title: Dara Ó Briain

text: From 16 April 2012, Ó Briain presented an eight-episode series of "" with co-host Marcus du Sautoy on Dave. Each episode was themed and Ó Briain along with a guest attempted to solve various conundrums posted by du Sautoy. Series 2 began on 1 May 2013. On 6 November 2012, Ó Briain began presenting a series called "Dara Ó Briain's Science Club", in which he and other celebrities discuss science issues. The first edition of this programme features Ed Byrne talking about how closely related he is to the Neanderthals. Each episode in the series includes a short animated history that has been created by the UK animation and illustration agency 12Foot6.


title: Dara Ó Briain

text: In 2013, Ó Briain joined Jack Dee, Chelsee Healey, Greg James, Melanie C and Philips Idowu in "Through Hell and High Water", a Comic Relief challenge which involved British celebrities canoeing the most difficult rapids of the Zambezi River. They raised over £1 million for the charity.


title: Dara Ó Briain

text: "Dara and Ed's Great Big Adventure", a 2015 three-part fly-on-the-wall television series, followed Ó Briain and Ed Byrne on their journey by car down the Pan-American Highway.


title: Dara Ó Briain

text: In June 2015, "Dara Ó Briain Meets Stephen Hawking", in which Ó Briain travels to Cambridge for a series of interviews with theoretical physicist Stephen Hawking, aired on BBC One.


title: Dara Ó Briain

text: From January to March 2016, Ó Briain presented "Tomorrow's Food", a three-episode series alongside Angela Hartnett, Chris Bavin and Dr Shini Somara. The BBC One show looked at the technologies and produce in farms, supermarkets, kitchens and restaurants around the world.


title: Dara Ó Briain

text: Ó Briain presented the 2016 reboot of "Robot Wars" starting on 24 July, as well as the subsequent two series in 2017.


title: Dara Ó Briain

text: He hosted a revival of the classic quiz show "Blockbusters", which began airing on Comedy Central on 21 March 2019 until 5 December 2019.


title: Dara Ó Briain

text: In June 2019, he was the host of "The Family Brain Games". He co-hosted this with Dr. Hannah Critchlow, who was responsible for the psychological analysis and supported by Dr. Adam Hampshire. This programme was won by the Smith Family of Newmilns, Ayrshire.


title: Dara Ó Briain

text: On 23 June 2022, Ó Briain was confirmed to star as a contestant in series 14 of C4 comedy game show "Taskmaster". He won the second episode of the series with 30 points, becoming the first person in the show's history to win the maximum possible amount of points on offer in a single episode, and later went on to win the series with the highest-ever total score.


title: Dara Ó Briain

text: Ó Briain had a cameo role as a generalised alternative comedian in the 2013 British film "The Look of Love" directed by Michael Winterbottom.


title: Dara Ó Briain

text: Ó Briain married his wife Susan, a surgeon, in 2006; they live in West London with their three children, one daughter (born 2008) and two sons (born 2011 and 2015). He was best man at his best friend Ed Byrne's wedding in 2008 after Byrne had previously been Ó Briain's best man. He describes himself as looking like "one of Tony Soprano's henchmen, on a bad day", and said that in 2008, "living in London I probably only get recognised about once a day. And that's okay by me. I'm not a celebrity. And I certainly don't see myself as one".


title: Dara Ó Briain

text: Ó Briain is an atheist, but has said that he also sees himself as "ethnically Catholic": "I'm staunchly atheist, I simply don't believe in God, even if he believes in me. But I'm still Catholic, of course. Catholicism has a much broader reach than just the religion. I'm technically Catholic, it's the box you have to tick on the census form: 'Don't believe in God, but I do still hate Rangers.


title: Dara Ó Briain

text: His surname is the original Irish form of O'Brien. He said, "My dad was involved in the Irish language movement and changed it. Even Irish people are now confused by it".


title: Dara Ó Briain

text: Ó Briain is a fan of English football club Arsenal, and he is also a fan of Gaelic games. When his tweet congratulating London on knocking Sligo out of the 2013 Football Championship was read out on "The Sunday Game", Ó Briain expressed amazement and vowed to try to have one read out every week. Ó Briain has also expressed an interest in Irish cricket, and has written about the subject for "The Guardian" newspaper.


title: Dara Ó Briain

text: Ó Briain was one of fifteen members of a racing greyhound syndicate for several years. The December 2009 transmission of "Three Men Go to Ireland" featured their dog Snip Nua who, by the time of transmission, had been put down following injuries sustained in a race. Ó Briain was so upset about the death that he and his fellow syndicate members immediately disbanded the syndicate permanently. In early 2010, a series of small demonstrations were held outside some of Ó Briain's tour venues, urging him to publicly denounce the sport of greyhound racing due to the dog's death.


title: Murdoch family

text: Members of the Murdoch family are prominent international media magnates and media tycoons with roots in Australia and the United Kingdom, along with their media assets in the United States. Some members have also been prominent in the arts, clergy, and military.


title: Murdoch family

text: Five generations of the family are descended from two Scottish immigrants to Australia: the Reverend James Murdoch (1818–1884), a minister of the Free Church of Scotland and his wife Helen, née Garden (1826–1905). Both were from the Pitsligo area of Aberdeenshire and migrated to the Colony of Victoria in 1884.


title: Murdoch family

text: The media mogul Rupert Murdoch is known for being one of the founders and the owner of formerly the world's largest media company News Corporation, a company that was spun-off in mid 2013 splitting its entertainment assets to 21st Century Fox and its media publishing assets to form the new News Corp. Currently the Murdochs still have the controlling interest in the remains of the acquisition of 21st Century Fox by The Walt Disney Company that was spun-off to Fox Corporation, and still remain as top executives of News Corp.


title: Murdoch family

text: Their eldest child, the Rev. Patrick Murdoch was born in Pitsligo and raised at Rosehearty, Aberdeenshire. He was ordained at Cruden, Aberdeenshire, where he also married Annie Brown (in 1882). At the age of 34, Murdoch emigrated with his wife and parents to Victoria. He was prominent there as a Presbyterian minister and published several books on theology. Two of Patrick and Annie Murdoch's six children achieved prominence, Sir Keith Murdoch and Ivon George Murdoch.


title: Murdoch family

text: Nora Curle Smith, née Murdoch, was born in Pitsligo and married David Curle Smith (1859–1922). A pioneering electrical engineer, David Curle Smith was in charge of the municipal electricity supply at Kalgoorlie, Western Australia during the early 20th century, invented a pioneering electric stove, which he patented in 1906. To promote the stove, Nora Curle Smith wrote the world's first cookbook for electric stoves, which featured 161 recipes and operating instructions for the stove, under the name "H. Nora Curle Smith": "Thermo-Electrical Cooking Made Easy" (1907; reprinted 2011).


title: Murdoch family

text: Sir Walter Murdoch , who was born at Rosehearty, was a prominent Australian academic and essayist. He married Violet Catherine Hughston in 1897. Murdoch published his first essay, "The new school of Australian poets", in 1899 and for many years he wrote a weekly column titled "Books and Men" for the "Melbourne Argus" (under the pen name of "Elzevir"). His academic career began with an appointment in 1904 as an assistant lecturer in English at Melbourne University. In 1913, he was appointed founding Professor of English at the University of Western Australia (UWA). During the 1920s, his essays were syndicated across Australia through the Herald & Weekly Times newspaper group run by his nephew, Sir Keith Murdoch (see below). Collections of Walter Murdoch's writings were published in book form from the 1930s onward. He was appointed a Companion of the Order of St Michael & St George (CMG) in 1939, served as Chancellor of UWA in 1943–48 and was made a Professor Emeritus upon his retirement. Violet Murdoch died in 1952 and 10 years later Murdoch remarried, to Barbara Marshall Cameron. He was appointed a Knight Commander of the Order of St Michael & St George (KCMG) in 1964.


title: Murdoch family

text: In Perth, Sir Walter Murdoch is commemorated by the names of both Murdoch University and the suburb surrounding its main campus: Murdoch.


title: Murdoch family

text: Keith Arthur Murdoch, later Sir Keith Murdoch, was born in West Melbourne and grew up in the Melbourne suburb of Camberwell. He became prominent as a journalist, while serving as a war correspondent during World War I. In 1921, Murdoch was appointed chief editor of the "Melbourne Herald" and in 1928 became managing director of its parent company, The Herald and Weekly Times Ltd. That same year he married Elisabeth Joy Greene (1909–2012), who was later prominent as the philanthropist Dame Elisabeth Murdoch (1909–2012). Murdoch was knighted in 1933. During World War II, Sir Keith Murdoch served briefly in an Australian government role, as Director-General of Information.


title: Murdoch family

text: Lieutenant Ivon George Murdoch and bar, saw action with the 8th Battalion (AIF) on the Western Front during World War I.


title: Murdoch family

text: Rupert Murdoch , , born in Melbourne, is a major international media proprietor – he chairs two United States-based companies that control most of his assets: News Corp and Fox Corporation. Murdoch's career as a media proprietor began in 1952, when he inherited his father's stake in News Limited. The company's only major asset was an Adelaide daily newspaper distributed only in South Australia, "The News". During the 1950s and 1960s, News Ltd acquired daily and weekly newspapers, including suburban and provincial publications, throughout Australia and New Zealand. From 1968, Murdoch bought British newspapers, beginning with the weekly "News of the World" and the daily "The Sun".


title: Murdoch family

text: Murdoch made his first acquisition in the United States in 1973, when he purchased the "San Antonio Express-News". Soon afterwards, he founded a US supermarket tabloid "Star", and in 1976, he purchased the "New York Post".


title: Murdoch family

text: In 1981, Murdoch acquired the London "Times" and "Sunday Times". He bought a major stake in 20th Century Fox in 1984, which became the basis of a new US free to air television network, Fox Broadcasting Company. To satisfy a legal requirement that only US citizens could own US television stations, Murdoch became a naturalised US citizen in 1985, and consequently forfeited his Australian citizenship.


title: Murdoch family

text: During the 1980s and 1990s, Murdoch became involved in pay television interests throughout the world, including Foxtel in Australia, STAR TV and Tata Sky in Asia and BSkyB, Sky Italia and Sky Deutschland in Europe. NewsCorp also came to control both a major international publishing house HarperCollins, and Dow Jones & Company, which includes "The Wall Street Journal".


title: Murdoch family

text: Prue Murdoch (born in Adelaide) has held directorial roles within the News Corporation empire. She has been married twice:


title: Murdoch family

text: Elisabeth Murdoch (born in Sydney), is a media executive and company director and has been married twice.


title: Murdoch family

text: Lachlan Murdoch (born in London), is a media executive and company director; he married the British-Australian model and actress Sarah Murdoch, née O'Hare (b. 1972) in 1999; the couple have three children, Kalan Alexander Murdoch (b. 2004), Aidan Patrick Murdoch (b. 2006) and Aerin Elisabeth Murdoch (b. 2010).


title: Murdoch family

text: James Murdoch (born in London), is a media executive and company director. In 2000, he married the US public relations specialist and climate change activist Kathryn Hufschmid. The couple have three children, Anneka Murdoch (b. 2003), Walter Murdoch (b. 2006) and Emerson Murdoch (b. 2008).


title: Light machine gun

text: A light machine gun (LMG) is a light-weight machine gun designed to be operated by a single infantryman, with or without an assistant, as an infantry support weapon. LMGs firing cartridges of the same caliber as the other riflemen of the same combat unit are often referred to as squad automatic weapons.


title: Light machine gun

text: While early light machine guns fired full-powered rifle cartridges, modern light machine guns often fire smaller-caliber rifle cartridges than medium machine guns – generally the same intermediate cartridge fired by a service's standard assault rifle – and are usually lighter and more compact. Some LMGs, such as the Russian RPK, are modifications of existing designs and designed to share the same ammunition. Adaptations to the original rifle generally include a larger magazine, a heavier barrel to resist overheating, a more robust mechanism to support sustained fire and a bipod.


title: Light machine gun

text: A light machine gun is also defined by its usage as well as its specifications: some machine guns – notably general-purpose machine guns – may be deployed either as a light machine gun or a medium machine gun. Deployed on a tripod and used for sustained fire, it is a medium machine gun; if deployed with a bipod with the operator in a prone position and firing short bursts, it is a light machine gun.


title: Light machine gun

text: Light machine guns are also designed to be fired from the hip or on the move as a form of suppressive fire intended to pin down the enemy. Marching fire is a specific tactic that relies on this capability.


title: Light machine gun

text: Lighter modern LMGs have enabled them to be issued down at the fireteam level, with two or three at the section/squad level.


title: Light machine gun

text: Many light machine guns (such as the Bren gun or the M1918 Browning Automatic Rifle) were magazine-fed. Others, such as the Hotchkiss M1922, could be fed either from a belt/strip or from a box magazine. Modern light machine guns are designed to fire smaller caliber rounds and, as such, tend to be belt-fed (from a container attached to the gun) or from a detachable high-capacity drum magazine, but some, such as the FN Minimi, will also accept standard rifle magazine feeding as an auxiliary measure when belted ammunition has been exhausted.


title: Light machine gun

text: In 1903, French military theorists noticed that the heavy machine guns of the day were of little use in infantry assaults. They determined that "the machine gun must learn to walk". They researched the possibility of a light machine gun which could be carried by troops. A marching fire tactic was theorised, using incidental suppressive fire, with the advancing troops considered a deadlier threat than the un-aimed bullets, causing the enemy to fall back. The prototype guns were not approved for production, and none were in service when World War I began. The French quickly brought the prototypes to mass production to boost the firepower of advancing infantry.


title: Light machine gun

text: By the end of World War II, light machine guns were usually being issued on a scale of one per fire team or squad, and the modern infantry squad had emerged with tactics that were built around the use of the LMG to provide suppressive fire.


title: Light machine gun

text: The following were either exclusively light machine guns, had a light machine gun variant or were employed in the light machine gun role with certain adaptations.


title: Population of Canada by province and territory

text: Canada is divided into 10 provinces and three territories. The majority of Canada's population is concentrated in the areas close to the Canada–US border. Its four largest provinces by area (Ontario, Quebec, British Columbia, and Alberta) are also its most populous; together they account for 86.5% of the country's population. The territories (the Northwest Territories, Nunavut, and Yukon) account for over a third of Canada's area but are home to only 0.32% of its population, which skews the national population density value.


text: Canada's population grew by 5.24% between the 2016 and 2021 censuses. With the exceptions of Newfoundland and Labrador and the Northwest Territories, all territories and provinces increased in population from 2016 to 2021. In terms of percent change, the fastest-growing province or territory was Yukon with an increase of 12.1% between 2016 and 2021, followed by Prince Edward Island with 7.99% growth.


text: Generally, provinces steadily grew in population along with Canada. However, some provinces such as Saskatchewan, Prince Edward Island, and Newfoundland and Labrador experienced long periods of stagnation or population decline. Ontario and Quebec were always the two most populous provinces in Canada, with over 60% of the population at any given time. The demographic importance of the West steadily grew over time, while the importance of Atlantic Canada steadily slipped.


text: Canada's population has increased every year since Confederation in 1867: see List of population of Canada by year.


text: Current provinces and territories population growth rate are based on the Statistics Canada 2021 Census of Population.


text: The population of Canada increased every year since Confederation in 1867. The first national census of the country was taken in 1871, and it covered the four provinces which were part of Canada at the time. It recorded a population of 1,620,851 in Ontario, 1,191,516 in Quebec, 387,800 in Nova Scotia and 285,594 in New Brunswick The population of each of these provinces continued to grow every year uninterrupted. However, their growth was slow in the late 19th century because there were few economic opportunities. As a result, many Canadians opted to emigrate in the United States for work.


text: This phenomenon hit Quebec especially hard. Approximately 900,000 Quebec residents (French Canadian for the great majority) left for the United States between 1840 and 1930. However, Quebec's population losses to emigration during this period were largely offset by its natural population growth. Indeed, until the middle of the 20th century, Quebec had a birth rate considerably higher than most of its contemporary industrialized societies. This period of high French-Canadian population growth is nicknamed .


text: Population growth in the Northwest Territories, and then the Western Provinces, picked up when the Canadian government passed the "Dominion Lands Act" in 1872 to encourage the settlement of the Canadian Prairies, and to help prevent the area from being claimed by the United States. The act gave a claimant for free, the only cost to the farmer being a $10 administration fee. Any male farmer who was at least 21 years of age and agreed to cultivate at least of the land and build a permanent dwelling on it (within three years) qualified. The population of the Canadian prairies grew rapidly in the last decade of the 19th century, and the population of Saskatchewan quintupled from 91,000 in 1901 to 492,000 in 1911. The vast majority of these people were immigrants from Europe.


text: Early counts of Northwest Territories' population tend to exclude the Indigenous citizens of the nations whose countries comprised the territory, such as the Dene of Denendeh or Inuit of Inuit Nunangat. The territory's population drops at the turn of the 20th and 21st centuries are due to its reduction in size, as Yukon, then Saskatchewan and Alberta were carved out of its territory, and the same with Nunavut a century later. Yukon's population spike at the turn of the 20th century is due to the Klondike Gold Rush, when an estimated 100,000 people tried to reach the Klondike goldfields between 1896 and 1899, of whom only around 30,000 to 40,000 eventually did.


text: Generally, provinces steadily grew in population along with Canada. However, some provinces experienced long periods of stagnation or population decline. After peaking in 1891, Prince Edward Island's population started to decline every year until 1941, after which the province started growing again. In Saskatchewan, after a rapid population explosion at the beginning of the century that propelled the province to being the 3rd largest in the country, its population declined during the Great Depression, and its growth had been slow ever since. From 1931 to 2016, Saskatchewan's population increased by only 19.2%, well below the national average. Newfoundland and Labrador, on the other hand, experienced slow but continuous growth until the 1990s, when the cod fisheries collapsed, and their population started to fall.


text: After the collapse of the Canadian birth rate, most provinces now sustain their population with immigration from the developing world. The number of new immigrants increases every year.


text: The demographic weight of each province in Canada has always constituted a sensitive issue. In 1840, the Durham Report recommended that Upper Canada (now Ontario) and Lower Canada (now Quebec) be united into one province. The newly created Legislative Assembly of the Province of Canada was required to have equal representation from Canada East (now Quebec) and Canada West (now Ontario), even though the population of Canada East was considerably larger. In 1840, the population of Canada East was estimated at 670,000, while the population of Canada West was estimated to be 480,000. Lord Durham had not recommended this approach, and had instead proposed that the representation should be based on the respective populations of the two regions. The British government rejected that recommendation and instead implemented sectional equality, apparently to give the English-speaking population of the new province a dominant voice in the provincial government.


text: However, the 1851 census revealed that Canada West's population had surpassed Canada East's. This fact fuelled demands in Canada West for the end of sectional equality and the move toward allocating seats in the legislation on the basis of population, nicknamed "rep by pop". This was a hotly contested issues at the constitutional conferences leading up to confederation, and the colonies reached a comprise in which the seats in the federal lower house (House of commons) would be allocated by population, and the seats in the federal upper house (Senate) would be allocated on the basis of three defined regionsOntario, Quebec and the Maritimesthat would each have 24 seats.


text: Since Confederation, Ontario and Quebec were always Canada's two most populous provinces. However, their combined demographic weight decreased from over 80% at Confederation to just over 60% in 2016. The Atlantic provinces also lost importance within Canada, from around 20% at Confederation to under 7% today. The West's importance, however, has only increased, from insignificant levels in 1871 to over 30% of the country in 2016. In the first half of the 20th century, the most populous western province was Saskatchewan, but its population was later eclipsed by British Columbia, Alberta, and Manitoba.


text: The issue of the demographic weight of each provinces came up during the negotiations for the Patriation of the Constitution, and especially discussions around the amending formula of the constitution. The final formula stipulates that minor changes to the constitution had to be approved by the Parliament of Canada and the Legislature of 7 provinces representing at least 50% of the Canadian population. This essentially meant that either Ontario or Quebec had to agree to any constitutional amendments that affect all provinces.


text: Quebec had managed to maintain a stable demographic weight within to Canada during the first half of the 20th century due to its high birth rate. However, their importance began to slip as their birth rate started to fall in the 1960s. Quebec wanted to make it up through immigration, and for this purpose created its Ministry of Immigration in 1968, and negotiated for increased powers in this field with the federal government. However, new immigrants to Canada disproportionally go the Ontario, British Columbia and Alberta, fuelling their rise in demographic weight. In response, a Canada–Québec Accord was concluded in 1991 which, among other things, guaranteed Quebec an immigration rate proportional to its demographic weight in Canada. This provision was not fulfilled, as in 2005, immigration to Quebec represented only 16.5% of all immigration to Canada.


text: Quebec also attempted to maintain its weight within the Canadian House of Commons during the constitutional negotiations of the early 1990s. Under the Charlottetown Accord, in exchange for Quebec losing Senate seats under a Triple-E Senate (dropping from 24 to 6), Quebec was guaranteed never to be allotted less than 25% of the seats in the House of Commons. The Accord was ultimately defeated in a public referendum.


title: McLaren 720S

text: The McLaren 720S is a Supercar designed and manufactured by British automobile manufacturer McLaren Automotive. It is the second all-new car in the McLaren "Super Series", replacing the 650S beginning in May 2017.


title: McLaren 720S

text: The 720S was launched at the Geneva Motor Show on 7 March 2017 and is built on a modified carbon monocoque, which is lighter and stiffer than the previous model, the 650S.


title: McLaren 720S

text: The 720S is the first all-new car to be introduced by McLaren as a part of its new plan to launch 15 new cars into the market by 2022. The 720S according to McLaren is 91% new as compared to its predecessor.


title: McLaren 720S

text: The 720S features McLaren's new M840T engine which is an evolution of the M838T used in the 650S. It is a twin-turbocharged V8 engine. The engine has a rated power output of at 7,500 rpm, giving the car its name; the maximum torque is at 5,500 rpm.


title: McLaren 720S

text: The ProActive Chassis Control II active suspension system used in the 720S is an evolution of the system used in the 650S but is lighter than the previous version. The new system features accelerometers on the top and pressure sensors at the bottom of the dampers to precisely communicate to the car's onboard computer the driving conditions in real-time for optimum suspension settings. The system uses findings from a PhD course at the University of Cambridge.


title: McLaren 720S

text: The carbon fibre tub used in the 720S' chassis is based on the similar principle of the "MonoCage" unit in the P1 but is lighter than its predecessor. Called the "MonoCage II", the tub allows for dihedral doors with large cutouts for easier entry and exit. It also reduces the size of the pillars of the roof, improving visibility for the driver. The same tub underpins the Senna, Speedtail and the Elva sports cars.


title: McLaren 720S

text: The interior is designed to be a blend of modern and race-inspired elements. Alcantara and Weir leather upholstery along with carbon fibre trim is standard. A Bowers and Wilkins audio system and fixed carbon fibre racing seats are included as an option. The main focus of the interior is the driver and this is reflected by the new digital display behind the steering wheel which retracts to a thin screen to reveal vital information to the driver when the car is in track mode. The touch screen on the centre console is angled away from the driver but vital controls are designed to be in the driver's easy reach. The car comes with two driving modes, default and comfort with the former focusing on an enhanced track driving experience.


title: McLaren 720S

text: According to McLaren the 720S can accelerate to in 2.9 seconds, to in 7.8 seconds, can achieve a maximum speed of , and has a time of 10.3 seconds. The 720S also comes with Variable Drift Mode, which manipulates the stability control to help drift the car.


title: McLaren 720S

text: McLaren claims class-leading efficiency for the new 720S, with CO emissions of 249 g/km and combined fuel economy of —both of these figures represent an improvement of around 10% from the 650S.


title: McLaren 720S

text: The McLaren 720S features twin-hinged butterfly doors and many design features from the McLaren F1. The headlights hide air vents that funnel incoming air to two small radiators in front of the wheels. The doors feature air channels that direct air to the engine. The rear of the car features thin LED taillights similar to those on the McLaren P1, and two round exhaust pipes. The design was inspired by the great white shark and features a teardrop-shaped cockpit. All of the exterior features result in an improvement of 50% more downforce than the 650S. The interior of the car includes a folding driver display and carbon fibre accents.


title: McLaren 720S

text: McLaren Special Operations unveiled the McLaren 720S Velocity just one day after the 720S was revealed. It featured Nerello Red and Volcano Red paint scheme, and a carbon fibre bonnet. In addition to those, the wheels are lightweight aluminium painted metallic bronze. The interior has Carbon Black Alcantara trim with red highlights and carbon fibre accents.


title: McLaren 720S

text: The 720S Spider was introduced in December 2018 as the brand's new open-top flagship sports car. Due to the integral roll structure of the monocoque used in the 720S, the Spider did not need additional bracing to compensate for the loss of a fixed roof. The modified monocoque loses the spine running from front to the rear of the car and is dubbed the "Monocage II-S". Due to the loss of the roof, the 720S Spider uses traditional dihedral doors. The Spider weighs more than its coupé counterpart due to the retractable hardtop system. The Spider marks the debut of new 10-spoke alloy wheels and new exterior colour options.


title: McLaren 720S

text: The roof is a single piece of carbon fibre and takes 11 seconds for operation, 6 seconds quicker than the 650S Spider. The roof can be operated at speeds up to . The Spider uses the "flying buttress" as used on all convertible McLaren models. There is an added window on the buttress of the car to increase rear visibility. The retractable window between the roll-over hoops is carried over from the 650S Spider.


title: McLaren 720S

text: The engine and the transmission remain the same as the coupé with the engine generating the same amount of power. The Spider can accelerate to from a standstill in 2.9 seconds, to in 7.9 seconds and on to a top speed of with the top closed. The top speed reduces by with the top retracted.


title: McLaren 720S

text: Unveiled on 3 March 2020, the 765LT is a limited (765 units worldwide) version of the 720S and the successor to the 675LT as a Super Series Longtail car, focused on track performance. The M840T engine is now rated at at 7,500 rpm and of torque at 5,500 rpm achieved with a higher-capacity fuel pump, forged aluminium pistons and a three-layer head gasket from the Senna.


title: McLaren 720S

text: The top speed is lowered from the 720S's to due to added drag created by the added high downforce parts, although the 765LT weighs less than the 720S at in its lightest configuration and has a quicker time of 2.8 seconds. It also can hit in 7.0 seconds and complete a quarter-mile dash in 9.9 seconds according to McLaren. A US-spec McLaren 765LT was tested by "Road & Track" with a quarter-mile time of 11.6 seconds at , which equates to 0–100 km/h in the high-3 range and 0–200 km/h in the mid-10 range. In addition, it stopped at 92 feet from 60-0 mph.


title: McLaren 720S

text: The Senna's brake calipers are also available as an extra-cost option; McLaren claims these have four times the thermal conductivity as conventional carbon ceramics, while Pirelli Trofeo R tyres are standard. Suspension changes involve a reduction in ride height and the use of lightweight main springs with secondary "helper" units as well as an upgraded Proactive Chassis Control system. The aerodynamics are redesigned to produce 25% more downforce than the 720S, featuring front fender vents, a larger front splitter and a longer active wing element at the rear at the cost of less noise insulation, thinner-gauge glass and stiffened engine mounts. The rear of the car also features a quad-exit full titanium exhaust to distinguish it from the 720S. Production was limited to 765 cars globally with customer deliveries in October 2020.


title: McLaren 720S

text: It is a version of 720S coupé celebrating the 25th anniversary of McLaren F1 GTR #59's 1995 24 Hours of Le Mans race win. It includes:


title: McLaren 720S

text: Unveiled on the 27 July 2021, the convertible is a limited (765 units worldwide) version of 765LT coupe. It uses the same M840T engine which produces . The Spider weighs less than the 720S Spider at , making it heavier than the coupe.


title: McLaren 720S

text: The McLaren 720S GT3X won the 2021 Goodwood Festival of Speed hill climb, by setting the fastest time at the shootout final, sprinting up the hill in 45.01 seconds.


title: McLaren 720S

text: The McLaren 720S GT3 is a motorsport version of the 720S designed to take part in GT3 races. The car was revealed in August 2018 with a price of $564,000 and McLaren said that 90% of the car was different from the road-legal 720S. It was originally teased through renderings in November 2017.


title: McLaren 720S

text: In March 2021, McLaren announced the 720S GT3X, a track-only car based on the 720S GT3 which isn't limited by the restrictions put in place by the FIA for GT3-class cars.


title: McLaren 720S

text: McLaren 720S GT3X wins 2021 Goodwood Festival hill climb , set the fastest time at the 2021 Goodwood Festival of Speed’s famous hill climb timed shootout final, sprinting up the hill in just 45.01 seconds.


title: McLaren 720S

text: LEGO Speed Champions McLaren 720S model kit, which also includes a minifigure car designer with design studio desk, went on sale June 2017.


title: Pus

text: Pus is an exudate, typically white-yellow, yellow, or yellow-brown, formed at the site of inflammation during bacterial or fungal infection. An accumulation of pus in an enclosed tissue space is known as an abscess, whereas a visible collection of pus within or beneath the epidermis is known as a pustule, pimple or "spot".


title: Pus

text: Pus consists of a thin, protein-rich fluid (historically known as "liquor puris") and dead leukocytes from the body's immune response (mostly neutrophils). During infection, macrophages release cytokines, which trigger neutrophils to seek the site of infection by chemotaxis. There, the neutrophils release granules, which destroy the bacteria. The bacteria resist the immune response by releasing toxins called leukocidins. As the neutrophils die off from toxins and old age, they are destroyed by macrophages, forming the viscous pus. Bacteria that cause pus are called pyogenic.


title: Pus

text: Although pus is normally of a whitish-yellow hue, changes in the color can be observed under certain circumstances. Pus is sometimes green because of the presence of myeloperoxidase, an intensely green antibacterial protein produced by some types of white blood cells. Green, foul-smelling pus is found in certain infections of "Pseudomonas aeruginosa". The greenish color is a result of the bacterial pigment pyocyanin that it produces. Amoebic abscesses of the liver produce brownish pus, which is described as looking like "anchovy paste". Pus from anaerobic infections can more often have a foul odor.


title: Pus

text: In almost all cases when there is a collection of pus in the body, a clinician will try to create an opening to drain it. This principle has been distilled into the famous Latin aphorism ""Ubi pus, ibi evacua"" ("Where there is pus, evacuate it").


title: Pus

text: Some disease processes caused by pyogenic infections are impetigo, osteomyelitis, septic arthritis and necrotizing fasciitis.


title: Pus

text: A great many species of bacteria may be involved in the production of pus. The most commonly found include:


title: Pus

text: "Practically all major wounds suppurated. Pus was the most common subject of converse [among surgeons], because it was the most prominent feature in the surgeon's work. It was classified according to degrees of vileness."


title: Pus

text: "If a patient was lucky... a thick cream-colored odorless fluid would appear within five or six days";


title: Pus

text: "On the other hand, if the pus gradually became watery, blood tinged and foul smelling, it was designated 'sanious'


title: Pus

text: It later came to be understood that "laudable" pus generally implied an invasion of relatively benign staphylococcus, while "ill-conditioned" pus usually meant the more dangerous streptococcus was present.


title: Baby shower

text: A baby shower is a party of gift-giving, drinking beers or a ceremony that has different names in different cultures. It celebrates the delivery or expected birth of a child or the transformation of a woman into a mother.


title: Baby shower

text: The term "shower" is often assumed to mean that the expectant mother is "showered" with gifts. A related custom, called a bridal shower, may have derived its name from the custom in the 19th century for the presents to be put inside a parasol, which when opened would "shower" the bride-to-be with gifts. Alternatively the term possibly denotes a "first showing" of the new baby to the wider family and circle of friends, although the baby shower is usually held before the birth of the baby.


title: Baby shower

text: Traditionally, baby showers are given only for the family's first child, and only women are invited, though this has changed in recent years, now allowing showers being split up for different audiences: workplace, mixed-sex, etc. Activities at baby showers include gift-giving and playing themed games.


title: Baby shower

text: Baby shower games vary, sometimes including standard games such as bingo, and sometimes being pregnancy-themed, such as "guess the mother's measurements" or "guess the baby". These games help the close friends attend the shower bond with the mother and enable the new family to say thanks ahead of time, figuring out who is willing and able to help them with the challenges of bringing up.


title: Baby shower

text: According to etiquette authority Miss Manners, because the party centers on gift-giving, the baby shower is typically arranged and hosted by a close friend rather than a member of the family, since it is considered improper for families to beg for gifts on behalf of their members. However, this custom varies by culture or region and in some it is expected and customary for a close female family member to host the baby shower, often the baby's maternal grandmother.


title: Baby shower

text: When a baby shower is held after a baby's birth, an invitation to attend the shower may be combined with a baby announcement. In the US, if a baby shower does not happen before the arrival of the baby, a sip-and-see party or other similar events can be organized after the birth.


title: Baby shower

text: Guests bring small gifts for the expectant mother. Typical gifts related to babies include diapers, blankets, baby bottles, clothes, and toys. It is common to open gifts during the party; sometimes the host will make a game of opening gifts.


title: Baby shower

text: The baby shower is a family's first opportunity to gather people together to help play a part in their child's life. The new parents may wish to call on people to assist in the upbringing of their child, and help educate the child over time. People around the family, who care for them, want to be involved in the child's life, and a baby shower presents an opportunity for them to give gifts and be of help, showing their love for the family. If it happens before the birth, it allows the new family to thank everyone before the stress of a new baby and lack of sleep begins.


title: Baby shower

text: The term "baby shower" is relatively new, but the celebrations and rituals associated with pregnancy and childbirth are both ancient and enduring.


title: Baby shower

text: While continuing the traditions from the 1950s, modern technology has altered the form a baby shower takes: games can include identifying baby parts on a sonogram. Moreover, although traditional baby showers were female-exclusive, mixed-sex showers have increased in frequency.


title: Baby shower

text: Baby showers and other social events to celebrate an impending or recent birth are popular around the world. They are often women-only social gatherings.


title: Baby shower

text: Some baby showers are directed at fathers. These may be more oriented towards drinking beer, watching sports, fishing, or playing video games. The primary nature of these gifts is diapers and/or diaper-related items. The organization of the diaper party is typically done by the friends of the father-to-be as a way of helping to prepare for the coming child. These parties may be held at local pubs/bars, a friend's house, or the soon-to-be grandfather's house. In the United Kingdom, this is called "wetting the baby's head", and is generally more common than baby showers. However, with the growth of American cultural influence- accelerated through celebrities via social media sites like Instagram, baby shower decorations are becoming more common in the United Kingdom. Wetting the baby's head is traditionally when the father celebrates the birth by having a few drinks and getting drunk with a group of friends.


title: Baby shower

text: There has been some controversy over these, with Judith Martin calling them a "monstrous imposition", although she was referring to the attitude of demanding gifts and not necessarily the male version of a baby shower.


title: Baby shower

text: In Hungary, such an event is called Milking party held by tradition in favor of the mother to be blessed with breast milk for the newborn. Practically it is the last day-off of the father for some time as he is expected to stay home to help. No similar domestic custom exists for mothers, such as a baby shower decoration. Gifts for the baby are given on the first visit to his/her home. This, due to health concerns, happens at the appropriate and suitable time for each counterpart.


title: The Ipcress File (film)

text: The Ipcress File is a 1965 British espionage film directed by Sidney J. Furie and starring Michael Caine. The screenplay, by Bill Canaway and James Doran, was based on Len Deighton's novel "The IPCRESS File" (1962). It received a BAFTA award for the Best British film released in 1965. In 1999, it was included at number 59 on the BFI list of the 100 best British films of the 20th century.


title: The Ipcress File (film)

text: This film and its sequels were a deliberately downbeat alternative to the hugely successful James Bond films, even though some of the production team were previously involved with the 007 movies.


title: The Ipcress File (film)

text: A scientist called Radcliffe is kidnapped from a train and his security escort killed. Harry Palmer, a British Army sergeant with a criminal past, now working for a Ministry of Defence organisation, is summoned by his superior, Colonel Ross, and transferred to a section headed by Major Dalby. Ross suspects that Radcliffe's disappearance is connected to the fact that sixteen other top British scientists have inexplicably left their jobs at the peak of their careers. He threatens Dalby that his group will go if Radcliffe cannot be recovered. Palmer is then introduced as a replacement for the dead security escort.


title: The Ipcress File (film)

text: Afterwards, Dalby briefs his agents that the main suspect is Eric Grantby and his chief of staff, codenamed "Housemartin", and tells the team to find out where they are at present. Palmer is also introduced to and befriends Jock Carswell. Using a Scotland Yard contact, Palmer locates Grantby but, when Palmer tries to stop Grantby getting away, he is attacked by Housemartin.


title: The Ipcress File (film)

text: Housemartin is arrested later but, before he can be questioned, he is killed by men impersonating Palmer and Carswell. Suspecting that Radcliffe is being held in a certain disused factory, Palmer orders a search, but nothing is found except a piece of audiotape marked "IPCRESS" that produces meaningless noise when played. Dalby then points out that the paper on which Grantby had written a false phone number is the programme for an upcoming military band concert. There they encounter Grantby and a deal is struck for Radcliffe's return.


title: The Ipcress File (film)

text: The exchange goes as planned but, as they are leaving, Palmer shoots a man in the shadows who turns out to be a CIA agent. Subsequently, another CIA operative threatens to kill Palmer if he discovers that the death was not a mistake. Some days later, it becomes clear that while Radcliffe is physically unharmed, his mind has been affected and he can no longer function as a scientist. Carswell has discovered a book titled "Induction of Psychoneurosis by Conditioned Reflex under Stress" – IPCRESS – which he believes explains what has happened to Radcliffe and the other scientists. Carswell borrows Palmer's car to test his theory on Radcliffe, but is shot before reaching him.


title: The Ipcress File (film)

text: Believing that he himself must have been the intended target, Palmer goes home to collect his belongings and there discovers the body of the second CIA agent. When he returns to the office, the IPCRESS file is missing from his desk. Ross had previously asked him to microfilm the file and Palmer now believes that he is being set up. When he informs Dalby what has happened and that he suspects Ross, Dalby tells him to leave town for a while.


title: The Ipcress File (film)

text: On the train to Paris, Palmer is kidnapped and wakes up imprisoned in a cell in Albania. After several days without sleep, food and warmth, Grantby reveals himself as his kidnapper. Having previously read the file, Palmer realises that they are preparing to brainwash him. He uses pain to distract himself, but after many sessions under stress from disorientating images and loud electronic sounds, he succumbs. Grantby then instills a trigger phrase that will make Palmer follow any commands given to him.


title: The Ipcress File (film)

text: Palmer eventually manages to escape and discovers that he is really still in London. He phones Dalby, who is in Grantby's company at the time. Dalby uses the trigger phrase and gets Palmer to call Ross to the warehouse where he had been held. As Dalby and Ross arrive, Palmer holds them both at gunpoint. Dalby accuses Ross of killing Carswell; Ross tells Palmer that he had been suspicious of Dalby and was investigating him.


title: The Ipcress File (film)

text: Dalby now uses the trigger phrase again and tells Palmer to "Shoot the traitor now". As Palmer wavers, his hand strikes against a piece of equipment and the pain reminds him of his conditioning. Dalby goes for his gun and Palmer shoots him.


title: The Ipcress File (film)

text: Ross then remarks that, in choosing Palmer for the assignment, he had hoped that Palmer's tendency to insubordination would be useful. When Palmer reproaches Ross for endangering him, he is told that this is what he is paid for.


title: The Ipcress File (film)

text: Deighton was hired to write a screenplay for the James Bond film "From Russia with Love", but later was let go because of a lack of progress. However, Deighton's brief involvement with Eon Productions led him to sell the film rights to his Harry Palmer novels to the Bond series co-producer Harry Saltzman, who had previously been known for producing "kitchen-sink realist" dramas. Among other crew members who worked on "The Ipcress File" and had also worked on the Bond films up to this point were the production designer Ken Adam, the film editor Peter Hunt and the film score composer John Barry.


title: The Ipcress File (film)

text: Harry Saltzman gave Jimmy Sangster a copy of the novel to read. Sangster enjoyed the book and was eager to adapt the novel, suggesting Michael Caine to play the main role and Sidney J. Furie as director. However, Saltzman would not commit to the timeframe that Sangster insisted upon.


title: The Ipcress File (film)

text: Sangster embellished Deighton's protagonist by removing the ambiguity of the novel. There it is only in Chapter 5 that Palmer remarks, "My name isn't Harry, but in this business it's hard to remember whether it ever had been". But from the opening scenes of the film, Sangster's screenplay identifies Caine's character clearly as someone who cares little for authority, who indulges in quick repartee and has an interest in good food. Newspaper cuttings shown in Palmer's kitchen are actually cookery articles written for "The Observer" by Deighton, who was an accomplished cook himself. For a scene where Palmer prepares a meal, Deighton attempted to teach Caine how to crack an egg with one hand, which Caine could not manage. As a result, the hands in close-up are really Deighton's.


title: The Ipcress File (film)

text: Saltzman wanted "The Ipcress File" to be an ironic and downbeat alternative to the portrayal of espionage in Ian Fleming's novels about the spy James Bond and the film series which followed from them. He also wanted it to be more in the style of his previous realist films. "The Ipcress File" therefore became the first of the nominally rival Harry Palmer series and some aspects are reminiscent of film noir. In contrast to Bond's public school background and playboy lifestyle, Palmer is a working class Londoner who lives in a Notting Hill bedsit and has to put up with red tape and inter-departmental rivalries. The action is set entirely in "a gritty, gloomy, decidedly non-swinging" London with humdrum locations, aside from the Royal Albert Hall.


title: The Ipcress File (film)

text: The film was made at Pinewood Studios with sets designed by the art directors Peter Murton and Ken Adam. The film was shot on location around London in the widescreen screen ratio using Techniscope. In this format, the normal 35mm film frame is split in half, each now taking up only two perforations on the edges of the film stock rather than usual four. The format was introduced by Technicolor Italia in 1963 and allowed for a greater depth of field as it was shot with shorter focal length lenses than used in the anamorphic widescreen processes. This allowed cinematographer Otto Heller to construct images in deep focus, shooting behind objects and allowing both the objects in the foreground and the action taking place in the background to be in focus.


title: The Ipcress File (film)

text: John Barry, who had worked on all of the Bond films up to this time, composed the music score for the soundtrack. As opposed to the electric guitar which carried the melody in the "James Bond Theme", Barry made prominent use of a cimbalom. The complex electronic sound effect of the brain-washing process was conceived by sound engineer Norman Wanstall and created by the BBC Radiophonic Workshop.


title: The Ipcress File (film)

text: When the film premiered at the Leicester Square Theatre in London on 18 March 1965, the film critic for "The Times" had mixed feelings about it. While enjoying the first part of the film, and generally praising Michael Caine, the critic found the second half bewildering to the extent that the characters "cease to be pleasantly mystifying and become just irritatingly obscure." A review in "Variety" was largely positive, describing the film as "anti-Bond" for its unglamorous depiction of espionage, and praising Caine's understated performance but criticizing the sometimes "arty-crafty" camera work.


title: The Ipcress File (film)

text: Subsequently, the film has come to be recognized as a classic. "The Ipcress File" is included on the British Film Institute's BFI 100, a list of 100 of the best British films of the 20th century, at No. 59. The review website Rotten Tomatoes sampled 31 critics resulting in an aggregate rating of 98%.


title: The Ipcress File (film)

text: The film won the BAFTA Award for Best British Film, and Ken Adam won the award for 'Best British Art Direction, Colour'.


title: The Ipcress File (film)

text: Screenwriters Bill Canaway and James Doran received a 1966 Edgar Award from the Mystery Writers of America for Best Foreign Film Screenplay.


title: The Ipcress File (film)

text: There were two immediate sequels starring Harry Palmer: "Funeral in Berlin" (1966) and "Billion Dollar Brain" (1967). Decades later Michael Caine returned to the character in Harry Alan Towers's "Bullet to Beijing" (1995) and "Midnight in Saint Petersburg" (1996).


title: Group theory

text: The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.


title: Group theory

text: Various physical systems, such as crystals and the hydrogen atom, and three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.


title: Group theory

text: The early history of group theory dates from the 19th century. One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 2004, that culminated in a complete classification of finite simple groups.


title: Group theory

text: Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields. Early results about permutation groups were obtained by Lagrange, Ruffini, and Abel in their quest for general solutions of polynomial equations of high degree. Évariste Galois coined the term "group" and established a connection, now known as Galois theory, between the nascent theory of groups and field theory. In geometry, groups first became important in projective geometry and, later, non-Euclidean geometry. Felix Klein's Erlangen program proclaimed group theory to be the organizing principle of geometry.


title: Group theory

text: Galois, in the 1830s, was the first to employ groups to determine the solvability of polynomial equations. Arthur Cayley and Augustin Louis Cauchy pushed these investigations further by creating the theory of permutation groups. The second historical source for groups stems from geometrical situations. In an attempt to come to grips with possible geometries (such as euclidean, hyperbolic or projective geometry) using group theory, Felix Klein initiated the Erlangen programme. Sophus Lie, in 1884, started using groups (now called Lie groups) attached to analytic problems. Thirdly, groups were, at first implicitly and later explicitly, used in algebraic number theory.


title: Group theory

text: The different scope of these early sources resulted in different notions of groups. The theory of groups was unified starting around 1880. Since then, the impact of group theory has been ever growing, giving rise to the birth of abstract algebra in the early 20th century, representation theory, and many more influential spin-off domains. The classification of finite simple groups is a vast body of work from the mid 20th century, classifying all the finite simple groups.


title: Group theory

text: The range of groups being considered has gradually expanded from finite permutation groups and special examples of matrix groups to abstract groups that may be specified through a presentation by generators and relations.


title: Group theory

text: The first class of groups to undergo a systematic study was permutation groups. Given any set "X" and a collection "G" of bijections of "X" into itself (known as "permutations") that is closed under compositions and inverses, "G" is a group acting on "X". If "X" consists of "n" elements and "G" consists of "all" permutations, "G" is the symmetric group S; in general, any permutation group "G" is a subgroup of the symmetric group of "X". An early construction due to Cayley exhibited any group as a permutation group, acting on itself () by means of the left regular representation.


title: Group theory

text: In many cases, the structure of a permutation group can be studied using the properties of its action on the corresponding set. For example, in this way one proves that for , the alternating group A is simple, i.e. does not admit any proper normal subgroups. This fact plays a key role in the impossibility of solving a general algebraic equation of degree in radicals.


title: Group theory

text: The next important class of groups is given by "matrix groups", or linear groups. Here "G" is a set consisting of invertible matrices of given order "n" over a field "K" that is closed under the products and inverses. Such a group acts on the "n"-dimensional vector space "K" by linear transformations. This action makes matrix groups conceptually similar to permutation groups, and the geometry of the action may be usefully exploited to establish properties of the group "G".


title: Group theory

text: Permutation groups and matrix groups are special cases of transformation groups: groups that act on a certain space "X" preserving its inherent structure. In the case of permutation groups, "X" is a set; for matrix groups, "X" is a vector space. The concept of a transformation group is closely related with the concept of a symmetry group: transformation groups frequently consist of "all" transformations that preserve a certain structure.


title: Group theory

text: The theory of transformation groups forms a bridge connecting group theory with differential geometry. A long line of research, originating with Lie and Klein, considers group actions on manifolds by homeomorphisms or diffeomorphisms. The groups themselves may be discrete or continuous.


title: Group theory

text: Most groups considered in the first stage of the development of group theory were "concrete", having been realized through numbers, permutations, or matrices. It was not until the late nineteenth century that the idea of an abstract group as a set with operations satisfying a certain system of axioms began to take hold. A typical way of specifying an abstract group is through a presentation by "generators and relations",


title: Group theory

text: A significant source of abstract groups is given by the construction of a "factor group", or quotient group, "G"/"H", of a group "G" by a normal subgroup "H". Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in number theory. If a group "G" is a permutation group on a set "X", the factor group "G"/"H" is no longer acting on "X"; but the idea of an abstract group permits one not to worry about this discrepancy.


title: Group theory

text: The change of perspective from concrete to abstract groups makes it natural to consider properties of groups that are independent of a particular realization, or in modern language, invariant under isomorphism, as well as the classes of group with a given such property: finite groups, periodic groups, simple groups, solvable groups, and so on. Rather than exploring properties of an individual group, one seeks to establish results that apply to a whole class of groups. The new paradigm was of paramount importance for the development of mathematics: it foreshadowed the creation of abstract algebra in the works of Hilbert, Emil Artin, Emmy Noether, and mathematicians of their school.


title: Group theory

text: An important elaboration of the concept of a group occurs if "G" is endowed with additional structure, notably, of a topological space, differentiable manifold, or algebraic variety. If the group operations "m" (multiplication) and "i" (inversion),


title: Group theory

text: are compatible with this structure, that is, they are continuous, smooth or regular (in the sense of algebraic geometry) maps, then "G" is a topological group, a Lie group, or an algebraic group.


title: Group theory

text: The presence of extra structure relates these types of groups with other mathematical disciplines and means that more tools are available in their study. Topological groups form a natural domain for abstract harmonic analysis, whereas Lie groups (frequently realized as transformation groups) are the mainstays of differential geometry and unitary representation theory. Certain classification questions that cannot be solved in general can be approached and resolved for special subclasses of groups. Thus, compact connected Lie groups have been completely classified. There is a fruitful relation between infinite abstract groups and topological groups: whenever a group "Γ" can be realized as a lattice in a topological group "G", the geometry and analysis pertaining to "G" yield important results about "Γ". A comparatively recent trend in the theory of finite groups exploits their connections with compact topological groups (profinite groups): for example, a single "p"-adic analytic group "G" has a family of quotients which are finite "p"-groups of various orders, and properties of "G" translate into the properties of its finite quotients.


title: Group theory

text: During the twentieth century, mathematicians investigated some aspects of the theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a consequence, the complete classification of finite simple groups was achieved, meaning that all those simple groups from which all finite groups can be built are now known.


title: Group theory

text: During the second half of the twentieth century, mathematicians such as Chevalley and Steinberg also increased our understanding of finite analogs of classical groups, and other related groups. One such family of groups is the family of general linear groups over finite fields.


title: Group theory

text: physical objects, when those objects admit just a finite number of structure-preserving transformations. The theory of Lie groups,


title: Group theory

text: which may be viewed as dealing with "continuous symmetry", is strongly influenced by the associated Weyl groups. These are finite groups generated by reflections which act on a finite-dimensional Euclidean space. The properties of finite groups can thus play a role in subjects such as theoretical physics and chemistry.


title: Group theory

text: Saying that a group "G" "acts" on a set "X" means that every element of "G" defines a bijective map on the set "X" in a way compatible with the group structure. When "X" has more structure, it is useful to restrict this notion further: a representation of "G" on a vector space "V" is a group homomorphism:


title: Group theory

text: where GL("V") consists of the invertible linear transformations of "V". In other words, to every group element "g" is assigned an automorphism "ρ"("g") such that for any "h" in "G".


title: Group theory

text: This definition can be understood in two directions, both of which give rise to whole new domains of mathematics. On the one hand, it may yield new information about the group "G": often, the group operation in "G" is abstractly given, but via "ρ", it corresponds to the multiplication of matrices, which is very explicit. On the other hand, given a well-understood group acting on a complicated object, this simplifies the study of the object in question. For example, if "G" is finite, it is known that "V" above decomposes into irreducible parts (see Maschke's theorem). These parts, in turn, are much more easily manageable than the whole "V" (via Schur's lemma).


title: Group theory

text: Given a group "G", representation theory then asks what representations of "G" exist. There are several settings, and the employed methods and obtained results are rather different in every case: representation theory of finite groups and representations of Lie groups are two main subdomains of the theory. The totality of representations is governed by the group's characters. For example, Fourier polynomials can be interpreted as the characters of U(1), the group of complex numbers of absolute value "1", acting on the "L"-space of periodic functions.


title: Group theory

text: A Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term "groupes de Lie" first appeared in French in 1893 in the thesis of Lie's student Arthur Tresse, page 3.


title: Group theory

text: Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations (differential Galois theory), in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations.


title: Group theory

text: Groups can be described in different ways. Finite groups can be described by writing down the group table consisting of all possible multiplications . A more compact way of defining a group is by "generators and relations", also called the "presentation" of a group. Given any set "F" of generators formula_4, the free group generated by "F" surjects onto the group "G". The kernel of this map is called the subgroup of relations, generated by some subset "D". The presentation is usually denoted by formula_5 For example, the group presentation formula_6 describes a group which is isomorphic to formula_7 A string consisting of generator symbols and their inverses is called a "word".


title: Group theory

text: Combinatorial group theory studies groups from the perspective of generators and relations. It is particularly useful where finiteness assumptions are satisfied, for example finitely generated groups, or finitely presented groups (i.e. in addition the relations are finite). The area makes use of the connection of graphs via their fundamental groups. For example, one can show that every subgroup of a free group is free.


title: Group theory

text: There are several natural questions arising from giving a group by its presentation. The "word problem" asks whether two words are effectively the same group element. By relating the problem to Turing machines, one can show that there is in general no algorithm solving this task. Another, generally harder, algorithmically insoluble problem is the group isomorphism problem, which asks whether two groups given by different presentations are actually isomorphic. For example, the group with presentation formula_8 is isomorphic to the additive group Z of integers, although this may not be immediately apparent. (Writing formula_9, one has formula_10)


title: Group theory

text: Geometric group theory attacks these problems from a geometric viewpoint, either by viewing groups as geometric objects, or by finding suitable geometric objects a group acts on. The first idea is made precise by means of the Cayley graph, whose vertices correspond to group elements and edges correspond to right multiplication in the group. Given two elements, one constructs the word metric given by the length of the minimal path between the elements. A theorem of Milnor and Svarc then says that given a group "G" acting in a reasonable manner on a metric space "X", for example a compact manifold, then "G" is quasi-isometric (i.e. looks similar from a distance) to the space "X".


title: Group theory

text: Given a structured object "X" of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This occurs in many cases, for example


title: Group theory

text: The axioms of a group formalize the essential aspects of symmetry. Symmetries form a group: they are closed because if you take a symmetry of an object, and then apply another symmetry, the result will still be a symmetry. The identity keeping the object fixed is always a symmetry of an object. Existence of inverses is guaranteed by undoing the symmetry and the associativity comes from the fact that symmetries are functions on a space, and composition of functions is associative.


title: Group theory

text: Frucht's theorem says that every group is the symmetry group of some graph. So every abstract group is actually the symmetries of some explicit object.


title: Group theory

text: The saying of "preserving the structure" of an object can be made precise by working in a category. Maps preserving the structure are then the morphisms, and the symmetry group is the automorphism group of the object in question.


title: Group theory

text: Applications of group theory abound. Almost all structures in abstract algebra are special cases of groups. Rings, for example, can be viewed as abelian groups (corresponding to addition) together with a second operation (corresponding to multiplication). Therefore, group theoretic arguments underlie large parts of the theory of those entities.


title: Group theory

text: Galois theory uses groups to describe the symmetries of the roots of a polynomial (or more precisely the automorphisms of the algebras generated by these roots). The fundamental theorem of Galois theory provides a link between algebraic field extensions and group theory. It gives an effective criterion for the solvability of polynomial equations in terms of the solvability of the corresponding Galois group. For example, "S", the symmetric group in 5 elements, is not solvable which implies that the general quintic equation cannot be solved by radicals in the way equations of lower degree can. The theory, being one of the historical roots of group theory, is still fruitfully applied to yield new results in areas such as class field theory.


title: Group theory

text: Algebraic topology is another domain which prominently associates groups to the objects the theory is interested in. There, groups are used to describe certain invariants of topological spaces. They are called "invariants" because they are defined in such a way that they do not change if the space is subjected to some deformation. For example, the fundamental group "counts" how many paths in the space are essentially different. The Poincaré conjecture, proved in 2002/2003 by Grigori Perelman, is a prominent application of this idea. The influence is not unidirectional, though. For example, algebraic topology makes use of Eilenberg–MacLane spaces which are spaces with prescribed homotopy groups. Similarly algebraic K-theory relies in a way on classifying spaces of groups. Finally, the name of the torsion subgroup of an infinite group shows the legacy of topology in group theory.


title: Group theory

text: Algebraic geometry likewise uses group theory in many ways. Abelian varieties have been introduced above. The presence of the group operation yields additional information which makes these varieties particularly accessible. They also often serve as a test for new conjectures. (For example the Hodge conjecture (in certain cases).) The one-dimensional case, namely elliptic curves is studied in particular detail. They are both theoretically and practically intriguing. In another direction, toric varieties are algebraic varieties acted on by a torus. Toroidal embeddings have recently led to advances in algebraic geometry, in particular resolution of singularities.


title: Group theory

text: Algebraic number theory makes uses of groups for some important applications. For example, Euler's product formula,


title: Group theory

text: captures the fact that any integer decomposes in a unique way into primes. The failure of this statement for more general rings gives rise to class groups and regular primes, which feature in Kummer's treatment of Fermat's Last Theorem.


title: Group theory

text: Analysis on Lie groups and certain other groups is called harmonic analysis. Haar measures, that is, integrals invariant under the translation in a Lie group, are used for pattern recognition and other image processing techniques.


title: Group theory

text: In combinatorics, the notion of permutation group and the concept of group action are often used to simplify the counting of a set of objects; see in particular Burnside's lemma.


title: Group theory

text: The presence of the 12-periodicity in the circle of fifths yields applications of elementary group theory in musical set theory. Transformational theory models musical transformations as elements of a mathematical group.


title: Group theory

text: In physics, groups are important because they describe the symmetries which the laws of physics seem to obey. According to Noether's theorem, every continuous symmetry of a physical system corresponds to a conservation law of the system. Physicists are very interested in group representations, especially of Lie groups, since these representations often point the way to the "possible" physical theories. Examples of the use of groups in physics include the Standard Model, gauge theory, the Lorentz group, and the Poincaré group.


title: Group theory

text: Group theory can be used to resolve the incompleteness of the statistical interpretations of mechanics developed by Willard Gibbs, relating to the summing of an infinite number of probabilities to yield a meaningful solution.


title: Group theory

text: In chemistry and materials science, point groups are used to classify regular polyhedra, and the symmetries of molecules, and space groups to classify crystal structures. The assigned groups can then be used to determine physical properties (such as chemical polarity and chirality), spectroscopic properties (particularly useful for Raman spectroscopy, infrared spectroscopy, circular dichroism spectroscopy, magnetic circular dichroism spectroscopy, UV/Vis spectroscopy, and fluorescence spectroscopy), and to construct molecular orbitals.


title: Group theory

text: Molecular symmetry is responsible for many physical and spectroscopic properties of compounds and provides relevant information about how chemical reactions occur. In order to assign a point group for any given molecule, it is necessary to find the set of symmetry operations present on it. The symmetry operation is an action, such as a rotation around an axis or a reflection through a mirror plane. In other words, it is an operation that moves the molecule such that it is indistinguishable from the original configuration. In group theory, the rotation axes and mirror planes are called "symmetry elements". These elements can be a point, line or plane with respect to which the symmetry operation is carried out. The symmetry operations of a molecule determine the specific point group for this molecule.


title: Group theory

text: In chemistry, there are five important symmetry operations. They are identity operation (E), rotation operation or proper rotation (C), reflection operation (σ), inversion (i) and rotation reflection operation or improper rotation (S). The identity operation (E) consists of leaving the molecule as it is. This is equivalent to any number of full rotations around any axis. This is a symmetry of all molecules, whereas the symmetry group of a chiral molecule consists of only the identity operation. An identity operation is a characteristic of every molecule even if it has no symmetry. Rotation around an axis (C) consists of rotating the molecule around a specific axis by a specific angle. It is rotation through the angle 360°/"n", where "n" is an integer, about a rotation axis. For example, if a water molecule rotates 180° around the axis that passes through the oxygen atom and between the hydrogen atoms, it is in the same configuration as it started. In this case, , since applying it twice produces the identity operation. In molecules with more than one rotation axis, the C axis having the largest value of n is the highest order rotation axis or principal axis. For example in boron trifluoride (BF), the highest order of rotation axis is C, so the principal axis of rotation is C.


title: Group theory

text: In the reflection operation (σ) many molecules have mirror planes, although they may not be obvious. The reflection operation exchanges left and right, as if each point had moved perpendicularly through the plane to a position exactly as far from the plane as when it started. When the plane is perpendicular to the principal axis of rotation, it is called σ (horizontal). Other planes, which contain the principal axis of rotation, are labeled vertical (σ) or dihedral (σ).


title: Group theory

text: Inversion (i ) is a more complex operation. Each point moves through the center of the molecule to a position opposite the original position and as far from the central point as where it started. Many molecules that seem at first glance to have an inversion center do not; for example, methane and other tetrahedral molecules lack inversion symmetry. To see this, hold a methane model with two hydrogen atoms in the vertical plane on the right and two hydrogen atoms in the horizontal plane on the left. Inversion results in two hydrogen atoms in the horizontal plane on the right and two hydrogen atoms in the vertical plane on the left. Inversion is therefore not a symmetry operation of methane, because the orientation of the molecule following the inversion operation differs from the original orientation. And the last operation is improper rotation or rotation reflection operation (S) requires rotation of  360°/"n", followed by reflection through a plane perpendicular to the axis of rotation.


title: Group theory

text: Very large groups of prime order constructed in elliptic curve cryptography serve for public-key cryptography. Cryptographical methods of this kind benefit from the flexibility of the geometric objects, hence their group structures, together with the complicated structure of these groups, which make the discrete logarithm very hard to calculate. One of the earliest encryption protocols, Caesar's cipher, may also be interpreted as a (very easy) group operation. Most cryptographic schemes use groups in some way. In particular Diffie–Hellman key exchange uses finite cyclic groups. So the term group-based cryptography refers mostly to cryptographic protocols that use infinite nonabelian groups such as a braid group.


title: James Packer

text: James Douglas Packer (born 8 September 1967) is an Australian billionaire businessman and investor. Packer is the son of Kerry Packer , a media mogul, and his wife, Roslyn Packer . He is the grandson of Sir Frank Packer. He inherited control of the family company, Consolidated Press Holdings Limited, as well as investments in Crown Resorts and other companies. He is the former executive chairman of Publishing and Broadcasting Limited (PBL) and Consolidated Media Holdings, which predominantly owned media interests across a range of platforms, and a former executive chairman of Crown Resorts.


title: James Packer

text: , Packer's net worth was assessed as 5.72 billion by the "Financial Review Rich List", ranking him as the fifteenth-wealthiest Australian; he was the richest person in Australia in 2006 and 2007. "Forbes Asia" magazine assessed Packer's net worth at 3.6 billion in January 2019, the ninth-richest Australian.


title: James Packer

text: In June 2022, the Federal Court approved Blackstone's takeover of Crown Casinos, delivering Packer 3.36 billion in exchange for his 37 per cent stake in the company, which he has been involved with since 1999.


title: James Packer

text: James Packer was born in Sydney, the son of philanthropist Roslyn (née Weedon) and media mogul Kerry Packer. His grandfather was the media proprietor Sir Frank Packer.


title: James Packer

text: Packer was educated at Cranbrook School in Bellevue Hill, Sydney. After obtaining the Higher School Certificate (HSC) at Cranbrook, he began working at his father's extensive Newcastle Waters cattle station in the Barkly Tableland of the Northern Territory, where he was a jackeroo. Packer has stated he did not attend university as he "didn't have the marks".


title: James Packer

text: Packer is the major shareholder and a director of Crown Resorts Limited, one of Australia's largest casino groups. In October 2017, Crown's market capitalisation was over A$8 billion. Every year Crown's Australian resorts attract over 31 million visits.


title: James Packer

text: Following the dotcom crash of 2000–2001, Packer acquired stakes in the online classified sites SEEK and Carsales.com, believing that newspaper companies relying heavily on classified advertising were vulnerable to online companies in categories including employment and vehicle listings.


title: James Packer

text: Packer purchased a 25% stake in SEEK for A$33 million in August 2003. He sold most of his stake six years later for A$440 million. At Packer's urging, the magazine group then controlled by his family, Australian Consolidated Press, acquired a 41% stake in online advertiser Carsales in October 2005. The deal, initially valued at A$100 million, was eventually worth A$462 million to Packer-controlled entities.


title: James Packer

text: In March 2006, Packer began discussing whether to sell Channel Nine and the Australian Consolidated Press magazine group to help fund his move into the international gaming and tourism business. Given changes in media due to the Internet and pay-TV, Packer was concerned about the future of free-to-air television. On 17 October 2006, Packer's team finalised a deal to sell 50% of the media assets—which also included a 50% stake in web portal Ninemsn and a 51% stake in Carsales—to private equity group CVC Asia Pacific for A$4.5 billion, plus an additional A$1 billion in equity in the new company, which would be called PBL Media.


title: James Packer

text: In June 2007, Packer sold another 25% share of the joint-venture PBL Media to CVC for $515 million. In October 2008, Packer wrote down his final 25% stake in PBL Media to zero. By the end of 2012, debt from CVC's acquisition had overwhelmed Channel Nine and US hedge funds ousted CVC, taking complete ownership.


title: James Packer

text: Packer was a director of Australian Telecommunications company One.Tel, which was declared insolvent during May 2001. The collapse of One.Tel cost PBL A$327 million. Packer admitted at a PBL annual general meeting that he had learned "painful lessons" from the collapse of One.Tel. Later at the liquidator's inquiry over the collapse he denied that he was apologising for his own conduct; instead, he claimed, "I was making an apology for accepting the bona fides of Mr. [Jodee] Rich and the executive directors of One.Tel."


title: James Packer

text: In April 2014, Lachlan Murdoch and Packer agreed to a A$40 million settlement over the One.Tel failure. The settlement was approved by the Supreme Court of New South Wales on 17 April 2014, with A$14.93 million to be paid by the Packer family's Consolidated Press Holdings, A$11.77 million to be paid by Packer's Crown Resorts and A$13.3 million to be paid by News Corp.


title: James Packer

text: Since his father's death, Packer has moved away from the family's traditional media businesses and focused on creating a worldwide gambling empire: Crown Resorts. Crown is one of Australia's largest gambling and resort groups. It has businesses and investments in the integrated resort and casino sectors in Australia and Macau, and wholly owns and operates a high-end casino in London, Crown Aspinall's. In October 2017, Crown's market capitalization was over $8 billion. Crown's two Australian resorts, Crown Melbourne and Crown Perth, feature over 2,750 hotel rooms, villas, gambling areas, resort pools, spas, restaurants and retail, convention centres and live entertainment venues. Every year Crown's Australian resorts and casinos attract over 31 million visits. Over one third of Crown's revenue in fiscal 2016 was estimated to be generated from international visitors, mostly from Asia. Crown announced investment of over A$4.1 billion between fiscal 2007 and fiscal 2017, to upgrade and open new attractions at its Australian resorts, including the significant development A$2 billion Crown Sydney Hotel Resort which is expected to open in 2020.


title: James Packer

text: In 2009, Crown lost 250 million in failed casino investment company in the US, Fontainebleau Resorts. Crown also paid 242 million for a stake in Station Casinos which is now considered almost worthless.


title: James Packer

text: As at 30 June 2013, Crown held a 33.7% equity interest in MCE. Crown's initial investment in Melco Crown Entertainment was 600 million, the market cap of Crown's investment as at 30 October 2013, was 6.2 billion. At Crown's annual meeting in October 2013 Packer said "Crown's investment through our partnership with Melco International Development has now grown to be one of the largest Australian joint-venture partnerships operating inside China". Crown completed the sell down of this investment in May 2017.


title: James Packer

text: Betfair Australasia was formed as a 50/50 joint venture between Crown Resorts and Betfair Group plc. In August 2014, Crown Resorts announced it had acquired Betfair Group plc's 50% equity interest in Betfair Australasia Pty Limited (Betfair Australasia) for consideration of $10 million.


title: James Packer

text: In 2011, Packer's ASX-listed Crown Limited acquired a 100% interest in Aspinall's Club in London, developed through a joint venture between Crown and Packer's family friend, Damian Aspinall, the son of John Aspinall. Crown has since rebranded Aspinall's Club to Crown Aspinall's.


title: James Packer

text: Together with Damian Aspinall, Packer's Crown Resorts holds a 50% equity interest in a group of casino complexes in the UK called Aspers, which operate four regional casinos in Newcastle upon Tyne, Stratford, East London, Milton Keynes and Northampton. Packer's bid for a UK "supercasino" based in Cardiff fell through when only one licence was granted, to the northern city of Manchester.


title: James Packer

text: In December 2014, Crown Resorts signed a deal with Matthew Tripp, which gave Crown Resorts control over Tripp's online betting platform, CrownBet, formerly known as BetEasy. In April 2016 CrownBet pleaded guilty to five counts of breaching laws by publishing illegal betting advertising that offered inducements for NSW residents to gamble. According to the NSW Department of Justice, CrownBet "sought to have the matters finalised without conviction in Downing Centre Local Court ... but Magistrate Joanne Keogh said convictions were necessary for general deterrence to others in the industry and to protect the vulnerable. CrownBet was convicted of the five offences and ordered to pay a total of $10,500 in fines and also ordered to pay ... legal costs of $10,000."


title: James Packer

text: On 6 October 2020, Packer appeared before an independent inquiry into Crown's suitability to hold casino licence in NSW. When questioned over impropriety, illegality and corruption, Packer admitted that while a director of Crown he made “shameful” and “disgraceful” threats against businessman Ben Gray. In February 2021, the inquiry found that Crown was unsuitable to hold a casino licence due in part to Packer's threats to Ben Gray, as well as its "continued commercial relationships with junket operators who had links to Triads and other organised crime groups.” While under questioning by the inquiry, Packer revealed he has been diagnosed with bipolar disorder.


title: James Packer

text: In February 2022, The Blackstone Group acquired Crown Resorts for A$8.9 billion (US$6.4 billion). Packer held 37% of Crown Resorts stock at the time of the sale. He received A$3.36 billion for his shares.


title: James Packer

text: Packer purchased an 18% stake in Network Ten in 2010, quickly offloading half to Lachlan Murdoch. Three months later, after a dispute with Murdoch over a senior management appointment, Packer resigned his Network Ten board seat. There was also speculation that he resigned due to a conflict of interest with his interests in Consolidated Media Holdings. Following the implementation of CBS's restructure of Network Ten announced in August 2017, Packer will no longer have an interest in Network Ten.


title: James Packer

text: In late May 2011, Packer made a reported A$80 million investment in daily deals sites Scoopon and Catch of the Day through a partnership between his Consolidated Press Holding and several other investors, including Andrew Bassat, a co-founder of Seek.com.au.


title: James Packer

text: In December 2012, Packer and producer-filmmaker Brett Ratner formed a joint venture, RatPac Entertainment. The first film financed by RatPac was a major success. "Gravity", a space thriller directed by Alfonso Cuaron and starring Sandra Bullock and George Clooney, generated the strongest-ever October opening in the US and took box office receipts of more than 100 million in its first five days.


title: James Packer

text: "We all know it [producing movies] is a high-risk business and when your first movie starts like this all you can say is 'thank you'", Packer said. Packer sold his investment in RatPac for an undisclosed amount in April 2017. According to "Filmink" "Who knows what sort of legacy James Packer is going to leave when he shuffles off this mortal coil, but I maintain the films he helped finance...will stand out among the more positive achievements."


title: James Packer

text: In October 2014, Packer bought out Peter Holmes à Court's 37.5% share of the ownership of South Sydney Rabbitohs NRL club, becoming Russell Crowe's partner in the Blackcourt League Investments Pty Limited venture.


title: James Packer

text: In late 2016, Israeli Police started looking into reports that Packer gave members of Prime Minister Benjamin Netanyahu's family gifts and benefits. Packer, who is trying to gain residency in Israel, has taken the first step and registered with Israeli tax authorities. In February 2018, Packer was mentioned in an Israeli Police report recommending the prosecution of Netanyahu on corruption charges for accepting bribes, and acting against the interests of the state of Israel. Packer is mentioned in the report to have provided Netanyahu and his family members with champagne, cigars, jewelry and clothing valued at approximately US$100,000. In May 2019, Packer sold half of his stake in Crown Resorts to Lawrence Ho.


title: James Packer

text: Packer owns residential property in Bondi Beach and in Bellevue Hill, in Sydney's eastern suburbs. The Packer family also have pastoral property holdings in , called "Ellerston Station", and, since 2018, owned by his sister, Gretel.


title: James Packer

text: Packer and actress Kate Fischer separated in 1998 after five years together and a two-year engagement.


title: James Packer

text: Packer married Jodhi Meares at his home in Bellevue Hill, Sydney in October 1999; the relationship lasted two years, and the couple separated in 2002.


title: James Packer

text: Following the breakdown of his first marriage, and the development of a friendship with American actor Tom Cruise, Packer began attending the Church of Scientology in Australia, taking courses on the Church's Dundas business centre in 2002. He subsequently confirmed his involvement with Scientology, saying he had found it "helpful". He later distanced himself from the church.


title: James Packer

text: Packer later married part-time model and singer Erica Baxter, whom he wed in the equivalent of a civil ceremony on 20 June 2007. The wedding was at the Antibes town hall, and the second ceremony took place at Hotel du Cap – Eden Roc in Cap d'Antibes on the French Riviera. Together, Packer and Baxter have three children: daughter Indigo, born 27 July 2008, son Jackson Lloyd, born 1 February 2010, and daughter Emmanuelle Sheelah, born 22 September 2012. According to "The Hollywood Reporter", Packer met struggling actress Charlotte Kirk in November 2012 when she was 20 and Packer was 45, and the two embarked on a relationship. In September 2013 James and Erica Packer announced they were separating.


title: James Packer

text: Packer was involved in a public physical brawl at Bondi Beach in 2014 with David Gyngell, a long-term friend and head of Channel Nine. Gyngell and Packer were both fined $500 for offensive behaviour over the incident.


title: James Packer

text: Packer and American singer-songwriter Mariah Carey became engaged in January 2016, but had broken up by October. At the time it was alleged that the break-up was a result of Carey's extravagant spending and rows over her reality show "Mariah's World", but Packer later said that the relationship had just been a "mistake" for both sides. In November 2017, Packer paid Carey a multi-million dollar settlement, in response to a lawsuit pursued by Carey citing an "inconvenience fee".


title: James Packer

text: Packer first appeared on various wealth lists in 2006, following the death of his father the previous year and the intergeneration transfer of the bulk of Kerry Packer's wealth to his son, James. James Packer's wealth was valued at A$7.25 billion. A television report on 21 June 2007 alleged that Packer had lost in excess of A$1 billion over the previous six months in 2007 due to poor investment decisions and falling profits. The 2008 "BRW" Rich 200 listed Packer as the third-richest person in Australia with a personal wealth of A$6.1 billion, behind Fortescue Metals Group chief executive Andrew Forrest and Westfield Group's Frank Lowy. That was the first time in 21 years that a member of the Packer family had not topped the list. According to "BRW", Packer's wealth dipped to an estimated A$3 billion during 2009. In its 2013 "BRW Rich 200" list, Packer was ranked third with his wealth estimated at A$6.0 billion, a boost of A$1.1 billion on the previous year. In the 2014 wealth rankings by "BRW", Packer's wealth was assessed at A$7.19 billion, making him the third-richest Australian. In 2015 "BRW" Rich 200, Packer's net worth was assessed at A$6.08 billion, making him the seventh-richest Australian. , Packer's net worth, according to the "Financial Review" Rich List, the successor of the "BRW" Rich 200, was assessed at 5.72 billion, making him the fifteenth wealthiest Australian.


title: James Packer

text: In January 2009, "The Sunday Telegraph" reported that due to ongoing financial problems, Packer's wealth dropped to under A$3 billion; also reporting that Packer listed for sale his Mangusta yacht and delayed the purchase of a Boeing business jet. Yet by mid-2010, it was reported that Packer owned a number of assets including "Ellerston Z" (a superyacht), "Arctic P" (a luxury cruise ship and former ice-breaker), a private jet, a 12-seater Sikorsky S-76 helicopter, and a variety of cars.


title: James Packer

text: , "Forbes" magazine estimated Packer's wealth at 3.6 billion, down from the 6.60 billion published by "Forbes" in their 2014 list of the richest people in Australia. In the 2017 "Forbes" list of the 50 Richest Australians, Packer's net worth was assessed at 3.9 billion, making him the ninth-richest Australian.


title: James Packer

text: James Packer is the founder of both the Packer Family Foundation and Crown Resorts Foundation. In July 2014, the two foundations launched their 200 million National Philanthropic Fund, one of Australia's largest philanthropic commitments. According to the two foundations, they are working together to promote Indigenous education opportunities, the arts and culture, and partnerships with organisations that encourage and foster social cohesion. Underlying these priorities are learning, accessibility and engagement outcomes for young Australians – staying engaged with school and learning is the key to long-term positive outcomes, and this is the approach and message that the partner organisations are delivering.


title: Muon

text: A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 "e" and a spin of , but with a much greater mass. It is classified as a lepton. As with other leptons, the muon is not thought to be composed of any simpler particles; that is, it is a fundamental particle.


title: Muon

text: The muon is an unstable subatomic particle with a mean lifetime of , much longer than many other subatomic particles. As with the decay of the non-elementary neutron (with a lifetime around 15 minutes), muon decay is slow (by subatomic standards) because the decay is mediated only by the weak interaction (rather than the more powerful strong interaction or electromagnetic interaction), and because the mass difference between the muon and the set of its decay products is small, providing few kinetic degrees of freedom for decay. Muon decay almost always produces at least three particles, which must include an electron of the same charge as the muon and two types of neutrinos.


title: Muon

text: Like all elementary particles, the muon has a corresponding antiparticle of opposite charge (+1 "e") but equal mass and spin: the antimuon (also called a "positive muon"). Muons are denoted by and antimuons by . Formerly, muons were called "mu mesons", but are not classified as mesons by modern particle physicists (see ""), and that name is no longer used by the physics community.


title: Muon

text: Muons have a mass of , which is approximately 207 times that of the electron, "m". More precisely, it is There is also a third lepton, the tau, approximately 17 times heavier than the muon.