan East Circuit (山南東道, headquartered in modern Xiangyang), An Yuanxin (安元信).

After Ma Xisheng took the reins of the state, he began to run into conflicts with Gao Yu, and he was also suspicious of Gao due to the prior seeds of suspicion sewn by Emperor Zhuangzong and Gao Jixing (who, while alive, had publicly stated that he wanted to enter into a blood brotherhood with Gao because he believed that Gao would become Chu's ruler). In 929, with Ma Xisheng repeatedly requesting it, Ma Yin ordered Gao into retirement. Gao, in frustration, stated, "I am going to build a mansion in the hills to the west, for retirement. The pony [(employing a similar double entendre as Xu did)] has grown up and can bite now." Ma Xisheng heard the remark and became angry — so angry that he falsely announced that Gao had committed treason, and he slaughtered Gao and his family, without first informing Ma Yin. When Ma Yin heard this, he cried bitterly, but did not punish Ma Xisheng.

Ma Yin died in 930. He left instructions that his sons were to pass the throne to their younger brothers, and further ordered that anyone who spoke against this succession principle be put to death. Ma Xisheng thereafter took over control of the state.

Personal information

 * Father
 * Ma Yuanfeng (馬元豐), posthumously honored King Jingzhuang of Chu
 * Wife
 * Name unknown, mother of Ma Xizhen
 * Major Concubines
 * Consort Yuan, mother of Ma Xisheng and Ma Xiwang
 * Lady Chen, mother of Ma Xifan
 * Lady Hua, mother of Ma Xigao
 * Children (Ma Yin had at least 35 sons, but the names of most of them were lost to history)
 * Ma Xizhen (馬希振), became Taoist monk
 * Ma Xisheng (馬希聲) (899–932), later prince
 * Ma Xifan (馬希範) (899–947), later prince
 * Ma Xiwang (馬希旺) (d. ~933)
 * Ma Xigao (馬希杲) (poisoned by Ma Xifan 945)
 * Ma Xi'e (馬希萼), later prince
 * Ma Xiguang (馬希廣), later prince (died 950)
 * Ma Xichong (馬希崇), later prince
 * Ma Xizhan (馬希瞻) (died 949)
 * Ma Xineng (馬希能)
 * Ma Xiguan (馬希貫)
 * Ma Xiyin (馬希隱)
 * Ma Xijun (馬希濬)
 * Ma Xizhi (馬希知)
 * Ma Xilang (馬希朗)
 * daughter, Empress Ma of Southern Han, wife of Liu Yan
 * daughter, wife of Qian Chuansu (錢傳璛), son of Qian Liu the King of Wuyue

title: Ma Yin


text:
Trigonon

A trigonon (trígōnon, from Greek "τρίγωνον", "triangle") is a small triangular ancient Greek harp occasionally used by the ancient Greeks and probably derived from Assyria or Egypt. The trigonon is thought to be either a variety of the sambuca or identical with it.

A trigonon is represented on one of the Athenian red-figured vases from Cameiros in the island of Rhodes, dating from the 5th century BCE, which are preserved in the British Museum. The triangle is here an irregular one, consisting of a narrow base to which one end of the string was fixed, while the second side, forming a slightly obtuse angle with the base, consisted of a wide and slightly curved sound-board pierced with holes through which the other end of the strings passed, being either knotted or wound round pegs. The third side of the triangle was formed by the strings themselves, the front pillar, which in modern European harps plays such an important part, being always absent in these early Oriental instruments. A small harp of this kind having 20 strings was discovered at Thebes, Egypt in 1823.

title: Trigonon


text:
1990 Daytona 500

The 1990 Daytona 500 was the first stock car race of the 1990 NASCAR Winston Cup Series season and the 32nd iteration of the event. The race was held on Sunday, February 18, 1990, in Daytona Beach, Florida at Daytona International Speedway, a 2.5 miles (4.0 km) permanent triangular-shaped superspeedway. The race took the scheduled 200 laps to complete. On the final lap of the race, Whitcomb Racing driver Derrike Cope would manage to take advantage of a misfortunate Dale Earnhardt, when Earnhardt suffered a flat tire on the final turn of the race, allowing Cope to take the lead. The victory was Cope's first career NASCAR Winston Cup Series victory and his first victory of the season. To fill out the top three, Precision Products Racing driver Terry Labonte and Melling Racing driver Bill Elliott would finish second and third, respectively.

Background
Daytona International Speedway is one of three superspeedways to hold NASCAR races, the other two being Indianapolis Motor Speedway and Talladega Superspeedway. The standard track at Daytona International Speedway is a four-turn superspeedway that is 2.5 miles (4.0 km) long. The track's turns are banked at 31 degrees, while the front stretch, the location of the finish line, is banked at 18 degrees.

Entry list

 * (R) denotes rookie driver.

Qualifying
Qualifying was set by the 1990 Twin 125 Qualifiers. The top two positions were set by qualifying speeds held for the Twin 125 Qualifiers held on Saturday, February 10, with the top two qualifiers in the session earning the top two positions for the Daytona 500. The rest of the starting was set in the Twin 125 Qualifiers, held on Thursday, February 15 during two races. The top 14 finishers in the first race, excluding the pole position winner, would set the inside row from rows two to 15, and the top 14 finishers in the second race, excluding the outside pole position winner, would set the outside row from rows two to 15. The remaining non-qualifiers would set positions 31-40 based on qualifying speeds from the first qualifying session held on Saturday. If needed, up to two extra provisionals were given to teams high enough in the previous season's owner's standings that did not qualify for the race by either qualifying speed or from the Twin 125 Qualifiers.

Ken Schrader, driving for Hendrick Motorsports, would win the pole, setting a time of 45.798 and an average speed of 196.515 mph in Saturday's session.

19 drivers would fail to qualify.

Race review
On the Busch Pole for the third year in a row, Ken Schrader quickly passed several cars at the start after beginning the race in his backup car due to a practice crash. By the first caution flag, Schrader had driven up to second place. Geoff Bodine led the first lap of the race and the season. Two cars used to create film footage for the upcoming movie Days of Thunder, driven by Bobby Hamilton and Tommy Ellis, started the race in the last row, completing 100 miles before parking. Those cars were not listed in the official race results.

On Lap 27, Richard Petty (who started a promising 11th) spun ahead of Phil Parsons while running 13th. The spin left him with all four tires flat, meaning The King would need a wrecker to take him to the pits for new tires, and he would finish well down the order in 34th. During the yellow, Davey Allison (running 6th) pitted with the leaders and hit the pit wall. This was unnoticed by the television broadcast for several minutes; no injuries were reported but Mike Joy confirmed left front toe damage.

On Lap 43, an accident occurred between the tri-oval and Turn 1 involving Mike Alexander, Alan Kulwicki (who would continue), Phil Parsons, and 1989 NASCAR Busch Series champion and Winston Cup rookie Rob Moroso. Moroso said he touched Phil Parsons' left rear with his own right front after Parsons came down on him, and Parsons explained that he was attempting a pass on A. J. Foyt. After 58 laps, Schrader's run to the front was halted by an engine failure. Shortly after halfway, 1972 winner A. J. Foyt quit after experiencing a bizarre problem: In a mid-race interview with CBS's David Hobbs, Foyt claimed he had become intoxicated by fumes produced by his new racing helmet.

Dale Earnhardt dominated the race. He led 155 of the 200 laps, relinquishing the lead briefly to Bill Elliott, Mark Martin, Derrike Cope, Davey Allison, Geoff Bodine, Terry Labonte, and Bobby Hillin Jr. Daytona 500 rookies Jimmy Spencer and Jack Pennington led yellow flag laps early in the race.

Dale Earnhardt had the race in his grasp with a lead of more than 40 seconds with ten laps to go. On lap 193, Rick Wilson's car was experiencing engine trouble, and was reported to be leaking oil on the track. Geoff Bodine's car spun between turns 1 and 2, possibly due to the oil, which brought out the third and final caution of the day. Most of the leaders - including Earnhardt - ducked into the pits for tires and fuel. Earnhardt took on four fresh tires, as did Terry Labonte, Ricky Rudd and others. Geoff Bodine was able to change his flat-spotted tires and get back in the race, but not before he fell a lap down. Derrike Cope and Bobby Hillin Jr., however, stayed out during the caution, and cycled up to the front of the field. Cope's crew chief Buddy Parrott made the call to not pit and instead stay out on old tires, gambling on track position.

Seven cars were on the lead lap for the final restart. The top five were Derrike Cope, Bobby Hillin Jr., Dale Earnhardt, Terry Labonte, and Bill Elliott. As the cars were lining up for the restart, Earnhardt complained that Hillin bumped his left-rear fender. The green came back out with five laps to go. Earnhardt, with drafting help from Geoff Bodine, quickly dispatched of both Hillin and Cope simultaneously going into turn three. Earnhardt pulled out to a slight lead, with Cope (on old tires) tucking into second. Labonte passed Hillin for third.

Rick Wilson's sputtering engine finally let go, and a piece of the metal bell housing broke off and tumbled to a stop on the backstretch unnoticed. The white flag came out as the top four cars (Earnhardt, Cope, Labonte, Elliott) had broken away from the main draft. Going down the backstretch, with less than half a lap to go, Earnhardt ran over the bell housing debris and shredded the right rear tire. He held the wheel straight, let off the throttle and his car climbed up the banking of turn three. The pieces of the bell housing flew through the air, and ended up imbedded in Ricky Rudd's radiator. Spanaway, Washington's Derrike Cope dove under Earnhardt to shockingly take the lead in turn three. With only one turn remaining, Cope held off a last second challenge by Labonte and won his first ever Winston Cup victory. His previous best career finish was a 6th place at Charlotte in 1989. Earnhardt would manage to limp around to the finish line, and placed 5th. His crew later took the shredded tire and hung it on the wall of the race shop using the loss as motivation to win the 1990 Winston Cup championship. Meanwhile, Cope would become an overnight sensation appearing on The Late Show a week or so later to talk about his big win. Although it is considered one of the biggest upsets in NASCAR history, the ratings did not quite show it, as it drew a 7.3, the lowest in Daytona 500 history.

Standings after the race

 * Drivers' Championship standings
 * Note: Only the first 10 positions are included for the driver standings.

title: 1990 Daytona 500


text:
Separable state

In quantum mechanics, separable states are multipartite quantum states that can be written as a convex combination of product states. Product states are multipartite quantum states that can be written as a tensor product of states in each space. The physical intuition behind these definitions is that product states have no correlation between the different degrees of freedom, while separable states might have correlations, but all such correlations can be explained as due to a classical random variable, as opposed as being due to entanglement.

In the special case of pure states the definition simplifies: a pure state is separable if and only if it is a product state.

A state is said to be entangled if it is not separable. In general, determining if a state is separable is not straightforward and the problem is classed as NP-hard.

Separability of bipartite systems
Consider first composite states with two degrees of freedom, referred to as bipartite states. By a postulate of quantum mechanics these can be described as vectors in the tensor product space $$H_1\otimes H_2$$. In this discussion we will focus on the case of the Hilbert spaces $$H_1$$ and $$H_2$$ being finite-dimensional.

Pure states
Let $$\{|{a_i}\rangle\}_{i=1}^n\subset H_1$$ and $$\{|{b_j}\rangle\}_{j=1}^m \subset H_2$$ be orthonormal bases for $$H_1$$ and $$H_2$$, respectively. A basis for $$H_1 \otimes H_2$$ is then $$\{|{a_i}\rangle\otimes |{b_j}\rangle\}$$, or in more compact notation $$\{|a_i b_j \rangle\}$$. From the very definition of the tensor product, any vector of norm 1, i.e. a pure state of the composite system, can be written as

$$
 * \psi\rangle = \sum_{i,j} c_{i,j} (| a_i \rangle \otimes | b_j \rangle) =\sum_{i,j} c_{i,j} | a_i b_j \rangle,

where $$c_{i,j}$$ is a constant. If $$ |\psi\rangle$$ can be written as a simple tensor, that is, in the form $$|\psi\rangle = |\psi_1\rangle \otimes |\psi_2\rangle $$ with $$|\psi _i \rangle $$ a pure state in the i-th space, it is said to be a product state, and, in particular, separable. Otherwise it is called entangled. Note that, even though the notions of product and separable states coincide for pure states, they do not in the more general case of mixed states.

Pure states are entangled if and only if their partial states are not pure. To see this, write the Schmidt decomposition of $$|\psi\rangle$$ as
 * $$|\psi\rangle=\sum_{k=1}^{r_\psi} \sqrt{p_k} (|u_k\rangle\otimes|v_k\rangle),$$

where $$\sqrt{p_k}>0$$ are positive real numbers, $$r_\psi$$ is the Schmidt rank of $$|\psi\rangle$$, and $$\{|u_k\rangle\}_{k=1}^{r_\psi}\subset H_1$$ and $$\{|v_k\rangle\}_{k=1}^{r_\psi}\subset H_2$$ are sets of orthonormal states in $$H_1$$ and $$H_2$$, respectively. The state $$|\psi\rangle$$ is entangled if and only if $$r_\psi>1$$. At the same time, the partial state has the form
 * $$\rho_A\equiv \operatorname{Tr}_B(|\psi\rangle\!\langle\psi|) = \sum_{k=1}^{r_\psi} p_k \, |u_k\rangle\!\langle u_k|.$$

It follows that $$\rho_A$$ is pure --- that is, is projection with unit-rank --- if and only if $$r_\psi=1$$, which is equivalent to $$|\psi\rangle$$ being separable.

Physically, this means that it is not possible to assign a definite (pure) state to the subsystems, which instead ought to be described as statistical ensembles of pure states, that is, as density matrices. A pure state $$\rho=|\psi\rangle\!\langle\psi|$$ is thus entangled if and only if the von Neumann entropy of the partial state $$\rho_A\equiv\operatorname{Tr}_B(\rho)$$ is nonzero.

Formally, the embedding of a product of states into the product space is given by the Segre embedding. That is, a quantum-mechanical pure state is separable if and only if it is in the image of the Segre embedding.

For example, in a two-qubit space, where $$H_1=H_2=\mathbb{C}^2$$, the states $$|0\rangle\otimes|0\rangle$$, $$|0\rangle\otimes|1\rangle$$, $$|1\rangle\otimes|1\rangle$$, are all product (and thus separable) pure states, as is $$|0\rangle\otimes|\psi\rangle$$ with $$|\psi\rangle\equiv\sqrt{1/3}|0\rangle+\sqrt{2/3}|1\rangle$$. On the other hand, states like $$\sqrt{1/2}|00\rangle+\sqrt{1/2}|11\rangle$$ or $$\sqrt{1/3}|01\rangle+\sqrt{2/3}|10\rangle$$ are not separable.

Mixed states
Consider the mixed state case. A mixed state of the composite system is described by a density matrix $$\rho$$ acting on $$H_1 \otimes H_2$$. ρ is separable if there exist $$p_k\geq 0$$, $$\{ \rho_1^k \}$$ and $$\{ \rho_2^k \}$$ which are mixed states of the respective subsystems such that

\rho=\sum_k p_k \rho_1^k \otimes \rho_2^k $$

where

\sum_k p_k = 1. $$

Otherwise $$\rho$$ is called an entangled state. We can assume without loss of generality in the above expression that $$\{ \rho_1^k \}$$ and $$\{ \rho_2^k \}$$ are all rank-1 projections, that is, they represent pure ensembles of the appropriate subsystems. It is clear from the definition that the family of separable states is a convex set.

Notice that, again from the definition of the tensor product, any density matrix, indeed any matrix acting on the composite state space, can be trivially written in the desired form, if we drop the requirement that $$\{ \rho_1^k \}$$ and $$\{ \rho_2^k \}$$ are themselves states and $$\; \sum_k p_k = 1.$$ If these requirements are satisfied, then we can interpret the total state as a probability distribution over uncorrelated product states.

In terms of quantum channels, a separable state can be created from any other state using local actions and classical communication while an entangled state cannot.

When the state spaces are infinite-dimensional, density matrices are replaced by positive trace class operators with trace 1, and a state is separable if it can be approximated, in trace norm, by states of the above form.

If there is only a single non-zero $$p_k$$, then the state can be expressed just as $ \rho = \rho_1 \otimes \rho_2, $ and is called simply separable or product state. One property of the product state is that in terms of entropy,

 * $$ S(\rho) = S(\rho_1) + S(\rho_2). $$

Extending to the multipartite case
The above discussion generalizes easily to the case of a quantum system consisting of more than two subsystems. Let a system have n subsystems and have state space $$H = H_1 \otimes \cdots \otimes H_n$$. A pure state $$| \psi \rangle \in H$$ is separable if it takes the form

 * $$| \psi \rangle = | \psi_1 \rangle \otimes \cdots \otimes | \psi_n \rangle .$$

Similarly, a mixed state ρ acting on H is separable if it is a convex sum

 * $$\rho = \sum_k p_k \rho_1 ^k \otimes \cdots \otimes \rho_n ^k.$$

Or, in the infinite-dimensional case, ρ is separable if it can be approximated in the trace norm by states of the above form.

Separability criterion
The problem of deciding whether a state is separable in general is sometimes called the separability problem in quantum information theory. It is considered to be a difficult problem. It has been shown to be NP-hard in many cases and is believed to be so in general. Some appreciation for this difficulty can be obtained if one attempts to solve the problem by employing the direct brute force approach, for a fixed dimension. The problem quickly becomes intractable, even for low dimensions. Thus more sophisticated formulations are required. The separability problem is a subject of current research.

A separability criterion is a necessary condition a state must satisfy to be separable. In the low-dimensional (2 X 2 and 2 X 3) cases, the Peres-Horodecki criterion is actually a necessary and sufficient condition for separability. Other separability criteria include (but not limited to) the range criterion, reduction criterion, and those based on uncertainty relations. See Ref. for a review of separability criteria in discrete variable systems.

In continuous variable systems, the Peres-Horodecki criterion also applies. Specifically, Simon formulated a particular version of the Peres-Horodecki criterion in terms of the second-order moments of canonical operators and showed that it is necessary and sufficient for $$ 1\oplus1 $$-mode Gaussian states (see Ref. for a seemingly different but essentially equivalent approach). It was later found that Simon's condition is also necessary and sufficient for $$ 1\oplus n $$-mode Gaussian states, but no longer sufficient for $$ 2\oplus2 $$-mode Gaussian states. Simon's condition can be generalized by taking into account the higher order moments of canonical operators or by using entropic measures.

Characterization via algebraic geometry
Quantum mechanics may be modelled on a projective Hilbert space, and the categorical product of two such spaces is the Segre embedding. In the bipartite case, a quantum state is separable if and only if it lies in the image of the Segre embedding. Jon Magne Leinaas, Jan Myrheim and Eirik Ovrum in their paper "Geometrical aspects of entanglement" describe the problem and study the geometry of the separable states as a subset of the general state matrices. This subset have some intersection with the subset of states holding Peres-Horodecki criterion. In this paper, Leinaas et al. also give a numerical approach to test for separability in the general case.

Testing for separability
Testing for separability in the general case is an NP-hard problem. Leinaas et al. formulated an iterative, probabilistic algorithm for testing if a given state is separable. When the algorithm is successful, it gives an explicit, random, representation of the given state as a separable state. Otherwise it gives the distance of the given state from the nearest separable state it can find.

title: Separable state


text:
Jean-Claude Van Cauwenberghe

Jean-Claude Van Cauwenberghe (born 28 April 1944 in Charleroi), nicknamed "Van Cau", is a Belgian politician. He is member of the Parti Socialiste (Socialist Party; PS). He was the tenth Minister-President of Wallonia from 4 April 2000 until 30 September 2005. He resigned amid the ICDI affair and was replaced by Elio Di Rupo. He also served as mayor of Charleroi (1983-2000).

title: Jean-Claude Van Cauwenberghe