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Direct product

In mathematics, one can define a direct product of objects known, giving a new one. This generalizes the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one talks about the product in category theory, which formalizes these notions. Examples are the product of sets, groups and other algebraic structures; the product of topological spaces is another instance. There is the direct sum – in some areas this is used interchangeably, while in others it is a different concept. If we think of R as the set of real numbers the direct product R × R is just the Cartesian product. If we think of R as the group of real numbers under addition the direct product R × R still has as its underlying set; the difference between this and the preceding example is that R × R is now a group, so we have to say how to add their elements. This is done by defining + =. If we think of R as the ring of real numbers the direct product R × R again has as its underlying set.

The ring structure ring consists of addition defined by + = and multiplication defined by =. However, if we think of R as the field of real numbers the direct product R × R does not exist – naively defining addition and multiplication componentwise as in the above example would not result in a field since the element does not have a multiplicative inverse. In a similar manner, we can talk about the direct product of finitely many algebraic structures, e.g. R × R × R × R; this relies on the fact. That is, × C ≅ A × for any algebraic structures A, B, C of the same kind; the direct product is commutative up to isomorphism, i.e. A × B ≅ B of the same kind. We can talk about the direct product of infinitely many algebraic structures. In group theory one can define the direct product of two groups and, denoted by G × H. For abelian groups which are written additively, it may be called the direct sum of two groups, denoted by G ⊕ H, it is defined as follows: the set of the elements of the new group is the Cartesian product of the sets of elements of G and H, that is.

It has a normal subgroup isomorphic to G, one isomorphic to H. The reverse holds, there is the following recognition theorem: If a group K contains two normal subgroups G and H, such that K= GH and the intersection of G and H contains only the identity K is isomorphic to G × H. A relaxation of these conditions, requiring only one subgroup to be normal, gives the semidirect product; as an example, take as

1938 Jersey Airport disaster

The 1938 Jersey Airport disaster occurred at 10:50am on Friday 4 November 1938 when the Jersey Airways de Havilland D. H.86 airliner St Catherine's Bay crashed in the parish of Saint Brélade, 500 yards east of Jersey Airport, killing the pilot and all twelve passengers on board as well as farm hand Edmund Le Cornu, working on the ground. In terms of loss of life, it was the worst crash of a rigid aircraft on British territory to date and the second-worst overall crash of a British rigid aircraft after the crash of an Imperial Airways airliner in Belgium in 1933; the airliner had just taken off from Jersey en route to Southampton. The sky was overcast, with a cloud base of 120–150 feet; the aircraft had been inspected and was not carrying a full load. The Air Ministry investigation concluded; the pilot had made a climbing turn into the clouds and inadvertently allowed the aircraft to sideslip when he was still too close to the ground to avert disaster. The aircraft had exploded and several bodies had been thrown up to 40 feet away.

Among the dead were the daughter, son-in-law and baby granddaughter of surveyor and aerial archaeology pioneer G. A. Beazeley. "Jersey Air Disaster Inquest", The Times, 7 November 1938 "Crash that Caused 14 Deaths'An Error of Airmanship'", The Times, 19 April 1939 From Sea Eagle to Flamingo: a history of Channel Island Airways, Neville Doyle, 1991 Details on

Harry Rankin

Harry Rankin was a Vancouver lawyer and long term member of the Vancouver City Council. Rankin was born Harry Riffkin in Vancouver to secular Jewish immigrants from the Ukraine, his father worked at a factory. At 14, Rankin dropped out of secondary school to work in a bakery and through the trade union he got involved in politics. During World War Two he served in the army with Vancouver's Seaforth Highlanders, they fought in Italy. Rankin married a Jewish divorcee, they had a son, Phil Rankin, who went on to become a Vancouver lawyer. A documentary film, the Rankin File, was premiered in 2018, a biography and a background to the 1986 Vancouver mayoral election between Harry Rankin and Gordon Campbell. After the war he completed his secondary education and pursued undergraduate studies at the University of British Columbia, where he earned a law degree. During his time at U. B. C, he joined the Communist University Club serving as its vice-president. Communists were banned from joining the bar and the Law Society of British Columbia interviewed Rankin at length prior to admitting him to the bar about his views on God, whether he would defend his country if attacked, whether he was a member of the Communist Party of Canada called the Labor-Progressive Party, something he was able to deny as the Communist University Club was an independent and unaffiliated organization.

In the wake of the Law Society refusing to admit Gordon Martin to the bar on account of his being an avowed communist, Rankin had to sign a declaration that he was not a communist prior to being allowed to join. He went on to become head of the Law Society in 1979; as a lawyer, Rankin helped establish the province's legal aid system. In 1950 he was one of the founding members of a committee that created a list of lawyers who were willing to take on cases pro bono, preceding the establishment of the BC Legal Aid Society by 20 years. Rankin worked as a criminal lawyer and labour lawyer, he spent a significant amount of time working for First Nations clients, most notably in the much-publicised case of Fred Quilt. Rankin ran for office more than a dozen times before being elected to the Vancouver City Council in 1966 as the sole independent alderman on a council dominated by the conservative Non-Partisan Association. Vancouver's aldermen were elected through an "at large" system rather than by ward meaning voters from wealthier neighbourhoods were able to monopolise council elections and that only candidates who could afford a citywide campaign had a chance of being elected.

Rankin helped form the Committee of Progressive Electors as a left wing civic political party and it subsequently pushed for a ward-based electoral system to be introduced in Vancouver, culminating in a referendum in October 1973, at which the ward proposal was defeated. Rankin was a 20-year veteran of city council when he ran for mayor in 1986, losing to Gordon Campbell, he returned to city council as an alderman in the subsequent election and remained on the body until his retirement from politics in 1993. He died on February 26, 2002, from a heart attack, aged 81. Rankin's widow, Connie Fogal, is the former leader of the Canadian Action Party. Rankin's son, Phil Rankin, continues in his father's footsteps as a lawyer and advocate for legal aid, his grandson, Micah Rankin, is a law professor at Thompson Rivers University. His nephew, Lee Rankin is a lawyer and was a long-time councillor in Burnaby, British Columbia and was a federal Liberal candidate in 2000 and a BC Liberal candidate in the 2009 provincial election.

"Obituary: From gadfly to icon". Archived from the original on 2003-01-20. Retrieved 2011-11-17

List of awards and nominations received by Saoirse Ronan

Saoirse Ronan is an Irish and American actress who has received numerous awards and nominations. Ronan came to international prominence in 2007 with her co-starring role in Atonement, for which she received nominations for the Academy Award for Best Supporting Actress, the BAFTA Award for Best Actress in a Supporting Role, the Golden Globe Award for Best Supporting Actress, making her one of the youngest actresses to receive an Oscar nomination in this category. In 2015, Ronan starred in the romantic-drama film Brooklyn, for which she received nominations for the Academy Award for Best Actress, the BAFTA Award for Best Actress in a Leading Role, the Golden Globe Award for Best Actress – Motion Picture Drama, the Screen Actors Guild Award for Outstanding Performance by a Female Actor in a Leading Role. In 2017, Ronan was nominated yet again for the Academy Award for Best Actress, the BAFTA Award for Best Actress in a Leading Role, the Screen Actors Guild Award for Outstanding Performance by a Female Actor in a Leading Role, while winning the Golden Globe Award for Best Actress – Motion Picture Musical or Comedy, for her role in Lady Bird.

Two years yet again in 2019, Ronan was nominated yet again for the Academy Award for Best Actress, the BAFTA Award for Best Actress in a Leading Role, Golden Globe Award for Best Actress – Motion Picture Drama, for her role in Little Women. At 25 years and 6 months of age, Ronan is the 2nd youngest person to receive four Academy Award nominations, behind only Jennifer Lawrence; the Academy Awards are a set of awards given by the Academy of Motion Picture Arts and Sciences annually for excellence of cinematic achievements. The British Academy Film Award is an annual award show presented by the British Academy of Film and Television Arts; the Golden Globe Award is an accolade bestowed by the 93 members of the Hollywood Foreign Press Association recognizing excellence in film and television, both domestic and foreign. The Screen Actors Guild Awards are organized by the Screen Actors Guild‐American Federation of Television and Radio Artists. First awarded in 1995, the awards aim to recognize excellent achievements in television.

Awards for Saoirse Ronan on IMDb

Marcos Calero PĂ©rez

Marcos Calero Pérez known as Marcos is a Spanish professional footballer as a right back for CE Constància. Born in Palma, Balearic Islands, Marcos joined Villarreal CF's youth setup in 2007, aged 14. A forward, he was converted into a right back and, on 20 July 2012, moved to CD Atlético Baleares. In the 2012 summer, after making no senior appearances, Marcos joined Slovak 2. Liga club MFK Zemplín Michalovce, he was an undisputed starter for the club during the 2014–15 campaign, as his side achieved promotion to Super Liga. Marcos made his professional debut on 18 July 2015, starting in a 0–1 home loss against FK AS Trenčín. 2. Liga: 2014–15 Zemplín Michalovce official profile Futbalnet profile Marcos Calero at Soccerway

The Oakdale Affair and The Rider

The Oakdale Affair and The Rider is a collection of two short novels by American writers Edgar Rice Burroughs. "The Oakdale Affair", a contemporary tale, was written in 1917 under the working title of "Bridge and the Oskaloosa Kid", is a partial sequel to The Mucker, as Bridge, the protagonist, had been a secondary character in the earlier work. It was first published in Blue Book Magazine in March 1918. "The Rider", a Ruritanian romance, was written in 1915 and first published as "H. R. H; the Rider" as a serial in All-Story Weekly from December 14–18, 1918. The first book publication of the two stories brought them together in one volume as The Oakdale Affair and The Rider, issued by Edgar Rice Burroughs, Inc. in February 1937. Both works have since been published separately; the Oakdale Affair The Rider The copyrights for the stories in this collection have expired in the United States and thus now reside in the public domain there. Edgar Rice Burroughs Summary Project page for The Oakdale Affair Edgar Rice Burroughs Summary Project page for H.

R. H; the Rider ERB C. H. A. S. E. R ENCYCLOPEDIA entry for The Oakdale Affair ERB C. H. A. S. E. R ENCYCLOPEDIA entry for The Rider The text of The Oakdale Affair at