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Nitrogen-13

Nitrogen-13 (13N) is a radioisotope of nitrogen used in positron emission tomography (PET). It has a half-life of a little under ten minutes, so it must be made at the PET site. A cyclotron may be used for this purpose.

Nitrogen-13 is used to tag ammonia molecules for PET myocardial perfusion imaging.

Production
Nitrogen-13 is used in medical PET imaging in the form of 13N-labelled ammonia. It can be produced with a medical cyclotron, using a target of pure water with a trace amount of ethanol. The reactants are oxygen-16 (present as H2O) and a proton, and the products are nitrogen-13 and an alpha particle (helium-4).

 * 1H + 16O → 13N + 4He

The proton must be accelerated to have total energy greater than 5.66 MeV. This is the threshold energy for this reaction, as it is endothermic (i.e., the mass of the products is greater than the reactants, so energy needs to be supplied which is converted to mass). For this reason, the proton needs to carry extra energy to induce the nuclear reaction.

The energy difference is actually 5.22 MeV, but if the proton only supplied this energy, the reactants would be formed with no kinetic energy. As momentum must be conserved, the true energy that needs to be supplied by the proton is given by:

 * $$K =(1+m/M) |E|$$

where $$m$$ is the mass of 4He and $$M$$ is the mass of 13N ; therefore $$m/M$$ = 0,307 806 661. The presence of ethanol (at a concentration of ~5mM) in aqueous solution allows the convenient formation of ammonia as nitrogen-13 is produced. Other routes of producing 13N-labelled ammonia exist, some of which facilitate co-generation of other light radionuclides for diagnostic imaging.

Nitrogen-13 plays a significant role in the CNO cycle, which is the dominant source of energy in main-sequence stars more massive than 1.5 times the mass of the Sun.

Lightning may have a role in the production of nitrogen-13.

title: Nitrogen-13


text: Category:Olympic tennis players for Great Britain

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


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The American Voter

The American Voter, published in 1960, is a seminal study of voting behavior in the United States, authored by Angus Campbell, Philip Converse, Warren Miller, and Donald E. Stokes, colleagues at the University of Michigan. Among its controversial conclusions, based on one of the first comprehensive studies of election survey data (what eventually became the National Election Studies), is that most voters cast their ballots primarily on the basis of partisan identification (which is often simply inherited from their parents), and that independent voters are actually the least involved in and attentive to politics. This theory of voter choice became known as the Michigan Model. It was later extended to the United Kingdom by David Butler and Donald Stokes in Political change in Britain.

The American Voter established a baseline for most of the scholarly debate that has followed in the decades since. Criticism has followed along several different lines. Some argue that Campbell and his colleagues set the bar too high, expecting voters to be far more sophisticated and rational than is reasonable. Some scholars, most notably V. O. Key, Jr., in The Responsible Electorate, have argued, in part based on reinterpretation of the same data, that voters are more rational than The American Voter gives them credit for. His famous line "Voters are not fools" summarizes this view. Successors in the Michigan school have argued that in relying heavily on data from the 1956 presidential election, The American Voter drew conclusions that were not accurate over time; in particular, partisan identification has weakened in the years since 1956, a phenomenon sometimes known as dealignment (see political realignment).

The American Voter has served as a springboard from which many modern political scientists form their views on voting behavior even though the study only represents one specific time in one particular place.

Warren Miller (d. 1999) and Merrill Shanks from the University of California, Berkeley have revisited many of these questions in The New American Voter (1996), which argues against the dealignment notion, preferring the term "nonalignment" based on their conclusion that the decline in partisan identification is mostly a matter of new voters not aligning with a party rather than older voters abandoning their previous allegiances.

title: The American Voter


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Tarana, New South Wales

Tarana is a small town in the Central West of New South Wales, Australia in the City of Lithgow.

It is the former junction of the Oberon Branch railway with the Main Western Line. This branch line was notable for its steep 1 in 30 gradients and sharp 100 m curves.

History
The name Tarana comes from an Aboriginal word meaning watering hole. Tarana railway station was opened on 22 April 1872.

Heritage listings
Tarana has a number of heritage-listed sites, including:
 * Main Western railway: Tarana railway station

title: Tarana, New South Wales


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Roger Sowry

Roger Morrison Sowry (born 2 December 1958) is a former New Zealand politician. He is a member of the National Party, and was the deputy leader from 2001 to 2003.

Early life
Sowry was born in Palmerston North, and attended Tararua College in Pahiatua where he was head boy. His education included an American Field Service exchange to Minnesota in 1977, and a Diploma of Business Administration from Victoria University of Wellington. After working for a time at the Valuation Department, Sowry was employed by Hannahs, shoe manufacturers and retailers as a retail manager. He is Anglican, and married with four children.

Member of Parliament
Sowry joined the National Party in 1977, and was active in its youth wing. In the 1987 election, beat out anti-abortion activist Marilyn Pryor for the National candidacy to challenge Labour Party MP Margaret Shields in the Kapiti electorate. The challenge was unsuccessful, but a second attempt in the 1990 election was successful; he defeated Shields and entered Parliament. Sowry kept the seat until the 1996 election, when he unsuccessfully contested the new Otaki seat against Labour's Judy Keall and became a list MP.

In 1993, Sowry was appointed as his party's Junior Whip, and in 1995, he became Senior Whip.

Member of Cabinet
In December 1996, he was elevated to Cabinet, becoming Minister of Social Welfare. In 1998, the role was reorganized, becoming Minister of Social Services, Work and Income. He also served for a time as Minister in charge of War Pensions, Minister responsible for the Housing Corporation (state housing), and Associate Minister of Health. In January 1999, he was given special responsibility for co-ordinating National's relationship with the groups that it relied upon for support (Mauri Pacific, Mana Wahine, and others).

In October 2001, when Bill English displaced Jenny Shipley as leader of the National Party, Sowry (who had played a significant role in English's rise) became National's deputy leader. He remained in this position until English himself was displaced by Don Brash in October 2003.

Resignation
On 13 July 2004, Sowry announced that he would not seek re-election, saying that he was looking for a change of career. Sowry denied there were tensions between himself and the party's new leadership. Brash publicly praised Sowry's "outstanding contribution" over the years.

Until 2008 he was the Chief Executive of Arthritis New Zealand, subsequently moving to Saunders Unsworth, as a consultant on Government matters.

In the 2011 New Year Honours, Sowry was appointed an Officer of the New Zealand Order of Merit for services as a Member of Parliament. In 2013, Sowry was appointed a member of the Representation Commission to determine New Zealand electoral boundaries.

title: Roger Sowry


text: Category:Olympic tennis players for Australia


text:
Pillar coral

Pillar coral (Dendrogyra cylindrus) is a hard coral (order Scleractinia) found in the western Atlantic Ocean and the Caribbean Sea. It is the only species in the monotypic genus Dendrogyra. It is a digitate coral -that is, it resembles fingers (Latin digites) or a cluster of cigars, growing up from the sea floor without any secondary branching. It is large and can grow on both flat and sloping surfaces at depths down to 20 m (65 ft). It is one of the few types of hard coral in which the polyps can commonly be seen feeding during the day.

Description
Pillar coral forms an encrusted base from which grow vertical cylindrical, round-ended columns. This coral can grow to a height of 3 m with pillars more than 10 cm wide but is usually much smaller than this. The corallites from which the polyps protrude are smaller than 1 cm in diameter and arranged in shallow meandering valleys with low ridges in between. The skeleton of the coral is not usually visible because the polyps are typically extended during the daytime, unlike most other coral species. The mass of undulating tentacles gives the coral a furry appearance. This coral is usually some shade of beige or brown.

Distribution and habitat
Pillar corals are found in the warmer parts of the western Atlantic Ocean and the Caribbean Sea. Within its range, D. cylindrus is common in some places, but rare in other seemingly suitable locations. Some of the islands in the Bahamas have plentiful numbers of colonies as does the north coast of Jamaica. It used to be common on the reefs off the coast of Florida but has suffered from over-collection there. It seems to be absent from Bermuda and the coasts of Panama and Colombia. It usually grows on level or slightly sloping parts of the reef at depths between 1 and 20 m.

Biology
Pillar coral is a zooxanthellate species, with symbiotic dinoflagellate algae living within the tissues. In sunlight these undergo photosynthesis and most of the organic compounds they produce are transferred to their host, while they make use of the coral's nitrogenous wastes. These algae give the coral its brownish colour and restrict it to living in shallow water into which the sunlight can penetrate.

Pillar coral is a slow-growing, long-lived species. A number of columns grow up from a basal plate; if the whole colony is dislodged and topples over, new cylindrical pillars can grow vertically from the fallen coral. Some specimens have been found where this has happened more than once, and the history of the colony can be deduced from its shape. If a pillar gets detached and becomes lodged in a suitable position, it can continue to live, sending up new pillars from the base and other parts of the column.

Each pillar coral clonal colony is either male or female, an evolutionary life history strategy described as gonochoric. However, hermaphroditic events have been recorded for the species. Sexual reproduction takes place with gametes being released into the water column where fertilisation takes place. The larvae that develop from the eggs are planktonic and drift with the currents before settling on the seabed to found new colonies.

Status
The IUCN Red List of Threatened Species lists pillar coral as being Critically Endangered under criteria A2bce. This is because recruitment and survival rates of juveniles is low and this coral is particularly susceptible to both bleaching and white plague disease. It is resistant to strong wave action but can be wrecked by hurricanes and tropical storms. However, broken fragments regenerate well. Some of the localities in which it is found are in marine parks and in these it should be safe from human disturbance. In addition, the advent of stony coral tissue loss disease in Florida and the Caribbean is causing local extinctions and may have species-level effects on this species as it is infected at an early stage of the disease progression. Finally, it is a gonochoric species which was never particularly common within its range, making its reproductive potential lower than might otherwise be expected.

The species is functionally extinct in Florida, USA, and mostly survives in captivity.

title: Pillar coral


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Gerringong, New South Wales

Gerringong is a town located about ten minutes drive south of Kiama, and about twenty minutes north of Nowra in the Illawarra region of New South Wales, Australia in the Municipality of Kiama. At the, Gerringong had a population of 3,966. One theory says that the name derives from an Aboriginal word meaning "fearful place".

History
Aboriginal people of the Dharawal language group are the original inhabitants and traditional custodians of the area now known as Gerringong and its surroundings.

The first Europeans to pass through the district on land were probably survivors of the wreck of the Sydney Cove who trekked more than 700 km along the coast, during 1797. George Bass explored the nearby coast, later in 1797, during his voyage that revealed the existence of the Shoalhaven River to the colonial settlers.

The first Europeans working in the area were red cedar cutters, who were first recorded as having visited and logged in the area in 1814. As in much of coastal New South Wales, the cleared land was used for dairy farming and cedar cutting died out, as the cedar trees disappeared. Dairy farming became the predominant primary industry and remains so to this day. Gerringong had a small boat harbour used for the export of cedar and dairy produce.

The Surveyor-General John Oxley and Assistant Surveyor-General James Meehan led two separate but concurrent expeditions passing through the Gerringong area in late 1819. Oxley proceeded down the coast by sea to the Shoalhaven. Meehan went overland, starting from the Minnamurra River and meeting Oxley at the Shoalhaven. Oxley's report of good soil in the area increased interest in agricultural settlement.

In 1824, Governor Brisbane reserved 600 acres (2.4 km2) for the present Gerringong township. In 1827, Michael Hindmarsh and his family were granted 640 acres (2.6 km2) and became the first settler in the Gerringong area. In 1829, Gerringong was incorporated into the postal system.

Aboriginal people in the area of Gerringong continued to state their ownership of it—including Hindmarsh's grant—in the 1840s. By then, the settlers' clearing of the sub-tropical rainforest was transforming the landscape completely—to lush pastures suited to dairy cattle—and depriving the original inhabitants of the land, environment and land-based food sources upon which they had depended for thousands of years. Effectively barred from private land, they were confined to unalienated 'government' land.

Alne Bank homestead was built in 1851 for the Hindmarsh family, who still live there today and occasionally open it for inspection.

In 1854, a town plan for Gerringong was approved and the Governor proclaimed it a village. In 1872, the business area, Church of England church and some houses were destroyed by a bush fire.

In the late 1860s and 1870s, locals advocated the erection of a jetty at the Boatharbour. In 1880 a 200-foot-long jetty was completed but it was too short to allow coastal ships to berth. One ship that did call there was Dairy Maid, a small wooden-hulled steamer built in the Rock Davis shipyard. The jetty was extended, in the mid-1880s, first by 200-feet and subsequently another 100 feet. The 500-foot-long jetty was extensively damaged in fierce storms in 1891. It was rebuilt but, during that work, was damaged again by stormy weather in 1892, necessitating more repairs. A new crane was installed in 1893. The jetty was probably used to land materials for railway construction.

In 1893, the South Coast railway line was extended to Gerringong, leading to the end of shipping from the town. The disused jetty was given to the local council, for use as bridge material, around 1901. The last standing remnants of the jetty were washed away in 1904.

By 1897, the dispossession was complete; local Aborigines had "dwindled to a handful" living in a camp just south-west of Gerringong, at Crooked River and another camp at 'Ooirie Creek' (now Ooarie Creek) near Omega, whose inhabitants were later relocated. The lives of the surviving Aborigines were, for many years, controlled by the Aborigines Protection Board, and subject to the disdain of many —if not all  —white inhabitants.

Telephone services were extended to Gerringong by June 1915 and electricity was connected in 1928.

In 1954, Gerringong Municipal District amalgamated with Kiama Municipal Council. The town water supply was connected in 1971, signalling an end to tanks attached to each house. Land along the coastal fringe tends to receive higher rainfall than the interior water catchment areas, which are often in rainshadow. In 2002, the town sewerage system was connected.

Modern Gerringong
At the, Gerringong and the surrounding area had a population of 3,966. There is still an Aboriginal presence in Gerringong. In 2016, 2.5% of the population identified as indigenous.

The main local industries are agriculture (including dairying and vineyards), tourism and retail trade. Others enjoy the seaside lifestyle but commute to work in Wollongong or Nowra and even Sydney.

The town has a modern primary school, a town hall (built 1948), a large retirement village and a tourist industry. Especially in the summer months, when visitors (mostly from Sydney and Canberra) attend the beaches for swimming, surfing, fishing and the restaurants and cafés. There are two vineyards.

The Gerringong and District Historical Society runs the Heritage Museum, containing scale models of buildings, a photographic record of motor racing on Seven Mile Beach in the 1920s, and a display on the local dairying industry.

Transport
Gerringong railway station is served by NSW TrainLink's South Coast Line. Services are provided by diesel trains, which connect with electric trains to Sydney at Kiama. Local bus companies connect Gerringong to Kiama and Nowra on a daily basis, and interstate buses connect it with Sydney and Melbourne and all stops in between.

In 2012, a major Princes Highway upgrade commenced in Gerringong. The upgrade provides 7.5 kilometres of upgraded highway and includes two new interchanges with access to Gerringong and Gerroa. This major infrastructure project includes a new overpass over the Omega rail level crossing, major highway widening, additional exits, and safer on and off ramps. The $329 million upgrade was officially opened on 20 August 2015.

Geography
The boundaries of the Gerringong District range from Mount Pleasant and Omega in the north, to Rose Valley, Willow Vale and Foxground in the west, and to Broughton Village, Toolijooa, Harley Hill, Gerroa and Seven Mile Beach in the south. In the centre of the area lies the town of Gerringong itself, and the nearby area of Werri Beach.

The Kiama and Gerringong area is marketed as "Where the Mountains Meet the Sea" by Kiama Council. A spur of Saddleback Mountain reaches down to Mt Pleasant to the north of Gerringong township, ending the Illawarra escarpment, which starts north of Wollongong. The area is famous for its coastline, which includes sea cliffs, beaches surrounded by rolling hills and countryside that stays green year-round.

The spur of Saddlback Mountain that separates Gerringong from Kiama was very significant in the town's history. The steep road over the spur made using the port of Kiama difficult. Gerringong would need its own small port, until the railway from Kiama opened in 1893 after tunnels were cut through the basalt rock of the spur.

The Princes Highway bypasses Gerringong township on its western edge, with two exits, one at Fern St and an underpass at Belinda Street, 2 km further south. Gerringong and Werri Beach were previously two separate localities, but have now grown together without any definitive boundary.

Werri Lagoon, which sometimes empties to the sea at the northern end of Werri Beach, used to naturally exit near the Gerringong Surf Club at the south end, until human intervention occurred in the 1960s. Bridges Road used to be access to a bridge which provided access to Werri Beach.

Werri Lagoon is now part of the Kiama Coast Walk, which stretches from Loves Bay, north of Kiama, to Werri Lagoon. The walking track extends for six kilometres and took eleven years to prepare and construct. It opened in October 2009.

Gerringong's Boatharbour—its traditional spelling—was used extensively for shipping timber and dairy produce in the 19th century. The Boatharbour provides little shelter from a black nor'easter and relatively little from the heavy seas associated with an east coast low. There is a boat ramp there and it is the location of Gerringong's ocean swimming pool.

Gerringong's geology is basically basalt, emplaced in the Permian period.

Climate
Gerringong is the most northerly coastal town that is entirely within an oceanic climate (Köppen: Cfb), although it is at a dominated latitude of subtropical climates along the coast the low average record temperatures are more similar to the second category. The city has warm summers and mild winters. Rainfall is spread relatively evenly throughout the year with the wettest months being in autumn and the driest in spring.

Politics
Gerringong is part of the Municipality of Kiama. Local residents are represented by the Member of NSW Parliament for Kiama, currently Gareth Ward. The area is represented by the Federal Member for Gilmore, currently Fiona Phillips.

Notable people

 * Mick Cronin, rugby league player, owner of local pub
 * Sally Fitzgibbons, pro surfer
 * Lloyd Rees, artist; the area was the subject of many of his landscape works from the 1930s to the 1980s.
 * Ashton Sims, rugby league player, played for the Gerringong Lions as a junior, currently plays for the Toronto Wolfpack
 * Korbin Sims, rugby league player, played for the Gerringong Lions as a junior, currently plays for the St. George Illawarra Dragons
 * Tariq Sims, rugby league player, played for the Gerringong Lions as a junior, currently plays for the St. George Illawarra Dragons
 * Grace Stewart, Australian field hockey representative
 * Rod Wishart, rugby league player
 * Ben Fryer, lead guitarist from Pacific Avenue

title: Gerringong, New South Wales


text:
Umm Salama

Hind bint Abi Umayya (هِنْد ابِنْت أَبِي أُمَيَّة, Hind ʾibnat ʾAbī ʾUmayya, c. 580 or 596 –  680 or 683), better known as Umm Salamah (أُمّ سَلَمَة) or Hind al-Makhzūmiyya (هِنْد ٱلْمَخْزُومِيَّة) was the sixth wife of Muhammad.

"Umm Salama" was her kunya meaning, "mother of Salama". She was one of the most influential female companions of Muhammad. She is recognized largely for recalling numerous Hadiths, or sayings and narrations attributed to Muhammad. Shia Muslims believe that Umm Salama was the most important wife of Muhammad after Khadija.

Before marriage with Muhammad
Umm Salama's birth name was Hind. Her father was Abu Umayya ibn Al-Mughira ibn Abdullah ibn Umar ibn Makhzum ibn Yaqazah also known as Suhayl or Zad ar-Rakib. He was an elite member of his Quraysh tribe, known for his great generosity, especially to travelers. Her mother was 'Ātikah bint 'Āmir ibn Rabī'ah, of the Firas ibn Ghanam branch of the Kinana.

Marriage to Abu Salama
Before her marriage to Muhammad, Umm Salama was married to Abu Salama Abd Allah ibn Abd al-Asad, whose mother was Barrah bint Abdul Muttalib. Abu Salama was Muhammad's foster brother and one of his close companions. Umm Salama bore with Abu Salama four children: Salama, Umar, Zaynab and Ruqayyah.

Conversion to Islam
Umm Salama and her husband Abu Salama were among the first who converted to Islam. Only Ali and a few others were Muslims before them. Despite intense anger and persecution from the powerful Quraysh in response to their conversions to Islam, Umm Salama and Abu Salama continued their devotion to Islam.

As the persecution grew in severity, the new Muslims began to look for life away from Mecca. Muhammad instructed his newly converted followers, including Umm Salama and Abu Salama, to make a migration to Abyssinia. Umm Salama abandoned her honorable life in her clan in Mecca to make the migration. While in Abyssinia, these Muslims were told that there had been a decrease in persecution along with an increase in numbers of Muslims in Mecca. This information caused Umm Salama, her husband, and the rest of the Muslim emigrants to travel back to Mecca. Upon their return to Mecca, the Quraysh again began viciously persecuting the Muslims. In response, Muhammad gave his followers instructions to make a migration to Medina, also known as the hijrah. Umm Salama, along with her husband and son planned to make the hijra together, however this was stopped when Umm Salama's clan forced her to stay in Mecca, while Abu Salama's clan took the child.

Umm Salama recounted this story: "Before we were out of Makkah, however, some men from my clan stopped us and said to my husband: 'Though you are free to do what you like with yourself, you have no power over your wife. She is our daughter. Do you expect us to allow you to take her away from us?' Then they pounced on him and snatched me away from him. My husband's clan, Banu 'Abd al-Asad, saw them taking me and became hot with rage. 'No! By Allah' they shouted, 'we shall not abandon the boy. He is our son and we have a first claim over him.' They took him by the hand and pulled him away from me."

- Umm Salama

Abu Salama made the trip to Medina alone, leaving his wife and child in Mecca. After some time, Umm Salama was permitted by the Quraysh to leave Mecca, and was given her son back by her husband's tribe. With her son, she completed the hijra and was reconnected with her husband.

Death of Abu Salama
During her marriage to Abu Salamah, Umm Salamah (in a story related by Ziyad ibn Abi Maryam) is said to have asked her husband to make agreement that when either of them died, the other would not remarry. However, in this tradition, Abu Salamah responded by instructing Umm Salamah to remarry after his death. He then prayed, "O God, provide Umm Salamah after me with a better man than me who will not grieve her or injure her!"

During the Battle of Uhud (March 625), Abu Salamah was severely injured. While Abu Salamah was dying due to these wounds, he recalled a story to Umm Salamah involving a message he had heard from Muhammad: "I heard the Messenger of God saying, 'Whenever a calamity afflicts anyone he should say, "Surely from God we are and to Him we shall certainly return."' And he would pray, 'O Lord, give me in return something better from it which only You, Exalted and Mighty can give'". This traditional story has been transmitted with various differences, but the fundamental principles of the hadith remain intact.

Her husband eventually died from the wounds he received in the Battle of Uhud. Umm Salamah remembered the hadith recalled by her husband prior to his death, and began reciting the given prayer.

Following Abdullah ibn Abdulasad's death in the battle of Uhud she became known as Ayyin al-Arab - "the one who had lost her husband". She had no family in Medina except her small children, but she was given support by both the Muhajirun and Ansar. After finishing the iddah of four months and ten days, the sufficient amount of time that a woman must wait after the death of her husband before she can remarry, Umm Salama got offers of marriage. Abu Bakr and then Umar asked to marry her, but she declined. Muhammad himself then proposed to Umm Salama. She initially hesitated in her acceptance, stating, "O Messenger of Allah, I have three characteristics. I am a woman who is extremely jealous and I am afraid that you will see in me something that will anger you and cause Allah to punish me. I am a woman who is already advanced in age and I am a woman who has a young family."

However, Muhammad appeased each of her concerns, "Regarding the jealousy you mentioned, I pray to Allah the Almighty to let it go away from you. Regarding the question of age you have mentioned, I am afflicted with the same problem as you. Regarding the dependent family you have mentioned, your family is my family."

Muhammad's era
Umm Salama was married to Muhammad at the age of 32. Umm Salamah was a widow with 3 children and a fourth born almost immediately after their marriage.

When Fatimah bint Asad (mother of the 4th Caliph Ali) died, Muhammad is said to have chosen Umm Salama as the guardian of Fatimah bint Muhammad. However, the latter Fatimah is thought to have married Ali in 1 AH or 2 AH, Fatimah bint Asad died in 4 AH, and Umm Salama married Muhammad in year 5, so any guardianship must have been purely nominal.

The verse of purification (05:06) in the Qur'an was revealed to Muhammad in her house.

Umm Salama and the wives of Muhammad
In the fourth year following the migration to Medina (4 AH), Umm Salama accepted a marriage proposal from Muhammad. After sharing her three reservations about the marriage, and hearing the response from Muhammad, Umm Salama was so pleased that she accepted the proposal. Umm Salama became the eldest of all of Muhammad's wives. She became the highest-ranking wife of Muhammad, only behind Khadija. Her elevated status among the rest of the wives was a result of her presence in many wars and her defense of the household of Muhammad. Attributes that distinguish Umm Salama from the rest of the wives of Muhammad include the following: Her role in Fatimah's upbringing (most prominent daughter of Muhammad, whom Umm Salama proclaimed displayed more knowledge than ever herself in all affairs), her political activism, her accounts of Muhammad's narrations, and her unwavering defense of Ali's personality and leadership following Muhammad's death.

The greatest attribute of the wives of Muhammad is demonstrated as being known as the "Mothers of the believers". They were also prohibited from marrying another man ever again. (33:53) The Qur'an indicates that the wives of Muhammad had to be role models in society (33:30-32). She was often looked up to by the rest of the wives of Muhammad due to her intelligence and political knowledge. Umm Salama herself narrated 378 Hadith, among them being some of the most important. She was the last of the wives of Muhammad to pass away.

Impact on Muhammad and society
Because of her beauty, knowledge, and wisdom, Umm Salama held a prominent role in the house of Muhammad and society. She was an exceptional wife of Muhammad in her faith and morals. As a woman, she carried out and completed all of her religious duties. During her marriage to Muhammad, she strived to keep him happy. She always held the utmost respect for him. She was known in society for her intelligence, political savvy, and activity in fighting for women's rights. Umm Salama was a woman most gifted in judgment. She was active in the movement for women's rights in early Islamic society too. She once asked Muhammad a very political question, "Why are men mentioned in the Quran and why are we not?" In a response from heaven to Muhammad, Allah declares that the two sexes are of total equality as members of the community and believers. It doesn't matter the sex, as long as the person is faithful and has the desire to obey Allah, they will earn his grace. This act by Umm Salama, sets the precedent and shows that women could go directly to Muhammad when unsatisfied with a gender role associated with them in society. This action by Umm Salama represented a veritable protest movement by the women. Umm Salama possessed very good judgment, rapid powers of reasoning, and unparalleled ability to formulate correct opinions.

Treaty of Hudaybiyya
Umm Salama acted as Muhammad's advisor during negotiations concerning the Treaty of Hudaybiyyah with the Meccans in 628 CE (6 AH) One of the main objects of this treaty was to determine the relations between Muhammad and the Muslims of Medina with the Quraysh in Mecca. The treaty was aimed at achieving peace between the two groups and allowing the Muslims to complete their annual pilgrimage to the Kaaba, known as Hajj, which they did the following year in 629 (7 AH). This treaty was essential since it established a 10-year peace deal between the two groups. The treaty was broken later in 629 (8 AH) which led to the conquest of Mecca.

After Muhammad
After Muhammad's death, Umm Salama continued to have an influence on Islam. Her numerous Hadith transmissions have had a lasting impact on the future of the religion. Umm Salama, along with one of Muhammad's other wives, Aisha, also took roles as imams, leading other women in worship.

Umm Salama also took a strong position in the Battle of the Camel, in which the factions of Aisha and Ali were in direct opposition. Umm Salama openly disagreed with the involvement of Aisha in the battle. She strongly supported the faction of Ali, and is said to have recalled stories in which Muhammad favors Ali and Fatimah to back up her opinions on the battle.

Umm Salama even sent her son, Umar, to fight for Ali's victory.

Umm Salama died around 64 AH. Although the date of her death is disputed, her son said that Umm Salama died at the age of 84. She was buried in the Baqi Cemetery. She was the last surviving of Muhammad's wives.

Hadith
Umm Salama and Aisha provided more Hadiths than any of the other wives of Muhammad. For Umm Salama, 378 narrations have been reported through the Sunni Muslims. Among the [Hadith] she narrated are:

Verse of purification 33:33
''And stay quietly in your houses, and make not a dazzling display, like that of the former Times of Ignorance; and establish regular Prayer, and give regular Charity; and obey Allah and His Messenger. And Allah only wishes to remove all abomination from you, ye members of the Family, and to make you pure and spotless.''

The verse of purification (Ayat al-Tathir) verse is given its name due to the mentioning of purity in the last line. According to Umm Salama, the verse of purification was revealed in her home when only Muhammad, Ali, Fatimah, Hasan, and Husayn were present. Scholars such as Tarbasi and Tha'labi have described Umm Salama narrating: "One day Lady Fatima having cooked some food brought it to my house for the Prophet. The Prophet said, 'O the light of my eyes, call Ali and your sons so that we may eat this food together.'" When all had gathered and they had eaten from that food, Angel Jibra'eel descended and revealed the following verse: Indeed God desires to repel all impurity from you, O People of the Household, and purify you with a thorough purification.

Upon hearing the verse, the Prophet laid out a cloak over them and said: "O God, these are the people of my household. They are my confidants and my supporters. O God, remove impurity from them and keep them thoroughly pure." Umm Salama relates, "As I heard this prayer from the Prophet, I said: 'O Messenger of God! Am I also with you?' To which he replied: 'You do not have the level of my Ahlul Bayt, but you are a lady of noble traits.'

Some exegesis, including Amina Wadud interpret the first line, "stay quietly in your houses, and make not a dazzling display, like that of the former Times of Ignorance" not to imply women shouldn't be allowed to go out at all, but rather to stress the limitation of going out for the aim of wanton display.

33:35
For Muslim men and women, for believing men and women, for devout men and women, for true men and women, for men and women who are patient and constant, for men and women who humble themselves, for men and women who give in Charity, for men and women who fast (and deny themselves), for men and women who guard their chastity, and for men and women who engage much in Allah's praise, for them has Allah prepared forgiveness and great reward.

Umm Salama sought out equality and autonomy for Muslim women and never hesitated to posit political questions to Muhammad. This verse initiated when Umm Salama asked Muhammad, "why are men mentioned in the Koran and why are we not?" She is quoted narrating, "I had asked the Prophet why the Koran did not speak of us as it did of men. And what was my surprise one afternoon, when I was combing my hair, to hear his voice from the minbar. I hastily did up my hair and ran to one of the apartments from where I could hear better" It is there that Umm Salama heard the verse.

title: Umm Salama


text:
Talk:EVA Air

Pronunciation
"(pronounced "E-V-A Air(ways)" <-- Does this match others' experience? I've certainly heard EVA pronounced as one word and not the letters, though I've only flown it twice and don't speak Chinese.  Thomas Craven (talk) 18:23, 15 March 2013 (UTC)

My entire life in both Canada and Thailand, it is always pronounced EVA (ee-va) Air - one word. 198.103.104.11 (talk) 03:45, 27 November 2013 (UTC)

 * It is popularly called "Eva Air" but the official pronunciation is "E-V-A" as shown in these official videos from the carrier: (at 0:32), and here  (at 0:42).  Regards, SynergyStar (talk) 07:30, 27 November 2013 (UTC)

A Commons file used on this page has been nominated for deletion
The following Wikimedia Commons file used on this page has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 10:30, 11 November 2018 (UTC)
 * EVA AIR logo.svg

Commons files used on this page have been nominated for speedy deletion
The following Wikimedia Commons files used on this page have been nominated for speedy deletion: You can see the reasons for deletion at the file description pages linked above. —Community Tech bot (talk) 09:21, 20 December 2019 (UTC)
 * EVA Air hello kitty A321.jpg
 * EVA Hello Kitty Meal.jpg
 * EVA air hello kitty economy.jpg

Why did they retire the 747 from their fleet?
I really miss the 747 being Eva airs fleet. Why did they retire it? 66.215.202.57 (talk) 19:42, 29 December 2022 (UTC)

Archived ref not used in the article
Sunnya343 (talk) 21:30, 27 March 2024 (UTC)
 * Destinations list 1994

title: Talk:EVA Air


text: Category:Olympic tennis players for Belarus


text:
Kernel (linear algebra)

In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part (or linear subspace) of the domain which the map maps to the zero vector. That is, given a linear map $L : V → W$ between two vector spaces $V$ and $W$, the kernel of $L$ is the vector space of all elements $v$ of $V$ such that $L(v) = 0$, where $0$ denotes the zero vector in $W$, or more symbolically: $$\ker(L) = \left\{ \mathbf{v} \in V \mid L(\mathbf{v})=\mathbf{0} \right\} = L^{-1}(\mathbf{0}).$$

Properties
The kernel of $L$ is a linear subspace of the domain $V$. In the linear map $$L : V \to W,$$ two elements of $W$ have the same image in $L$ if and only if their difference lies in the kernel of $V$, that is, $$L\left(\mathbf{v}_1\right) = L\left(\mathbf{v}_2\right) \quad \text{ if and only if } \quad L\left(\mathbf{v}_1-\mathbf{v}_2\right) = \mathbf{0}.$$

From this, it follows that the image of $V$ is isomorphic to the quotient of $W$ by the kernel: $$\operatorname{im}(L) \cong V / \ker(L).$$ In the case where $L$ is finite-dimensional, this implies the rank–nullity theorem: $$\dim(\ker L) + \dim(\operatorname{im} L) = \dim(V).$$ where the term refers to the dimension of the image of $L$, $$\dim(\operatorname{im} L),$$ while  refers to the dimension of the kernel of $V$, $$\dim(\ker L).$$ That is, $$\operatorname{Rank}(L) = \dim(\operatorname{im} L) \qquad \text{ and } \qquad \operatorname{Nullity}(L) = \dim(\ker L),$$ so that the rank–nullity theorem can be restated as $$\operatorname{Rank}(L) + \operatorname{Nullity}(L) = \dim \left(\operatorname{domain} L\right).$$

When $V$ is an inner product space, the quotient $$V / \ker(L)$$ can be identified with the orthogonal complement in $L$ of $$\ker(L)$$. This is the generalization to linear operators of the row space, or coimage, of a matrix.

Application to modules
The notion of kernel also makes sense for homomorphisms of modules, which are generalizations of vector spaces where the scalars are elements of a ring, rather than a field. The domain of the mapping is a module, with the kernel constituting a submodule. Here, the concepts of rank and nullity do not necessarily apply.

In functional analysis
If $L$ and $V$ are topological vector spaces such that $V$ is finite-dimensional, then a linear operator $L: V → W$ is continuous if and only if the kernel of $V$ is a closed subspace of $W$.

Representation as matrix multiplication
Consider a linear map represented as a $m × n$ matrix $W$ with coefficients in a field $L$ (typically $$\mathbb{R}$$ or $$\mathbb{C}$$), that is operating on column vectors $x$ with $V$ components over $A$. The kernel of this linear map is the set of solutions to the equation $Ax = 0$, where $0$ is understood as the zero vector. The dimension of the kernel of A is called the nullity of A. In set-builder notation, $$\operatorname{N}(A) = \operatorname{Null}(A) = \operatorname{ker}(A) = \left\{ \mathbf{x}\in K^n \mid A\mathbf{x} = \mathbf{0} \right\}.$$ The matrix equation is equivalent to a homogeneous system of linear equations: $$A\mathbf{x}=\mathbf{0} \;\;\Leftrightarrow\;\; \begin{alignat}{7} a_{11} x_1 &&\; + \;&& a_{12} x_2 &&\; + \;\cdots\; + \;&& a_{1n} x_n &&\; = \;&&& 0     \\ a_{21} x_1 &&\; + \;&& a_{22} x_2 &&\; + \;\cdots\; + \;&& a_{2n} x_n &&\; = \;&&& 0     \\ &&      &&            &&                    &&            &&\vdots\ \;&&&    \\ a_{m1} x_1 &&\; + \;&& a_{m2} x_2 &&\; + \;\cdots\; + \;&& a_{mn} x_n &&\; = \;&&& 0\text{.}     \\ \end{alignat}$$ Thus the kernel of A is the same as the solution set to the above homogeneous equations.

Subspace properties
The kernel of a $m × n$ matrix $K$ over a field $n$ is a linear subspace of $K^{n}$. That is, the kernel of $K$, the set $Null(A)$, has the following three properties:
 * 1) $Null(A)$ always contains the zero vector, since $A0 = 0$.
 * 2) If $x ∈ Null(A)$ and $y ∈ Null(A)$, then $x + y ∈ Null(A)$. This follows from the distributivity of matrix multiplication over addition.
 * 3) If $x ∈ Null(A)$ and $A$ is a scalar $c ∈ K$, then $cx ∈ Null(A)$, since $A(cx) = c(Ax) = c0 = 0$.

The row space of a matrix
The product Ax can be written in terms of the dot product of vectors as follows: $$A\mathbf{x} = \begin{bmatrix} \mathbf{a}_1 \cdot \mathbf{x} \\ \mathbf{a}_2 \cdot \mathbf{x} \\ \vdots \\ \mathbf{a}_m \cdot \mathbf{x} \end{bmatrix}.$$

Here, $a_{1}, ..., a_{m}$ denote the rows of the matrix $K$. It follows that $x$ is in the kernel of $A$, if and only if $x$ is orthogonal (or perpendicular) to each of the row vectors of $c$ (since orthogonality is defined as having a dot product of 0).

The row space, or coimage, of a matrix $A$ is the span of the row vectors of $A$. By the above reasoning, the kernel of $A$ is the orthogonal complement to the row space. That is, a vector $x$ lies in the kernel of $A$, if and only if it is perpendicular to every vector in the row space of $A$.

The dimension of the row space of $A$ is called the rank of A, and the dimension of the kernel of $A$ is called the nullity of $A$. These quantities are related by the rank–nullity theorem $$\operatorname{rank}(A) + \operatorname{nullity}(A) = n.$$

Left null space
The left null space, or cokernel, of a matrix $A$ consists of all column vectors $x$ such that $x^{T}A = 0^{T}$, where T denotes the transpose of a matrix. The left null space of $A$ is the same as the kernel of $A^{T}$. The left null space of $A$ is the orthogonal complement to the column space of $A$, and is dual to the cokernel of the associated linear transformation. The kernel, the row space, the column space, and the left null space of $A$ are the four fundamental subspaces associated with the matrix $A$.

Nonhomogeneous systems of linear equations
The kernel also plays a role in the solution to a nonhomogeneous system of linear equations: $$A\mathbf{x} = \mathbf{b}\quad \text{or} \quad \begin{alignat}{7} a_{11} x_1 &&\; + \;&& a_{12} x_2 &&\; + \;\cdots\; + \;&& a_{1n} x_n &&\; = \;&&& b_1     \\ a_{21} x_1 &&\; + \;&& a_{22} x_2 &&\; + \;\cdots\; + \;&& a_{2n} x_n &&\; = \;&&& b_2     \\ &&      &&            &&                    &&            &&\vdots\ \;&&&       \\ a_{m1} x_1 &&\; + \;&& a_{m2} x_2 &&\; + \;\cdots\; + \;&& a_{mn} x_n &&\; = \;&&& b_m     \\ \end{alignat}$$ If $u$ and $v$ are two possible solutions to the above equation, then $$A(\mathbf{u} - \mathbf{v}) = A\mathbf{u} - A\mathbf{v} = \mathbf{b} - \mathbf{b} = \mathbf{0}$$ Thus, the difference of any two solutions to the equation $Ax = b$ lies in the kernel of $A$.

It follows that any solution to the equation $Ax = b$ can be expressed as the sum of a fixed solution $v$ and an arbitrary element of the kernel. That is, the solution set to the equation $Ax = b$ is $$\left\{ \mathbf{v}+\mathbf{x} \mid A \mathbf{v}=\mathbf{b} \land \mathbf{x}\in\operatorname{Null}(A) \right\},$$ Geometrically, this says that the solution set to $Ax = b$ is the translation of the kernel of $A$ by the vector $v$. See also Fredholm alternative and flat (geometry).

Illustration
The following is a simple illustration of the computation of the kernel of a matrix (see, below for methods better suited to more complex calculations). The illustration also touches on the row space and its relation to the kernel.

Consider the matrix $$A = \begin{bmatrix} 2 & 3 & 5 \\ -4 & 2 & 3 \end{bmatrix}.$$ The kernel of this matrix consists of all vectors $(x, y, z) ∈ R^{3}$ for which $$\begin{bmatrix} 2 & 3 & 5 \\ -4 & 2 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix},$$ which can be expressed as a homogeneous system of linear equations involving $A$, $A$, and $A$: $$\begin{align} 2x + 3y + 5z &= 0, \\ -4x + 2y + 3z &= 0. \end{align}$$

The same linear equations can also be written in matrix form as: $$ \left[\begin{array}{ccc|c} 2 & 3 & 5 & 0 \\   -4 & 2 & 3 & 0  \end{array}\right]. $$

Through Gauss–Jordan elimination, the matrix can be reduced to: $$ \left[\begin{array}{ccc|c} 1 & 0 & 1/16 & 0 \\   0 & 1 & 13/8 & 0  \end{array}\right]. $$

Rewriting the matrix in equation form yields: $$\begin{align} x &= -\frac{1}{16}z \\ y &= -\frac{13}{8}z. \end{align}$$

The elements of the kernel can be further expressed in parametric vector form, as follows: $$\begin{bmatrix} x \\ y \\ z\end{bmatrix} = c \begin{bmatrix} -1/16 \\ -13/8 \\ 1\end{bmatrix}\quad (\text{where }c \in \mathbb{R})$$

Since $x$ is a free variable ranging over all real numbers, this can be expressed equally well as: $$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} = c \begin{bmatrix} -1 \\ -26 \\ 16 \end{bmatrix}. $$ The kernel of $y$ is precisely the solution set to these equations (in this case, a line through the origin in $R^{3}$). Here, since the vector $(−1,−26,16)^{T}$ constitutes a basis of the kernel of $z$. The nullity of $c$ is 1.

The following dot products are zero: $$ \begin{bmatrix} 2 & 3 & 5 \end{bmatrix} \begin{bmatrix} -1 \\ -26 \\ 16 \end{bmatrix} = 0 \quad\mathrm{and}\quad \begin{bmatrix} -4 & 2 & 3 \end{bmatrix} \begin{bmatrix} -1 \\ -26 \\ 16 \end{bmatrix} = 0, $$ which illustrates that vectors in the kernel of $A$ are orthogonal to each of the row vectors of $A$.

These two (linearly independent) row vectors span the row space of $A$—a plane orthogonal to the vector $(−1,−26,16)^{T}$.

With the rank 2 of $A$, the nullity 1 of $A$, and the dimension 3 of $A$, we have an illustration of the rank-nullity theorem.

Examples
2x_1 &\;+\;& 3x_2 &\;+\;& 5x_3 &\;=\;& 0 \\ -4x_1 &\;+\;& 2x_2 &\;+\;& 3x_3 &\;=\;& 0 \end{alignat}$$
 * If $L: R^{m} → R^{n}$, then the kernel of $L$ is the solution set to a homogeneous system of linear equations. As in the above illustration, if $L$ is the operator: $$ L(x_1,  x_2, x_3) = (2 x_1 + 3 x_2 + 5 x_3,\; - 4 x_1 + 2 x_2 + 3 x_3)$$ then the kernel of $L$ is the set of solutions to the equations $$ \begin{alignat}{7}
 * Let $C[0,1]$ denote the vector space of all continuous real-valued functions on the interval [0,1], and define $L: C[0,1] → R$ by the rule $$L(f) = f(0.3).$$ Then the kernel of $L$ consists of all functions $f ∈ C[0,1]$ for which $f(0.3) = 0$.
 * Let $C^{∞}(R)$ be the vector space of all infinitely differentiable functions $R → R$, and let $D: C^{∞}(R) → C^{∞}(R)$ be the differentiation operator: $$D(f) = \frac{df}{dx}.$$ Then the kernel of $D$ consists of all functions in $C^{∞}(R)$ whose derivatives are zero, i.e. the set of all constant functions.
 * Let $R^{∞}$ be the direct product of infinitely many copies of $R$, and let $s: R^{∞} → R^{∞}$ be the shift operator $$ s(x_1, x_2, x_3, x_4, \ldots) = (x_2, x_3, x_4, \ldots).$$ Then the kernel of $s$ is the one-dimensional subspace consisting of all vectors $(x_{1}, 0, 0, 0, ...)$.
 * If $A$ is an inner product space and $A$ is a subspace, the kernel of the orthogonal projection $V → W$ is the orthogonal complement to $A$ in $V$.

Computation by Gaussian elimination
A basis of the kernel of a matrix may be computed by Gaussian elimination.

For this purpose, given an $m × n$ matrix $W$, we construct first the row augmented matrix $$ \begin{bmatrix}A \\ \hline I \end{bmatrix},$$ where $I$ is the $n × n$ identity matrix.

Computing its column echelon form by Gaussian elimination (or any other suitable method), we get a matrix $$ \begin{bmatrix} B \\\hline C \end{bmatrix}.$$ A basis of the kernel of $W$ consists in the non-zero columns of $V$ such that the corresponding column of $A$ is a zero column.

In fact, the computation may be stopped as soon as the upper matrix is in column echelon form: the remainder of the computation consists in changing the basis of the vector space generated by the columns whose upper part is zero.

For example, suppose that $$A = \begin{bmatrix} 1 & 0 & -3 & 0 & 2 & -8 \\ 0 & 1 &  5 & 0 & -1 & 4 \\ 0 & 0 &  0 & 1 & 7 & -9 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}. $$ Then $$ \begin{bmatrix} A \\ \hline I \end{bmatrix} = \begin{bmatrix} 1 & 0 & -3 & 0 & 2 & -8 \\ 0 & 1 &  5 & 0 & -1 & 4 \\ 0 & 0 &  0 & 1 & 7 & -9 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \hline 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix}. $$

Putting the upper part in column echelon form by column operations on the whole matrix gives $$ \begin{bmatrix} B \\ \hline C \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 & 0 &  0 & 0 \\ 0 & 1 &  0 & 0 &  0 & 0 \\ 0 & 0 &  1 & 0 &  0 & 0 \\ 0 & 0 &  0 & 0 &  0 & 0 \\ \hline 1 & 0 & 0 & 3 & -2 & 8 \\ 0 & 1 &  0 & -5 & 1 & -4 \\ 0 & 0 &  0 & 1 & 0 & 0 \\ 0 & 0 &  1 & 0 & -7 & 9 \\ 0 & 0 &  0 & 0 & 1 & 0 \\ 0 & 0 &  0 & 0 & 0 & 1 \end{bmatrix}. $$

The last three columns of $A$ are zero columns. Therefore, the three last vectors of $C$, $$\left[\!\! \begin{array}{r} 3 \\ -5 \\ 1 \\ 0 \\ 0 \\ 0 \end{array} \right] ,\; \left[\!\! \begin{array}{r} -2 \\ 1 \\ 0 \\ -7 \\ 1 \\ 0 \end{array} \right],\; \left[\!\! \begin{array}{r} 8 \\ -4 \\ 0 \\ 9 \\ 0 \\ 1 \end{array} \right] $$ are a basis of the kernel of $B$.

Proof that the method computes the kernel: Since column operations correspond to post-multiplication by invertible matrices, the fact that $$\begin{bmatrix} A \\ \hline I \end{bmatrix}$$ reduces to $$\begin{bmatrix} B \\ \hline C \end{bmatrix}$$ means that there exists an invertible matrix $$P$$ such that $$ \begin{bmatrix} A \\ \hline I \end{bmatrix} P = \begin{bmatrix} B \\ \hline C \end{bmatrix}, $$ with $$B$$ in column echelon form. Thus $AP = B$, $IP = C $, and $ AC = B $. A column vector $$\mathbf v$$ belongs to the kernel of $$A$$ (that is $$A \mathbf v = \mathbf 0$$) if and only if $$B \mathbf w = \mathbf 0,$$ where $\mathbf w = P^{-1} \mathbf v = C^{-1} \mathbf v$. As $$B$$ is in column echelon form, $B \mathbf w = \mathbf 0$, if and only if the nonzero entries of $$\mathbf w$$ correspond to the zero columns of $B$. By multiplying by $C$, one may deduce that this is the case if and only if $$\mathbf v = C \mathbf w$$ is a linear combination of the corresponding columns of $C$.

Numerical computation
The problem of computing the kernel on a computer depends on the nature of the coefficients.

Exact coefficients
If the coefficients of the matrix are exactly given numbers, the column echelon form of the matrix may be computed with Bareiss algorithm more efficiently than with Gaussian elimination. It is even more efficient to use modular arithmetic and Chinese remainder theorem, which reduces the problem to several similar ones over finite fields (this avoids the overhead induced by the non-linearity of the computational complexity of integer multiplication).

For coefficients in a finite field, Gaussian elimination works well, but for the large matrices that occur in cryptography and Gröbner basis computation, better algorithms are known, which have roughly the same computational complexity, but are faster and behave better with modern computer hardware.

Floating point computation
For matrices whose entries are floating-point numbers, the problem of computing the kernel makes sense only for matrices such that the number of rows is equal to their rank: because of the rounding errors, a floating-point matrix has almost always a full rank, even when it is an approximation of a matrix of a much smaller rank. Even for a full-rank matrix, it is possible to compute its kernel only if it is well conditioned, i.e. it has a low condition number.

Even for a well conditioned full rank matrix, Gaussian elimination does not behave correctly: it introduces rounding errors that are too large for getting a significant result. As the computation of the kernel of a matrix is a special instance of solving a homogeneous system of linear equations, the kernel may be computed with any of the various algorithms designed to solve homogeneous systems. A state of the art software for this purpose is the Lapack library.

title: Kernel (linear algebra)


text:
2004 California Proposition 62

Proposition 62 was a California ballot proposition on the November 2, 2004 ballot. It failed to pass with 5,119,155 (46.1%) votes in favor and 5,968,770 (53.9%) against.

Officially known as the Voter Choice Open Primary Act, the proposition was an initiative constitutional amendment and statute that provided for a modified blanket primary (two-round) election system like that used in the state of Louisiana.

Under the provisions of the proposition, instead of traditional partisan primary elections for statewide offices (in which voters have to be registered with a political party to choose the nominee of that party in the primary), all candidates for election would appear on the primary election ballot (first round ballot), and all voters could vote for any candidate regardless of the party affiliation of the voter or candidates. The two candidates with the most votes (regardless of party or lack thereof) would later appear on the general election (second round) ballot.

Prop 62 would have affected elections to all statewide elected officers (Governor, Lieutenant Governor, Attorney General, Insurance Commissioner, Controller, Secretary of State, and Treasurer), for the California State Legislature, and for federal congressional elections (to both the U.S. House of Representatives and the U.S. Senate. The proposition did exempt presidential primary elections and elections of party central committees.

The provisions of Proposition 62 conflicted with those of Proposition 60, which the California State Legislature referred on the ballot. That proposition essentially re-affirmed the existing partisan primary system. The California Constitution provides that if the provisions of two approved propositions are in conflict, only the provisions of the measure with the higher number of "yes" votes at the statewide election take effect. Since Prop 60 passed and Prop 62 did not, the issue was moot.

Official summary

 * Requires primary elections where all voters may vote for any state or federal candidate regardless of how a voter or candidate is registered.
 * Exempts presidential nominations and elections of party-central committees.
 * Only the two primary election candidates receiving most votes for an office, whether they are candidates with "no party" or members of same or different party, would be listed on general election ballot.
 * In special primary election, candidate receiving majority vote is elected.
 * Requires political party's consent for identification of candidates' party registration on ballot and in other official election publications.

Summary of Legislative Analyst's Estimate of Net State and Local Government Fiscal Impact:
 * No significant net fiscal effect on state and local governments.

title: 2004 California Proposition 62


text:
Category:Russian tennis players

This category lists tennis players with Wikipedia articles who have notably represented the Russian Federation. Note that articles are sub-categorized by whether a player has done so in male or female competition, and also by particular notable competitions.

title: Category:Russian tennis players


text: Category:Olympic tennis players for Russia


text:
Richard Worth

Richard Westwood Worth (3 July 1948 – 10 May 2022) was a New Zealand politician of the New Zealand National Party. He was the Member of Parliament for Epsom from 1999 to 2005 and a list MP from 2005 to 2009.

Prior to entering Parliament, Worth studied law and business administration, and had a career in law and management. such as being the executive chair of the law firm Simpson Grierson. Worth joined the Royal New Zealand Naval Volunteer Reserves, rising to captain, and had the role of Chief of Naval Reserves for four years. He worked as consul to Columbia and honorary consul to Monaco.

Worth entered Parliament in 2005, after winning the Epsom electorate. He was in opposition from 2005 to 2008 and in government from 2008 until 2009. His roles in government included Minister of Internal Affairs, Minister for Land Information, and Associate Minister of Justice. He opposed the Civil Union Act 2004, which granted recognition of same-sex couples, proposed the creation of a National Day to replace Waitangi Day, and put forward a private members bill to address miscarriages of justice. As Minister for Land Information, Worth introduced the Reserves and Other Lands Disposal Bill in 2008 that sought to correct historic errors relating to land status.

Worth resigned from Parliament in June 2009. Party leader John Key said that Worth's conduct "[did] not befit a minister and I will not have him in my Cabinet", and said if he had not resigned he would have removed him from his Cabinet positions. While allegations about him were made public and police investigated, Worth was not charged. It was never publicly announced what caused Key to lose confidence in Worth and require his resignation. His roles after leaving Parliament included returning to the role of honorary consul to Monaco.

Worth was appointed an Officer of the Order of the British Empire (military division) in the 1994 New Year Honours for his work in the Naval Volunteer Reserves.

Early life and career
Born in Auckland, Worth obtained an LLB (Hons) and Master of Jurisprudence (First Class) from the University of Auckland and a Master of Business Administration (Distinction) from Massey University. He obtained a PhD from Royal Melbourne Institute of Technology (RMIT) with a thesis entitled The Closer Economic Relationship Between Australia and New Zealand: choices other than quiescence or withdrawal in the face of conflict?, which he completed in 2004.

Worth had a career in law and management, including being the executive chairperson of Simpson Grierson, one of New Zealand's larger law firms, from 1986 to 1999. He was the consul for Colombia for six years, and later, the honorary consul for Monaco for eight. He was also a director of Prada America's Cup (NZ) Limited, but would later quit after suggestions it was disloyal for an MP to be linked to a syndicate challenging the New Zealand team.

Worth joined the Royal New Zealand Naval Volunteer Reserves in 1968, rising to captain, and had the role of Chief of Naval Reserves from July 1990 to July 1994. Worth was appointed an Officer of the Order of the British Empire (military division) in the 1994 New Year Honours for his work in the Naval Volunteer Reserves. Worth has also been involved in the Order of St John who, in 2008, made him a Knight of the Order of St John.

Worth was married and had one daughter.

Electoral history and roles
Worth entered Parliament when he successfully stood as the National Party's candidate for the Auckland electorate of Epsom in the 1999 election, winning with a majority of 1,908. National did not win the election overall and so Worth became an Opposition MP. He was re-elected in the 2002 election with an increased majority of 5,619. In his first six years in Parliament, Worth served on the Regulations Review committee and Law and Order committee, and had appointments as the National Party spokesperson for defence, veterans' affairs and justice.

Worth lost his electorate seat in the 2005 election to the ACT New Zealand leader Rodney Hide. Hide had put out a tactical voting message calling on National voters to support him in order to elect a coalition partner for National; without winning Epsom, ACT was unlikely to win another electorate seat or to get five percent of the party vote, so would not enter Parliament. National and Worth continued to fight for the seat, but Worth lost by more than 3,000 votes. Worth was however elected as a list MP, and National's party vote in Epsom was the highest of any electorate in the country in that election. When John Key became National Party leader in November 2006, Worth was reassigned to the economic development portfolio.

At the 2008 election, Worth lost Epsom again, this time by nearly 13,000 votes, but was re-elected on the party list. National's highest party vote was again in Epsom. National also won the election overall. Worth became Minister of Internal Affairs, Minister for Land Information, Minister Responsible for Archives New Zealand, Minister Responsible for the National Library and Associate Minister of Justice. Worth was reportedly a contender for Speaker of the House, with the support of the previous speaker Jonathan Hunt, but Lockwood Smith was selected instead.

Policies and actions
Worth's maiden speech in February 2000 focused on trade, economics and Asia.

In 2002 he faced questions from his party for sightseeing in Cairo instead of attending a Maori Battalion service during an official trip to Egypt.

In 2005 he proposed the creation of a National Day to replace Waitangi Day. He proposed 24 May, the day that the New Zealand colony was granted a representative constitution by the British Parliament.

Worth was a member of the Select Committee hearing submissions about the Civil Union Bill. He was a strong opponent of the bill, which allowed legal recognition of same-sex couples though a second class of relationships besides marriage. Worth was concerned that civil unions were in effect marriages, and he described the government as "anti-family" and said that "marriage is a valuable institution in civil society and it is important that its value is not degraded or diminished by Act of Parliament." Worth said that civil unions would discriminate against non-sexual relationships, and proposed an amendment to the bill which would allow any two people, including family members and friends, to register a civil relationship that established certain rights such as right to visit in hospital or make medical decisions. Worth reported that this amendment had about one-third of the votes in the Committee stage and was not included into the bill. Ultimately the bill was passed and became the Civil Union Act 2004.

In 2007 Worth proposed a private members bill to address miscarriages of justice. However, the Ministry of Justice recommended to the Labour Government that they not adopt it. The Deputy Prime Minister of the time, Michael Cullen, wrote to Worth about his bill saying it was too broad and might have unwarranted constitutional and fiscal consequences, that the Government would not support it.

As Minister for Land Information, Worth introduced the Reserves and Other Lands Disposal Bill in 2008. This bill sought to correct historic oversights, errors or omissions relating to land status. It consisted of a number of specific reclassifications of land. The bill was ultimately enacted in 2015, after Worth had left Parliament.

In March 2009 he was reprimanded by his leader John Key for failing to mention that he was connected to a company that stood to gain from official visit to India. During the trip Worth both spoke on behalf of the Government and also arranged personal business deals. Worth did not consider there to be any conflict of interest. He later disengaged from his Indian business interests and stepped down as chair of the New Zealand India Trade Group.

Resignation
On 3 June 2009 Prime Minister John Key issued a press release announcing Richard Worth had resigned as a Minister. The press release stated that Worth had "advised me of some private matters in respect of which he felt it appropriate that he should resign as a Minister", and that Key would make no further comment about these matters.

The same day, the New Zealand Police issued a statement saying an allegation had been made against a sitting MP and that they were beginning a preliminary investigation. Key confirmed that Worth was the subject of a police investigation. Key would not say if the matter reported to police was the reason for the resignation, saying instead that Worth's conduct "[did] not befit a minister and I will not have him in my Cabinet, '' and had Worth not resigned he would have been sacked. The woman who laid the police complaint was never identified, with it only being revealed that she was a Korean businesswoman.

Key also stated that some weeks prior he had received a separate allegation that Richard Worth had "[made] a nuisance of himself towards women", which Key investigated and had received assurances that those allegations were not correct. This other accusation was presented to Key by then-leader of the Opposition, Phil Goff. The woman behind this allegation was revealed to be Neelam Choudary, an active member of the New Zealand Labour Party. According to Choudary, Worth first contacted her on 26 November 2008, and altogether, forty texts and sixty telephone calls ensued, continuing until 23 February 2009. Choudary, an ethnic Indian, alleged that she was offered a job as an ethnic affairs advisor or board member in return for romantic favours. She also alleged that inappropriate and vulgar telephone calls included asking her to buy transparent garments, and that his conduct was unacceptable and unwanted. Neelam Choudary herself faced scrutiny when it was later revealed that her husband, Kumar Akkineni Choudary, had been convicted the year before for his role in an immigration scam.

Worth declared that he was innocent of any crime. Prime Minister Key reiterated that there was no future for Worth within his Cabinet, and warned that suspension or expulsion from the National caucus was still a prospect. Worth resigned from Parliament on 12 June 2009 (effective 16 June 2009), citing that his role as a Member of Parliament was compromised due to "the avalanche of rumour and innuendo," and he wished to seek a new direction in international trade. After Worth's parliamentary resignation, Cam Calder took his place as the next eligible person on the current New Zealand National Party list.

In early July 2009 it was reported that the woman who made the original allegation to police had withdrawn her complaint and police dropped the matter. In November 2009, police announced that Worth would not face charges. As of July 2009, Choudary had not made the text exchanges public, though she sent copies of 34 texts from Worth, and her phone logs, to Key. Labour did not pursue the matter further. It was never publicly announced what caused Key to lose confidence in Worth and require his resignation.

Post-parliamentary career
In October 2010, the Ministry of Foreign Affairs and Trade announced that Worth had been reappointed honorary consul to Monaco, a role he had held before entering Parliament. Monaco had appointed him to the role at least a year prior, but Foreign Minister Murray McCully sought legal advice on whether he could refuse the application and held up the appointment until approving it in October 2010. As of April 2020, Worth still held the role which has seen him attend the wedding of Prince Albert II to Charlene Wittstock.

Worth died on 10 May 2022.

title: Richard Worth


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Lindsay Tisch

William Lindsay Tisch (born 9 October 1947), known as Lindsay Tisch, is a former New Zealand National Party politician.

Early life
Tisch was born in Auckland, New Zealand, in 1947. When he was a child, his family moved to Matamata. He obtained a diploma in agriculture from Lincoln College. He has worked as a farmer and a rural valuer, and was a management consultant. He was a director of Landcorp (1991–1997) and is a member of the Institute of Directors in New Zealand and the New Zealand Institute of Property Management.

Tisch is a Justice of the Peace, a trustee of the Pohlen Hospital Foundation based in Matamata, and a member of Matamata Lions Clubs.

Member of Parliament
He joined the National Party in 1966, and has held a number of senior roles in its organisational wing. In 1994 he served briefly as the party's president and was the party's campaign manager for the 1996 election. He was a member of Parliament from 1999 to 2017, when he retired.

Tisch was selected to replace John Luxton as National's candidate in the electorate of in the 1999 election. He defeated the Labour candidate by 5,000 votes. The name of the electorate was changed back to for the 2002 election and the 2005 election; Tisch was comfortably re-elected each time. The name referred to a little-known river past Morrinsville, and Tisch was successful in lobbying to have the electorate renamed after the Waikato River.

In the 2008 election, Tisch was re-elected in the recreated Waikato seat with a majority of 12,850 over Jacinda Ardern. He was further re-elected in the 2011 election and 2014 election, after which he retired.

In 2009, it was revealed Tisch was using a front company to maximise his accommodation allowance paid by the taxpayer. Tisch was claiming $410 a week which was paid to his property investment company, Heritage 653 Limited.

Tisch was never a minister but held senior parliamentary roles in the National Party and in the House of Representatives. He was the National Party junior whip (2002–2005) and senior whip (2005–2006) before taking on roles as Deputy Speaker of the House (2008–2011) and Assistant Speaker of the House (2011–2017). Under former leaders Bill English and Don Brash, Tisch was briefly National Party spokesperson for small business (2002–2005), civil defence and emergency services (2003–2004), and internal affairs (2003–2005).

Political views
Tisch held conservative views and opposed same-sex marriage law reform. In 2004, Tisch voted against the Civil Union Act 2004, a bill making it legal for those in same-sex as well as heterosexual relationships to enter into a civil-union. In 2005, Tisch voted for Gordon Copeland's Marriage (Gender Clarification) Amendment Bill, a bill which would have amended the Marriage Act to define marriage as only between a man and woman. In 2012 and 2013, Tisch voted against the Marriage (Definition of Marriage) Amendment Bill, a bill allowing same-sex couples to marry in New Zealand.

Honours
Tisch was one of the 3,632 recipients of the New Zealand 1990 Commemoration Medal, which he received for services to the public.

In the 2018 New Year Honours, Tisch was appointed a Companion of the Queen's Service Order for services as a Member of Parliament. In the 2020 New Year Honours, his wife, Leonie, was awarded the Queen's Service Medal, for services to health and the community.

title: Lindsay Tisch


text:
American National Election Studies

The American National Election Studies (ANES) are academically-run national surveys of voters in the United States, conducted before and after every presidential election. Although it was formally established by a National Science Foundation grant in 1977, the data are a continuation of studies going back to 1948. The study has been based at the University of Michigan since its origin and, since 2005, has been run in partnership with Stanford University. Its principal investigators for the first four years of the partnership were Arthur Lupia and Jon Krosnick. As of 2017, the principal investigators are Ted Brader and Vincent Hutchings of the University of Michigan and Shanto Iyengar of Stanford University.

The studies ask the same questions repeatedly over time and are frequently cited in works of political science. Early ANES data was the basis for The American Voter (1960). It is now used by scholars, students and journalists. It has allowed the detection of partisan bias in survey responses, showing that respondents' political affiliations contribute to their responses, extending even to questions with objective, known answers, such as whether or not Iraq had weapons of mass destruction.

In 2006, ANES opened the ANES Online Commons to allow interested scholars and survey professionals to propose questions for future surveys. In 2022, ANES received a $14 million grant to study the 2024 United States elections. University of Michigan professor Nicholas Valentino, Stanford University's Shanto Iyengar, Duke University's D. Sunshine Hillygus, and the University of Texas' Daron Shaw will be principal investigators.

title: American National Election Studies


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Eaton Hall, Cheshire

Eaton Hall is the country house of the Duke of Westminster. It is 1 mi south of the village of Eccleston, in Cheshire, England. The house is surrounded by its own formal gardens, parkland, farmland and woodland. The estate covers about 10872 acre.

The first substantial house was built in the 17th century. In the early 19th century it was replaced by a much larger house designed by William Porden. This in turn was replaced by an even larger house, with outbuildings and a chapel, designed by Alfred Waterhouse. Building started in 1870 and concluded about 12 years later. By 1960 the fabric of the house had deteriorated and, like many other mansions during this period, it was demolished, although the chapel and many of the outbuildings were retained. A new house was built but its design was not considered to be sympathetic to the local landscape, and in the late 1980s it was re-cased and given the appearance of a French château.

The house has been surrounded by formal gardens since the 17th century, the design of which has changed over the centuries in accordance with contemporary ideas and fashions, as has the surrounding parkland. A variety of buildings are included in the estate, some decorative, others built for the business of the estate; many of these are listed buildings. The house and estate are not normally open to the public, but the gardens are open on three days a year to raise money for charity, and some of the estate's buildings can be hired for charitable purposes.

Halls
Eaton Hall has been the country house of the Grosvenor family since the 15th century. There is evidence of a two-storey house on a moated site in the estate in a 17th century estate map and an 18th century engraving. A survey undertaken in 1798 showed that the building was still present.

Samwell Hall

The first substantial house was built for Sir Thomas Grosvenor, 3rd Baronet. He inherited the estate at the age of 8 when he succeeded his grandfather, Sir Richard Grosvenor, 2nd Baronet, who died in 1665. The new owner commissioned the architect William Samwell to design the house. Building started in 1675; much of the stone used was brought from the ruined Holt Castle in north Wales. By 1683 the cost of building the house had risen to over £1,000. An engraving of the time shows it to have been a substantial square house with three storeys and dormers. The entrance front had nine bays and a portico. The engraving also shows the earlier moated house to the south of the new house.

Porden Hall
By the time that Robert Grosvenor, then the 2nd Earl Grosvenor, and later the 1st Marquess of Westminster, inherited the estate in 1802, the Samwell Hall had become old-fashioned and in need of renovation. Grosvenor appointed William Porden to plan the improvements. Building started in 1803 and Porden (later assisted by Porden's son-in-law Joseph Kay) estimated it would take three years to build at a cost of £10,000. In the event it took just under 10 years and cost over £100,000. The previous house was encased and surrounded by "every possible permutation of the gothic style"; including turrets, pinnacles, arched windows, octagonal towers, and buttresses (both regular and flying). Two new wings were added in the first stage, and in the 1820s more wings were added, by this time under the direction of Benjamin Gummow. The interior of the house was as lavish as the exterior, with more Gothic detailing. The hangings for the state bed included 97 yd of purple damask and 103 yd of sarsenet (fine silk) trimmed with gold lace. When the future Queen Victoria visited in 1832 at the age of 13, she wrote in her journal: "The house is magnificent". Others described it as being "as extravagant and opulent as the very latest upholsterer-decorators could make it". A critic found it "the most gaudy concern I ever saw" and "a vast pile of mongrel gothic which ... is a monument of wealth, ignorance and bad taste". Richard Grosvenor, 2nd Marquess of Westminster, succeeded his father in 1845 and commissioned the Scottish architect William Burn to make alterations to the house. Burn raised the centre of the south front to make it look like a tower, and changed some of the external Gothic features. The architectural historian Nikolaus Pevsner described this house as a "spectacular Gothic mansion".

Waterhouse Hall
The 2nd Marquess died in 1869 and was succeeded by his son Hugh Lupus Grosvenor, initially the 3rd Marquess and from 1874 the 1st Duke of Westminster. He appointed Alfred Waterhouse to design another new hall. Again the core of the previous hall was retained; parts were refaced and re-modelled, other parts were completely rebuilt. A private wing was built for the use of the family, and this was joined to the main part of the hall by a corridor. Waterhouse also designed the chapel and a clock-house, and rebuilt most of the stabling. The work began in 1870, took 12 years to complete, and cost £803,000. The library was 90 ft long, the dining room with its ante room was 105 ft long, and the octagonal great hall contained an organ. For the interior, Henry Stacy Marks painted a frieze of the Canterbury Pilgrims for the morning room, Gertrude Jekyll painted panels for the drawing room, and in other rooms were paintings by Gainsborough, Stubbs and Reynolds. Pevsner wrote that it "was an outstanding expression of High Victorian originality", and added "this Wagnerian palace was the most ambitious instance of Gothic Revival domestic architecture anywhere in the country". The Daily Telegraph described it as "one of the most princely and beautiful mansions that these islands contain".

In 1902 the 2nd Duke gave the large alabaster, porphyry and green serpentine chimneypiece from the Ante-Drawing Room as a wedding present to his sister Lettice, Countess Beauchamp. In 1910 it was carefully dismantled and re-erected at her house, Madresfield Court, Malvern, by the architect Randall Wells, to become the focus of his new top-lit Staircase Hall, where it survives.

During both World Wars, parts of the hall were used as a hospital. In 1943, the Britannia Royal Naval College moved to the hall from Dartmouth when the college there was bombed. It moved back to Dartmouth in 1946, after which the hall was used as an officer cadet training unit until the end of National Service in 1958.

Dennys Hall and the present hall
By 1960 the hall needed repair and decoration, and dry rot was found in the roof. In 1963 Robert Grosvenor, 5th Duke of Westminster, decided to demolish the main part of the Waterhouse building and the private wing, retaining the chapel, clock tower and stables. A new building was commissioned by the Duke who appointed John Dennys, his wife's brother-in-law, as architect. Dennys had earlier worked on Saighton Grange on the Eaton estate. The intention was to build a modern, manageable home. The result was a rectangular, flat-roofed building, faced with white Travertine, its "whiteness [being] a stark contrast to the softness of the Cheshire landscape". Its construction began in 1971, it took less than $2 1/2$ years to build, and cost £459,000. The exterior had a central porte-cochère on the entrance front. The house followed an asymmetrical plan, with two storeys plus a basement containing a swimming pool. A central two-storey hall gave access to the principal rooms, with the main reception rooms being on the first floor. The decor included wall coverings in silk and woodblock floors.

As the hall was considered to be unsympathetic to its setting, it was later decided to change its exterior. This was undertaken by the Percy Thomas Partnership. Work on recasing the Dennys Hall to make it look more like a French château began in 1989 and was completed in 1991. The result has not been widely praised; the 2011 Cheshire Pevsner describes the building as "Château style, (Waterhouse's) Eaton style, but also Tesco style".

Associated structures
Adjacent to the hall are the remaining structures designed by Waterhouse. To the north is Eaton Chapel; this, with its clock tower, is a Grade I listed building. The decorative scheme of the interior of the chapel is based on the 'Te Deum'; it involves stained glass and stone mosaic, and was developed by Frederic Shields. Immediately to the north of the chapel is the Stable Court; this is listed at Grade II*. The buildings in the Stable Court are in brick, red stone, and half-timbering, with red tile roofs. The west range has a half-timbered upper storey with two gables, and a central gatehouse with turrets which are polygonal at the base and circular higher up and have conical roofs. On each side of the gatehouse are two-storey arcades with gables above. In the courtyard is a statue of a horse by Joseph Boehm, which is listed at Grade II. At the southeast corner of the stable yard is a postillion's house, dated 1873 and listed at Grade II*. In a lobby between the stable yard and the chapel is an artificial grotto, listed at Grade II. In the area around the Stable Court are further structures listed at Grade II. To the north is the Coachhouse Court, which consists of a coach-house, a covered court and a riding school. These were designed in the 1870s for the 1st Duke. To the north of this are Eaton Hall Cottages, four attached cottages, which were designed about the same time. In the forecourt between the Coachhouse Court and the cottages is a lodge, with gates, piers and screens. Near to the cottages is the former engine shed of the Eaton Hall Railway. To the east of the stable yard is a chapel-like sandstone game pantry dating from the 1870s.

From 1896 until 1947, the estate was served by the gauge Eaton Hall Railway. The line ran from the hall to a depot at Balderton on the Chester-Wrexham line, and a spur went to Cuckoo's Nest, where there was a repair yard. Part of the old railway route was re-opened in 1996.

Grounds
The estate covers an area of about 10872 acre, within which about 1235 acre of parkland and about 50 acre of formal gardens. These are listed at Grade II* on the National Register of Historic Parks and Gardens. The boundaries of the estate generally follow field boundaries but on the east side they follow the line of the River Dee.

History
In the 17th century, formal gardens were created around the Samwell Hall; these included such features as parterres and canals. However they were costly to maintain, and in the later part of the 18th century fashions changed to favour a more informal type of garden layout. Credit for designing the informal gardens at Eaton Hall has been given to Lancelot "Capability" Brown. Although one of Brown's documents dated 1764 shows that payment was made to him by the estate, it also notes that a plan for the garden had been drawn up by William Emes. From this, Marion Mako concludes that, as Brown was an engineer as well as a landscape gardener, the payment was for an engineering project rather than for landscaping. Emes had been influenced by Brown, although he had not been his pupil. With his clerk of works, Thomas Leggett, Emes worked in the estate for the next 10 years. When Robert Grosvenor (later the 1st Marquess) inherited the estate at the beginning of the 19th century, it had become run-down. The marquess appointed John Webb, a pupil of Emes, to improve the garden and the landscaping. Among Webb's innovations were new terrace walls behind the house, the levelling of Belgrave Avenue and the planting of 130,000 trees along it, and a serpentine lake to the east of the house alongside the River Dee. He also arranged for the construction of greenhouses and a kitchen garden. Fashions changed again, and in the 1820s William Andrews Nesfield was employed to design new parterres. He also built more terracing and a balustraded wall. Statues, stone urns and vases on pedestals were added to the garden. In 1852 the Camellia House was built; this was extended in 1870 to its final size of 385 ft long, 10 ft wide, and 18 ft high. The present kitchen garden was created the same year; this provided the food not only for the hall, but also for Grosvenor House in London. More greenhouses were built and, by about 1880, 56 gardeners were employed. There were other building works in the grounds. Waterhouse created a grotto between the chapel and the stable yard, and designed the Parrot House and a loggia (now known as the Temple). The Chester architect John Douglas designed the Dutch Tea House in the Tea Garden, and a number of service buildings in the estate. In 1897–98 Edwin Lutyens started to improve what had been known as the Italian Garden (and is now the Dragon Garden).

Work continued in the gardens and grounds during the 20th century. The 2nd Duke commissioned Detmar Blow, a pupil of Lutyens, to re-design parts of the gardens. With Fernand Billerey, he removed the parterres, built a canal leading away from the house, added hedged compartments to the terraces, and a pond at the base of the terraces (now the Lioness and Kudu Pond). During the Second World War, part of the parkland was requisitioned as an airfield, and in 1940 some of the garden buildings were damaged by a cluster of incendiary devices. After the war, improvement of the gardens did not resume until the 1960s, when the wives of the 4th and 5th Dukes worked with the designer James Russell. Since the early 1990s, the gardens have been further developed under the 6th Duke and his wife, Natalia, working with the garden designers Arabella Lennox-Boyd and Vernon Russell Smith.

Formal gardens
To the east of the house a series of terraces leads down to the Fish Pond. The retaining walls at the southern end of the upper terrace are listed at Grade II, as are the retaining walls at the end of the upper terrace and the steps leading down to the middle terrace. Stretching along the middle terrace is a long rectangular pool containing a three fountains. The retaining walls of this pool are listed at Grade II, as are the railings on the north and the south side of the terrace. On each side of the pool are two compartments framed by yew hedges. Between these compartments, on each side, is a statue by Raymond Smith. Both of these were made in 1852 for the 2nd Marquess and are listed at Grade II. The one to the north depicts a stag at bay, and that to the south a hunter on a rearing horse.

From the end of the pool, steps lead down to a smaller rectangular pool at right-angles to the first. The steps and the retaining wall at the end of the terrace are listed at Grade II. The retaining walls of the pool are also listed at Grade II. This area contains two statues by Jonathan Kenworthy. From this pool a path, known as the Broad Walk, stretches to the north and the south. At each end of the Broad Walk is a building designed by Waterhouse for the 3rd Marquess. At the north end is the Parrot House, dating from 1881–83, which is built in yellow terracotta. It is the form of a round colonnaded Ionic temple with a shallow domed roof. Above the colonnade and the inner drum are concentric balustrades. A flight of eleven steps leads up to the south entrance. The Parrot House is listed at Grade II. At the south end of the Broad Walk is a loggia, dating from about 1880. This is built in buff and red sandstone. At its front are three arches between Ionic columns. The loggia was built to enclose a Roman altar which was found in 1821 at a spring near Boughton and brought to Eaton in 1822. The loggia is listed at Grade II. To the east and west of the loggia are reconstructed Roman columns, each of which is listed at Grade II.

South of the loggia is the Dutch Tea Garden, which was laid out by C. E. Mallows in about 1905. The garden contains the Tea House which was designed by John Douglas. This has a cruciform plan and is a half-timbered building on a sandstone plinth. The roof is of red tiles, and sweeps upwards to a small spire surmounted by a weathercock. It is listed at Grade II. In the centre of the garden is a statue of Mercury and in front of the Tea House are two stone Talbots. To the north of the Tea House, on the path leading to the Broad Walk, is a pair of wrought iron gates made in 1913 for the 2nd Duke. The gates and their overthrow are listed at Grade II. To the south of the hall is a formal garden known as the Italian Garden. This contains a pool at the centre of which is the Dragon Fountain. The fountain is listed at Grade II. In the Italian Garden are two statues, also listed at Grade II, which were taken from the old hall when it was demolished; these are a statue of Joan of Eaton, and of the Norman Bishop Odo.

Leading from the north of the house is the Spring Walk, leading to the Kitchen Garden, in which food is grown for the family. To the east of the Kitchen Garden is the Camellia Walk, a long greenhouse filled with camellias. This is 388 ft long and is believed to be the longest glass corridor in the world. It is listed at Grade II. Some of the gates in this garden are believed to have been designed by Lutyens, and are listed at Grade II. Other walls and gates around the garden were designed by Waterhouse in about 1870, and are listed at Grade II*.

To the east of the house is the forecourt, which has as its centrepiece a pool containing an equestrian statue of the 1st Duke. This depicts the Duke on horseback holding aloft a falcon. It is in bronze and was made between 1870 and 1879 for the Duke by G. F. Watts. It is listed at Grade II*. The retaining walls of the pond are listed at Grade II. To the west of the forecourt are the Golden Gates which, together with their screens and lodges, are listed at Grade I. The other listed building in the gardens is a large stone urn on the east side of the Fish Pool dating from about 1880. This is richly carved, is 10 ft high, and stands on a circular pedestal which forms the final feature of the eastern view from the hall. It is listed at Grade II.

Other features
The grounds can be entered by a number of approaches, each of which contain structures of architectural importance. Belgrave Avenue, some 1.75 mi long, is a straight drive which leads from the Wrexham Road (B5445) to the Golden Gates and the forecourt on the east of the hall. Belgrave Lodge, on the south side of the avenue was built in 1899 to a design by John Douglas for the 1st Duke. It is built in red bricks with yellow stone plinths, bands and other dressings and is listed at Grade II. The associated lodge gates, piers and wing walls were designed at the same time by Douglas and are also listed at Grade II. Part way along the avenue, on its north side, is Upper Belgrave Lodge. This was also designed by Douglas for the 1st Duke, it is dated 1877, and is Grade II listed. Further along the avenue is a Grade II listed obelisk in red sandstone with a copper cap, dated 1890, designed by Douglas and Fordham. The Aldford Approach leads from the village of Aldford and crosses the River Dee by the Grade I listed Aldford Iron Bridge, which was built in 1824 by William Hazledine for the 1st Marquess. Iron Bridge Lodge, adjacent to this bridge, was designed by Douglas and Fordham in 1894 and is listed at Grade II. Also on this approach is Coachmore Hill Lodge which was designed in the 1880s by Douglas; it is listed at Grade II. On the approach, near the Dutch Tea Garden are gates with an overthrow, and piers dating from about 1870 in Classic Revival style, listed at Grade II.

From the north of the hall are two further approaches. The Eccleston Approach goes to the village of Eccleston, and slightly to the west, the Chester Approach bypasses the village, going through Eccleston Hill. Associated with these approaches are further listed buildings. Of these, the major structure is Eccleston Hill Lodge which was designed in 1881–82 by Douglas for the 1st Duke and is listed at Grade II*. This is a three-storey gatehouse tower with multiple attached smaller towers and a steeply hipped roof. The other structures are listed at Grade II and comprise Eccleston Lodge which was designed by Douglas and Fordham in 1894, its associated gates, piers and wing railings, a sandstone balustered causeway south of the lodge carrying the drive, a house called Eaton Boat, designed by Douglas about 1880, Garden Lodge designed by Waterhouse in 1881–83, a pair of gates, railings and screen walls adjoining the lodge dating from 1881–83 by Waterhouse, Stud Lodge storehouse and domestic offices, designed in 1883 by Douglas, the Stud Riding School, the Stud Stables, the house east of Stud, Eaton Estate Office, designed by Waterhouse in 1880, the North Lodge of 1881 by Waterhouse, the North Lodge gate and post from about 1881 also by Waterhouse, the Garden House of 1893 by Douglas and Minshull, and gates and gate piers to the south of Garden House.

Present day
Eaton Hall is a private residence and is not open to the public, but the gardens are open three days each year to raise money for charity. In the area of the Stable Court are a number of rooms which are used for exhibitions. The Carriage Museum holds the Westminster Collection of Carriages. The Exhibition Room houses a collection of items relating to the Grosvenor family, and the History Room contains items about the history of the family and illustrations of the hall at various stages in the past. The Stables include items relating to the family's horses. In the garden, the Parrot House contains an exhibition of paintings by the Victorian artist Henry Stacy Marks.

Some of the areas in the stable court are available for hire for charitable fund raising. The Long Room, which was refurbished in 1992 and now has the character of a large country house drawing room, can hold 150 people. The former saddle room is now a dining room. The carriage room and adjoining buildings have been converted into the Wolf Room, which has a movable stage and audio-visual facilities. It can seat 200 people and contains eight black-chalk pictures of birds by Joseph Wolf. The chapel is usually reserved for the family but in December each year it is used for carol concerts to raise money for charity.

Notes and references

 * Notes

 * References

 * Bibliography

title: Eaton Hall, Cheshire