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Talk:Scaffolding

Lead picture
The lead picture is great BUT I can't actually see the scaffolding unless the picture in much, much bigger. The fancy way to deal with this would be an little inset that shows a small portion of the picture, magnified many times. Any photoshop skills out there? ike9898 14:17, 18 March 2006 (UTC)

scaffolding material
Steel scaffolding, Q235/Q345

Two-Types of Scaffolds
There are two types of scaffolding. Suspended and supported. Supported scaffolds are built and designed above their supporting structure (think pipe frame scaffold). Suspended scaffolds are built and designed below their supporting structure (think window washing scaffold). —Preceding unsigned comment added by 204.17.104.230 (talk) 20:18, 16 January 2008 (UTC)

There is not much detail on types of scaffold. There should be more detail included as far as frame scaffold, tube and clamp (including types of clamps used), and multipurpose utility (used to hang drywall type) scaffolding. Fsabelhaus (talk) 15:02, 22 September 2011 (UTC)

I don't think that the latter is really considered scaffolding 96.231.74.150 (talk) —Preceding comment was added at 02:41, 19 March 2008 (UTC)

swivel beam clamps
why is it so hard to find out about the swivel beam clamp. —Preceding unsigned comment added by 89.211.50.83 (talk) 06:46, 4 September 2008 (UTC)

Answer: You can contact Qingdao scaffolding: the biggest scaffolding coupler/clamps manufacturer and supplier in China, can supply swivel beam clamp. —Preceding unsigned comment added by 60.209.240.223 (talk) 15:17, 22 November 2010 (UTC)

scaffolding offshore
i would like to find out more about the scaffolding used offshore Insert non-formatted text here —Preceding unsigned comment added by 91.84.213.244 (talk) 08:03, 19 November 2008 (UTC)

Image copyright problem with File:Sphinx in 1925.jpg
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hanging scaffolding
trying to find any information about hanging scaffolds. not suspended scaffolding or swing stages, but hanging scaffolding that gets its support from beams. basically building from the top down using beam clamps. —Preceding unsigned comment added by 71.56.114.11 (talk) 21:46, 23 July 2010 (UTC)

Ancient Africans
"The ancient Africans have also used wooden scaffoldings to support mosques." --LOL...Mosques were not around during the "ancient" period. Islam let alone African adherents to Islam did not become widespread to well after 600AD. This is not "ancient." 99.55.175.41 (talk) 03:23, 3 January 2011 (UTC)

'poles'
As far as I'm aware, they are never known as poles in the trade, but tubes. I intend to replace the use of the word 'pole' with 'tube' where appropriate. Markb (talk) 11:25, 18 February 2011 (UTC)

 * Tubes weren't used before the 1920s, cross-skilled from 2" water pipes. Before that, bamboo would have been known as poles, and was still in use in the Royal Engineers in the 1960s.

Merger proposal
I propose that Bamboo scaffolding be merged into [Scaffolding]]. In the Scaffolding article, there is a Specialty scaffolding section, listing numerous types of scaffolding, none of which has it's own article, except for Bamboo. I see no reason why Bamboo scaffolding needs its own article, unless there is going to be an individual article written for each type of scaffolding. Sarr Cat ∑;3 01:25, 7 February 2015 (UTC)

Of course bamboo scaffolding should be merged into this main article on scaffolding. In Southeast Asia the question would lead to the response "What? You mean there are other types of scaffolding?" — Preceding unsigned comment added by R.d.noonan (talk • contribs) 04:02, 18 January 2016 (UTC)
 * Agreed and ✅

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Chemical "scaffolding"
The article Salvinorin A links to this page when discussing the possible use of Salvinorin as a "scaffold" for other drug syntheses. Should a section talking about molecular scaffolds be added, or made into its own article? Or the link to this page removed from the Salvinorin article.

Best, Ths17sbu21 (talk) 15:45, 31 January 2020 (UTC)

Bamboo scaffolding picture
I'm a rope-worker, that's not nylon rope, but nylon zip ties.

Mediaeval scaffolding
The common size of scaffolding indents in tower walls of the late mediaeval indicates a standardised support system, although full details are unknown.

Wiki Education assignment: Content Area Literacy
— Assignment last updated by Megamac1616 (talk) 19:40, 9 April 2023 (UTC)

Bamboo scaffolding connections
How are they made? · · · Peter Southwood (talk): 19:10, 7 June 2023 (UTC)

title: Talk:Scaffolding


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The Beverley Sisters

The Beverley Sisters were an English female close harmony traditional pop vocal and light entertainment trio, consisting of three sisters from London. They were eldest sister Joy (born Joycelyn Victoria Chinery, 5 May 1924 – 31 August 2015), and twins Teddie (born Hazel P. Chinery, 5 May 1927) and Babs (born Babette Patricia Chinery, 5 May 1927 – 28 October 2018). The sisters were each appointed MBE in 2006.

The Beverley Sisters were most popular during the 1950s and 1960s, and became well-known through their radio and television appearances. Their style was loosely modelled on that of their American counterparts, The Andrews Sisters. Their notable successes included the Irving Berlin-penned "Sisters" and the Christmas songs "I Saw Mommy Kissing Santa Claus", "Little Donkey", and "Little Drummer Boy", while in the United States they charted with a version of Greensleeves. They also toured the cabaret circuit, and were known for their matching outfits, which they wore both on- and off-stage.

Early lives
The sisters were born in Bethnal Green, London to Victoria Alice Miles and George Arthur Chinery (married 1916), who were known as the music hall act Coram and Mills, and are related to the Lupino acting and performing family. The eldest, Joy, was born on 5 May 1924; the twins, Babs and Teddie, were born on Joy's third birthday, 5 May 1927. They were evacuated to Northamptonshire during the Second World War and received secretarial training.

Career
During the Second War, the sisters auditioned successfully to take part in an advertising campaign for the malt drink Ovaltine. Jock Ware, photographer for the Ovaltine poster campaign encouraged them to audition for BBC Radio. They did so in November 1944, changing their name to the Beverley Sisters on the advice of BBC producer Cecil Madden, who became their manager. They met Glenn Miller who, shortly before his disappearance, offered them the opportunity to record with members of his orchestra.

They first appeared in radio programmes for the Allied Expeditionary Forces, recorded in Bedford, then followed up on BBC Radio's Variety Bandbox.

Immediately after the war they toured with Eric Winstone and his Orchestra, and began making regular appearances on the BBC's early television programmes. They also performed for NBC in the US with surviving members of the Glenn Miller Orchestra. After their return to Britain, promoter Val Parnell booked them to appear at the London Palladium with Gracie Fields; although Fields refused, without explanation, to appear with them.

The following year they performed with Danny Kaye. The BBC gave them their own television series, initially called Three Little Girls on View but later renamed as Those Beverley Sisters, which ran for seven years and on which they gave live performances of popular songs of the day.

In 1951, they signed a recording deal with the UK Columbia record label, later moving to the Philips and Decca labels before returning to Columbia in 1960. Their biggest hits on the UK singles chart were versions of "I Saw Mommy Kissing Santa Claus" (no.6, 1953) and "Little Drummer Boy" (no.6, 1959), which were both Christmas hits. The Beverley Sisters appeared as themselves in the 1954 British film musical Harmony Lane directed by Lewis Gilbert and were Record Mirror "cover stars" for the 12 February 1955 issue.

In 1956, their version of the traditional song "Greensleeves", orchestrated by Roland Shaw, became their only US chart hit, reaching no.41 on the Billboard pop chart. Generally preferring live cabaret and television appearances over recording work, the song "Sisters", written by Irving Berlin and originally recorded in 1954 by Rosemary Clooney and her sister Betty, became their theme song; it has been claimed that Berlin wrote the song for the Beverley Sisters.

The sisters are widely credited as having been the highest paid female entertainers in the UK for more than 20 years. In 1952, 1958 and 1978, they appeared at the Royal Variety Performance. In January 1961, they appeared on the radio show, Desert Island Discs. They appeared on the television show Stars on Sunday. They were the subjects of This Is Your Life in 1969 when they were surprised by Eamonn Andrews. They also appeared in 1977 on the BBC TV's long running variety show The Good Old Days.

Their career was revitalised in the 1980s, after their children – who had begun performing together as the Foxes – invited them onstage at the London Hippodrome, encouraged by club owner Peter Stringfellow. A review in The Stage in March 1985 described the Sisters when appearing in Stringfellow's Hippodrome cabaret as "clad in shimmering pink" and said they had "acquired a glamour and universality that only time and experience can produce". The sisters began performing again for British troops, as well as in gay clubs in Britain, and they produced a new album, Sparkle. The Beverley Sisters drew comparison with the Spice Girls in the late 1990s, especially with regard to the marriages of Joy to England footballer Billy Wright and Posh Spice, Victoria to David Beckham.

They performed as part of the Queen's Golden Jubilee celebrations in 2002, and toured with Max Bygraves that year, the 50th anniversary of their appearance at the Royal Variety Performance. They also took part in the D-Day 60th anniversary memorial concerts in 2004.

They entered the Guinness World Records in 2002, as the world's longest surviving vocal group without a change in the original line up. As late as 2009, the sisters appeared in concerts and matinee shows in the United Kingdom. They forged links with the Burma Star Association, as well as McCarthy & Stone, where the sisters were invited to open each new housing development designed specifically for retired people. They later fully retired and lived near each other in Barnet.

Personal lives and honours
After a brief early marriage to American musician Roger Carocari (who adopted the surname Carey), later dissolved, Joy married the Wolverhampton Wanderers and England football captain Billy Wright on 28 July 1958 at Poole Register Office, a year before he retired as a player. They were married for 36 years until Wright died of cancer in September 1994. Joy died on 31 August 2015 at the age of 91.

Babs married Scottish dentist James Mitchell in 1963 but the marriage did not last. She suffered a cut forehead and shock when a passenger in a car accident in North Harrow on Boxing Day 1967 and was confined to a Harley Street Nursing Home for at least three weeks. Babs died on 28 October 2018, also at the age of 91, leaving no children.

Teddie was engaged to Alyn Ainsworth, but married the British waterskiing champion Peter Felix. She is the last surviving sister.

In the 2006 New Year Honours list the sisters were each appointed an MBE.

Discography
Robert Tredinnick, in the Gramophone Notes column of The Tatler in January 1952, opined the Beverleys were the best sister act on gramophone since the Boswell Sisters in the early 1930s and "have the gift of making their personalities apparent to an unseeing audience".

Albums

 * A Date with the Bevs (Philips, 1955)
 * The Enchanting Beverley Sisters (Columbia, 1960)
 * Those Beverley Sisters (Decca, 1960)
 * The World of the Beverley Sisters (Decca, 1961)
 * Together (EMI, 1985)
 * Sparkle (K-Tel, 1985)
 * Sisters, Sisters: An Evening with the Beverley Sisters (Pickwick, 1993)
 * Bless 'Em All (Pickwick, 1995)

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

title: The Beverley Sisters


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Bertil Ohlin

Bertil Gotthard Ohlin (23 April 1899 – 3 August 1979) was a Swedish economist and politician. He was a professor of economics at the Stockholm School of Economics from 1929 to 1965. He was also leader of the People's Party, a social-liberal party which at the time was the largest party in opposition to the governing Social Democratic Party, from 1944 to 1967. He served briefly as Minister of Commerce and Industry from 1944 to 1945 in the Swedish coalition government during World War II. He was President of the Nordic Council in 1959 and 1964.

Ohlin's name lives on in one of the standard mathematical models of international free trade, the Heckscher–Ohlin model, which he developed together with Eli Heckscher. He was jointly awarded the Nobel Memorial Prize in Economic Sciences in 1977 together with the British economist James Meade "for their pathbreaking contribution to the theory of international trade and international capital movements".

Biography
Bertil Ohlin was raised in Klippan, Scania with seven siblings, where his father Elis was a civil servant and bailiff. His mother Ingeborg influenced him with her left-liberal views on the society, with Nordic partnership and Karl Staaff as her role model. He received his B.A. from Lund University 1917 at the age of 18 and his MSc. from Stockholm School of Economics in 1919.

He obtained an M.A. from Harvard University in 1923 and his doctorate from Stockholm University a year after in 1924 at the age of 25. In 1925, he became a professor at the University of Copenhagen. In 1929, he debated with John Maynard Keynes and contradicted the latter's view on the consequences of the heavy war reparations payments imposed on Germany. (Keynes predicted a war caused by the burden of debt, but Ohlin thought that Germany could afford the reparations.) The debate was important in the modern theory of unilateral international payments. In 1930, Ohlin succeeded Eli Heckscher, his teacher, as a professor of economics, at the Stockholm School of Economics.

In 1937, Ohlin spent half a year at the University of California, Berkeley, as a visiting professor. He also worked as an outside expert for the Economic and Financial Organization of the League of Nations, together with Oskar Morgenstern and Jacques Rueff, supporting the EFO's work on economic depressions in the late 1930s.

Ohlin was party leader of the liberal Liberal People's Party from 1944 to 1967, the main opposition party to the Social Democrat Governments of the era, and from 1944 to 1945 was Minister of Commerce and Industry in the wartime government. His daughter Anne Wibble, representing the same party, served as Minister for Finance from 1991 to 1994.

Heckscher–Ohlin theorem
In 1933, Ohlin published a work that made him world-renowned, Interregional and International Trade. Ohlin built in it an economic theory of international trade from earlier work by Heckscher and his own doctoral thesis. It is now known as the Heckscher–Ohlin model, one of the standard model economists use to debate trade theory.

The model was a breakthrough because it showed how comparative advantage might relate to general features of a country's capital and labor, and how those features might change through time. The model provided a basis for later work on the effects of protection on real wages, and has been fruitful in producing predictions and analysis; Ohlin himself used the model to derive the Heckscher–Ohlin theorem, which predicts that capital-abundant countries export capital-intensive goods, while labor-abundant countries export the labor-intensive goods.

The Heckscher–Ohlin Theorem, which is concluded from the Heckscher–Ohlin model of international trade, states: trade between countries is in proportion to their relative amounts of capital and labor. In countries with an abundance of capital, wage rates tend to be high; therefore, labor-intensive products, e.g. textiles, simple electronics, etc., are more costly to produce internally. In contrast, capital-intensive products, e.g. automobiles, chemicals, etc., are less costly to produce internally. Countries with large amounts of capital will export capital-intensive products and import labor-intensive products with the proceeds. Countries with high amounts of labor will do the reverse.

The following conditions must be true:
 * The major factors of production, namely labor and capital, are not available in the same proportion in both countries.
 * The two goods produced either require more capital or more labor.
 * Labor and capital do not move between the two countries.
 * There are no costs associated with transporting the goods between countries.
 * The citizens of the two trading countries have the same needs.

The theory does not depend on total amounts of capital or labor, but on the amounts per worker. This allows small countries to trade with large countries by specializing in production of products that use the factors which are more available than its trading partner. The key assumption is that capital and labor are not available in the same proportions in the two countries. That leads to specialization, which in turn benefits the country's economic welfare. The greater the difference between the two countries, the greater the gain from specialization.

Wassily Leontief made a study of the theory that seemed to invalidate it. He noted that the United States had a lot of capital; therefore, it should export capital-intensive products and import labor-intensive products. Instead, he found that it exported products that used more labor than the products it imported. This finding is known as the Leontief paradox.

Awards and decorations

 * Order of the Polar Star - Ribbon bar, pre 1975.svg 🇸🇪 Commander Grand Cross of the Order of the Polar Star (4 June 1965)

Significant publications

 * The German Reparations Problem, 1930
 * The Cause and Phases of the World Economic Depression. Report presented to the Assembly of the League of Nations Geneva: Secretariat of the League of Nations; 1931.
 * Interregional and International Trade, 1933
 * Mechanisms and Objectives of Exchange Controls, 1937

title: Bertil Ohlin


text:
Nobel

Nobel often refers to:

 * Nobel Prize, awarded annually since 1901, from the bequest of Swedish inventor Alfred Nobel
 * The Nobel family, a prominent Swedish and Russian family; see there for the list of people with the surname

Nobel may also refer to:

Places

 * Nobel (crater), a crater on the far side of the Moon.
 * Nobel, Ontario, a village located in Ontario, Canada.
 * Nobel Square, public square in Cape Town, South Africa
 * Nobel Lake,Ukraine
 * Nobel, Rivne Oblast, village in Ukraine

Other uses

 * 6032 Nobel, a main-belt asteroid
 * Nobel (automobile) a licence-built version of the German Fuldamobil, manufactured in the UK and Chile
 * Nobel (TV series), a Norwegian television series about the country's military involvement in Afghanistan
 * Nobel (typeface), a geometric, sans-serif typeface.
 * The Nobel School, a secondary school in Stevenage, England.
 * Nobel (crater), Moon
 * Nobel Vega, Cuban actor

title: Nobel


text:
Norris McWhirter

Norris Dewar McWhirter (12 August 1925 – 19 April 2004) was a British writer, political activist, co-founder of The Freedom Association, and a television presenter. He and his twin brother Ross were known internationally for founding the reference book The Guinness Book of Records (known since 2000 as Guinness World Records) which they wrote and updated annually together between 1955 and 1975. After Ross's assassination by the Provisional Irish Republican Army (IRA), Norris carried on alone as editor.

Early life
Norris and Ross were the twin sons of William McWhirter, the editor of the Sunday Pictorial, and Margaret Williamson. In 1929, as William was working on the founding of the Northcliffe Newspapers chain of provincial newspapers, the family moved to Broad Walk, Winchmore Hill. Like their elder brother, Kennedy (born 1923), Norris and Ross were educated at Marlborough College and Trinity College, Oxford. Norris chose to complete his law degree in two years rather than the usual three. Between 1943 and 1946, Norris served as a sub-lieutenant with the Royal Naval Volunteer Reserve on escort duty in Atlantic and on board a minesweeper in the Pacific.

Sport
McWhirter was an excellent athlete. He recorded a time of 10.7s for the 100 metres whilst a student and later represented Scotland. He and his brother became sports journalists in 1950. In 1951, they published Get to Your Marks and that year they founded an agency to provide facts and figures to Fleet Street, setting out, in Norris McWhirter's words: "to supply facts and figures to newspapers, yearbooks, encyclopedias, and advertisers". At the same time, he became a founding member of the Association of Track and Field Statisticians.

McWhirter came to public attention while working for the BBC as a sports commentator. On 6 May 1954, he kept the time when Roger Bannister ran the first sub four-minute mile. After the race, he began his announcement:

"As a result of Event Four, the one mile, the winner was R. G. Bannister of Exeter and Merton colleges, in a time which, subject to ratification, is a track record, an English native record, a United Kingdom record, a European record, in a time of three minutes..."

at which the rest of McWhirter's announcement was drowned out in the enthusiastic uproar.

One of the athletes covered was runner Christopher Chataway, the employee at Guinness who recommended them to Sir Hugh Beaver. After an interview in which the Guinness directors enjoyed testing the twins' knowledge of records and unusual facts, the brothers agreed to start work on the book that became The Guinness Book of Records in 1954. In August 1955, the first slim green volume – 198 pages long – was at the bookstalls, and in four more months it was Britain's No. 1 nonfiction best-seller.

In 1954, the McWhirter brothers sued Daily Mail sports writer J. L. Manning for his critical piece about non-journalist (i.e. not members of the National Union of Journalists) sports writers. The McWhirters were awarded £300 in damages.

McWhirter was also part of the BBC commentary team for their Olympic Games coverage between 1960 and 1976.

Political activity
He was an active member of the Conservative Party in the early 1960s and fought, unsuccessfully, to recapture Orpington in the 1964 and 1966 UK general elections after its loss to the Liberals in the 1962 by-election.

His brother, Ross, was a critic of British government policy in Northern Ireland, and called for a "tougher" response by the Army against Irish republicans. Ross was shot dead by the Provisional IRA in 1975 at his home in Middlesex after offering a reward for information leading to the apprehension of those carrying out a bombing campaign in London at the time. Following Ross's murder, Norris co-founded the right-wing political organisation the National Association for Freedom (now The Freedom Association) in 1975. This organisation initiated legal challenges against the trade union movement in the UK, Campaign for Nuclear Disarmament (CND) and the European Economic Community (EEC) in Brussels. The organisation states that the work it undertakes falls within the following Eight Principles of a Free Society: Individual Freedom, Personal & Family Responsibility, The Rule of Law, Limited Government, Free Market Economy, National Parliamentary Democracy, Strong National Defences and a Free Press and Other Media. It continues its political activities to this day.

Norris was on the committee of the Free Czechoslovakia Campaign, founded by exiled Czech journalist Josef Josten in 1968 in response to the Soviet invasion of Czechoslovakia. Josten was referred to obliquely in the last two pages of his book Ross (see Bibliography below). Norris was also a member of the Secretariat of the anti-communist European Freedom Campaign, established in London at an Inaugural Rally at Westminster Central Hall on 10 December 1988.

Record Breakers
Both brothers were regulars on the BBC show Record Breakers. They were noted for their exceptional memory, enabling them to provide detailed answers to any questions from the audience about entries in the Guinness Book of Records.

After Ross's death, Norris continued to appear on the show, eventually making him one of the most recognisable people on children's television in the 1970s and 1980s. McWhirter was appointed a Commander of the Order of the British Empire in the 1980 New Year Honours.

Personal life and death
In 1957, McWhirter married Carole Eckert, who died in 1987; they had a son and a daughter. In 1990, he married his secretary, Tessa von Weichardt.

He retired from The Guinness Book of Records in 1985, though he continued in an advisory role until 1996. He continued to write, editing a new reference book, Norris McWhirter's Book of Millennium Records, in 1999.

In 1985, he launched an unsuccessful defamation case against the Independent Broadcasting Authority for the TV programme Spitting Image, which had inserted a subliminal image of McWhirter's face imposed on the body of a naked woman.

McWhirter died from a heart attack at his home in Kington Langley, Wiltshire, on 19 April 2004, aged 78. His memorial service – attended by, among others, Margaret Thatcher, John Gouriet, Jeremy Beadle, Christopher Gill (who read The Lesson), Jeffrey Archer, Gregory Lauder-Frost and Sir Roger Bannister (who read an appreciation) – was held in St Martin-in-the-Fields, Trafalgar Square, London, on 7 October 2004. He was interred at St Peter's Church, Kington Langley.

Selected bibliography

 * Sports and general encyclopaedia

 * Dunlop Illustrated Encyclopedia of Facts This later became the "Guinness Book of Answers"
 * Get To Your Marks (1951, with Ross McWhirter)
 * Guinness Book of Records (1955–1975, with Ross McWhirter)
 * Guinness Book of Records (1976–1985)
 * Guinness Sports Record Book (1977–1978)
 * Book of Millennium Records ISBN 1-85227-805-6

 * Personal

 * Ross: The Story of a Shared Life ISBN 0-902782-23-1
 * Winchmore Hill Lives S Delvin (1991) (Contributor) ISBN 0-7212-0896-7

 * Political

 * Treason at Maastricht (1994, with Rodney Atkinson, contributions by Daniel Hannan) – criticism of the Treaty of Maastricht and the Bilderberg Group
 *  Ross Was Right – The McWhirter File  (Covenant Pub., 29 Sep 2014) ISBN 978-085205-118-4

title: Norris McWhirter


text:
George Akerlof

George Arthur Akerlof (born June 17, 1940) is an American economist and a university professor at the McCourt School of Public Policy at Georgetown University and Koshland Professor of Economics Emeritus at the University of California, Berkeley. Akerlof was awarded the 2001 Nobel Memorial Prize in Economic Sciences, jointly with Michael Spence and Joseph Stiglitz, "for their analyses of markets with asymmetric information." He is the husband of United States Secretary of the Treasury Janet Yellen.

Early life and education
Akerlof was born in New Haven, Connecticut, on June 17, 1940, into a Jewish family. His mother was Rosalie Clara Grubber (née Hirschfelder), a housewife of German Jewish descent, and his father was Gösta Carl Åkerlöf, a chemist and inventor, who was a Swedish immigrant. George has an older brother, Carl, a physics professor at the University of Michigan. Akerlof attended Princeton Day School, before he graduated from the Lawrenceville School in 1958. He received a bachelor's in economics from Yale University in 1962, and earned his PhD in economics from Massachusetts Institute of Technology (MIT) in 1966. His dissertation was titled Wages and Capital under the supervision of Robert Solow, a noted economist who would later receive the Nobel Memorial Prize.

Academic career
After receiving his doctorate, Akerlof joined the faculty of the University of California, Berkeley, as an assistant professor of economics, although he taught for only one year before moving to India. In 1967, he spent some time as a visiting professor at the Indian Statistical Institute (ISI) in New Delhi and returned to the United States in September 1968. Akerlof then became an associate professor at Berkeley and voted for a tenure-track position at the university. He also served as a senior economist at the White House Council of Economic Advisers (CEA) from 1973 to 1974. In 1977, Akerlof spent a year as a visiting research economist for the Federal Reserve Board of Governors in Washington, D.C. where he met his future wife and coauthor, Janet Yellen. After that he hoped to be promoted to full professorship, however, Berkeley's department of economics failed to appoint him. Akerlof and Yellen then moved to the London School of Economics (LSE) in 1978, where he accepted a prestigious post as the Cassel Professor of Money and Banking, while she accepted a tenure-track lectureship. They remained in the United Kingdom for two years before returning to the United States.

In 1980, Akerlof becomes Goldman Professor of Economics at Berkeley and taught there for most of his career. In 1997, he took a leave of absence from Berkeley to accompany his wife when she was named chair of the Council of Economic Advisers (CEA). At Washington, Akerlof began working for the Brookings Institution as a senior fellow. They both returned to teaching at UC Berkeley in 1999. Akerlof remained an active faculty member at the university until his retirement. He was awarded Koshland Professor of Economics Emeritus in 2010. After that, he once again moved to Washington when Yellen confirmed to the Federal Reserve Board. Akerlof received a position as visiting scholar at the International Monetary Fund (IMF) from 2010 to 2014 and joined the McCourt School of Public Policy at Georgetown University as a university professor in 2014.

"The Market for Lemons" and asymmetric information
Akerlof is perhaps best known for his article, "The Market for Lemons: Quality Uncertainty and the Market Mechanism", published in the Quarterly Journal of Economics in 1970, in which he identified certain severe problems that afflict markets characterized by asymmetric information, the paper for which he was awarded the Nobel Memorial Prize. In Efficiency Wage Models of the Labor Market, Akerlof and coauthor/wife, Janet Yellen propose rationales for the efficiency wage hypothesis in which employers pay above the market-clearing wage, in contradiction to the conclusions of neoclassical economics. This work introduced gift-exchange game to economics.

Identity economics
Akerlof and collaborator Rachel Kranton of Duke University have introduced social identity into formal economic analysis, creating the field of identity economics. Drawing on social psychology and many fields outside of economics, Akerlof and Kranton argue that individuals do not have preferences only over different goods and services. They also adhere to social norms for how different people should behave. The norms are linked to a person's social identities. These ideas first appeared in their article "Economics and Identity", published in the Quarterly Journal of Economics in 2000.

Reproductive technology shock
In the late 1970s, Akerlof's ideas attracted the attention of some on both sides of the debate over legal abortion. In articles appearing in The Quarterly Journal of Economics, The Economic Journal, and other forums, Akerlof described a phenomenon that he labeled "reproductive technology shock." He contended that the new technologies that had helped to spawn the late twentieth century sexual revolution, modern contraceptives and legal abortion, had not only failed to suppress the incidence of out-of-wedlock childbearing but also had actually worked to increase it. According to Akerlof, for women who did not use them, these technologies had largely transformed the old paradigm of socio-sexual assumptions, expectations, and behaviors in ways that were especially disadvantageous. For example, the availability of legal abortion now allowed men to view their offspring as the deliberate product of female choice rather than as the joint product of sexual intercourse. Thus, it encouraged biological fathers to reject not only the notion of an obligation to marry the mother but also the idea of a paternal obligation.

While Akerlof did not recommend legal restrictions on either abortion or the availability of contraceptives his analysis seemed to lend support to those who did. Thus, a scholar strongly associated with liberal and Democratic-leaning policy positions has been approvingly cited by conservative and Republican-leaning analysts and commentators.

Looting
In 1993 Akerlof and Paul Romer published "Looting: The Economic Underworld of Bankruptcy for Profit", describing how under certain conditions, owners of corporations will decide it is more profitable for them personally to 'loot' the company and 'extract value' from it instead of trying to make it grow and prosper. For example:

"Bankruptcy for profit will occur if poor accounting, lax regulation, or low penalties for abuse give owners an incentive to pay themselves more than their firms are worth and then default on their debt obligations. Bankruptcy for profit occurs most commonly when a government guarantees a firm's debt obligations."

Norms and macroeconomics
In his 2007 presidential address to the American Economic Association, Akerlof proposed natural norms that decision makers have for how they should behave, and showed how such norms can explain discrepancies between theory and observed facts about the macroeconomy. Akerlof proposed a new agenda for macroeconomics, using social norms to explain macroeconomic behavior. He is considered together with Gary Becker as one of the founders of social economics.

He is a trustee of Economists for Peace and Security and co-director of the Social Interactions, Identity and Well-Being Program at the Canadian Institute for Advanced Research (CIFAR). He is on the advisory board of the Institute for New Economic Thinking. He was elected a fellow of the American Academy of Arts and Sciences in 1985.

Personal life
Akerlof was briefly married to an architect, Kay Leong; they wed in 1974 and divorced three years later, after he didn’t get promoted to a full professorship at Berkeley. Following their divorce, Kay moved to New York and remarried a fellow architect. In 1978, Akerlof married Janet Yellen, an economist who is the current United States Secretary of the Treasury and former chair of the Federal Reserve, as well as a professor emeritus at Berkeley's Haas School of Business. They have one child, a son named Robert, who was born in 1981. Robert Akerlof is also an economist, earned a bachelor's degree in economics and mathematics from Yale University and obtained his PhD in economics from Harvard University, currently working as an associate professor of economics at the University of Warwick.

Akerlof was one of the signees of a 2018 amici curiae brief that expressed support for Harvard in the Students for Fair Admissions v. President and Fellows of Harvard College lawsuit. Other signees of the brief include Alan B. Krueger, Cecilia E. Rouse, Robert M. Solow, Janet L. Yellen, as well as numerous others.

Official

 * George A. Akerlof at Georgetown University
 * George A. Akerlof at University of California, Berkeley
 * including the Nobel Prize Lecture December 8, 2001 Behavioral Macroeconomics and Macroeconomic Behavior
 * Identity Economics

Other

 * Biography at Encyclopædia Britannica
 * Profile and Papers at Research Papers in Economics/RePEc
 * Articles
 * Akerlof's criticism of Bush, February 12, 2003
 * Akerlof slams Bush government, July 29, 2003
 * Akerlof slams Bush government, July 29, 2003

title: George Akerlof


text:
Ross McWhirter

Alan Ross McWhirter (12 August 1925 – 27 November 1975) was, with his twin brother, Norris, the cofounder of the 1955 Guinness Book of Records (known since 2000 as Guinness World Records) and a contributor to the television programme Record Breakers. He was assassinated by the Provisional Irish Republican Army (IRA) in 1975.

Early life
McWhirter was the youngest son of William McWhirter, editor of the Sunday Pictorial, and Margaret "Bunty" Williamson. He was born at 10 Branscombe Gardens, Winchmore Hill, in London. In 1929, as William was working on the founding of the Northcliffe Newspapers Group chain of provincial newspapers, the family moved to Aberfoyle, in Broad Walk, Winchmore Hill. Ross McWhirter was educated at Chesterton School, Seaford, Marlborough College and Trinity College, Oxford.

Between 1943 and 1946, Ross served as a sub-lieutenant with the Royal Naval Volunteer Reserve aboard a minesweeper in the Mediterranean. McWhirter maintained his home and Guinness Publishing business in the Middlesex area as it became the Municipal Borough of Edmonton, then London Borough of Enfield, and finally as part of Greater London in 1965.

Career
Ross and Norris both became sports journalists in 1950. In 1951, they published Get to Your Marks, and earlier that year they had founded an agency to provide facts and figures to Fleet Street, endeavouring "to supply facts and figures to newspapers, yearbooks, encyclopaedias and advertisers."

While building their business, they both worked as sports journalists. They knew and covered runner Christopher Chataway, a Guinness employee who recommended them to Hugh Beaver. After an interview in 1954 in which the Guinness directors enjoyed testing the twins' knowledge of records and unusual facts, the brothers agreed to start work on the book that would become The Guinness Book of Records. In August 1955, the first slim green volume, 198 pages long, appeared at bookstalls, and within four more months it had become the UK's number one nonfiction bestseller. Both brothers were regulars on the BBC show Record Breakers. They were noted for their encyclopedic memories, enabling them to provide detailed answers to questions from the audience about entries in The Guinness Book of Records. Norris continued to appear on the programme after Ross's death.

In 1958, long after the legend of William Webb Ellis as the originator of rugby had become engrained in rugby culture, Ross managed to rediscover Ellis's grave in a cemetery in Menton in Alpes Maritimes (it has since been renovated by the French Rugby Federation).

In 1965, Ross and Norris were guests on the American panel game show I've Got a Secret, where they exhibited their memorisation of the Guinness Book of Records.

Politics
In the early 1960s, McWhirter was a Conservative Party activist and unsuccessfully fought the seat of Edmonton in the 1964 general election. Following his killing, his brother and others founded the National Association for Freedom (later the Freedom Association).

His views have been described as "right-wing".

Ireland
McWhirter advocated and lobbied for various restrictions on the freedom of the Irish community in Britain, such as compulsory registration with the local police and a requirement for signed photographs when renting flats or booking hotel rooms. In 1975, McWhirter offered a £50,000 reward for information leading to a conviction for several recent high-profile bombings in England that were publicly claimed by the Provisional Irish Republican Army (IRA). In doing so, McWhirter recognised that he could then be a target himself. This was described as a bounty by McWhirter, and considered a bounty by the IRA Army Council, a view that led directly to the events that followed. However, the idea was not originally his but that of John Gouriet.

Capital punishment
McWhirter advocated capital punishment for terrorism offences. During a press conference on 4 November 1975, he proposed that terrorism be classified as treason and as a result carry the death penalty.

Alleged links to British intelligence
In his 1981 book, former counterterrorism operative Gordon Winter of the South African Bureau of State Security recalled a briefing with his London-based handler Alf Bouwer warning him to be wary of McWhirter, who he claimed was a British intelligence operative and member of the right-wing, anti-immigration Society for Individual Freedom, which he described as a "front" for "disseminating Establishment-type propaganda."

Assassination
On 27 November 1975 at 6:45 p.m., McWhirter was shot and killed by Provisional IRA Volunteers Harry Duggan and Hugh Doherty, members of the Active Service Unit (ASU), later dubbed the Balcombe Street Gang, for whose capture McWhirter had offered a reward. McWhirter was shot at close range in the head and chest with a .357 Magnum revolver outside his home in Village Road, Bush Hill Park. He was taken to Chase Farm Hospital but died soon after being admitted. Duggan and Doherty were apprehended following the Balcombe Street siege and charged with murdering McWhirter in addition to nine other victims. They were sentenced to life imprisonment in 1977 but released in 1999 under the terms of the Good Friday Agreement.

Selected bibliography
Sports and general encyclopædia
 * Get to Your Marks (1951, with Norris McWhirter)
 * The Guinness Book of Records (1955–1975, with Norris McWhirter)
 * Ross: The Story of a Shared Life (Norris McWhirter) ISBN 0-902782-23-1,
 * Ross Was Right – The McWhirter File (Covenant Pub., 29 September 2014) ISBN 978-085205-118-4,

title: Ross McWhirter


text:
Kleve (district)

Kleve (Cleves in English use) or Kreis Kleve is a Kreis (local-government district) in the Lower Rhine region of northwestern North Rhine-Westphalia, Germany. Neighbouring districts are Borken, Wesel, and Viersen in Germany, and the Dutch provinces of Limburg and Gelderland.

History
The district in its current borders was created in 1975 when the former district of Kleve and Geldern was merged with the Rees District towns of Emmerich and Rees and the Moers District municipality of Rheurdt.

The two precursor districts had been created in 1816 when the whole of the Rhineland became a province of Prussia. Territorially they corresponded roughly to the historic Duchies of Cleves and Guelders.

Geography
The district is located in the lower valley of the Rhine, in the region where that river flows into the Netherlands.

Coat of arms
The coat of arms, which was granted in 1983, combines the shields of the two constituent duchies.

The dexter side depicts the emblem of the dukes of Cleves: On a red (gules) field a white (argent) escutcheon (shield shape) with an eightfold fleur-de-lys (escarbuncle/metal shield reinforcement). The sinister side shows a golden (or) lion (in rampant position) on a blue (azure) field (background): the emblem of the dukes of Geldern.

title: Kleve (district)


text:
List of monarchs of Liechtenstein

There have been 16 monarchs of the Principality of Liechtenstein since 1608. The current Prince of Liechtenstein is Hans-Adam II, since 13 November 1989. The current Hereditary Prince and Regent of Liechtenstein is Alois, since 15 August 2004.

Family tree
The names in bold signify official reigning monarchs of Liechtenstein.

title: List of monarchs of Liechtenstein


text:
Aristide Briand

Aristide Pierre Henri Briand (28 March 1862 – 7 March 1932) was a French statesman who served eleven terms as Prime Minister of France during the French Third Republic. He is mainly remembered for his focus on international issues and reconciliation politics during the interwar period (1918–1939).

In 1926, he received the Nobel Peace Prize along with German Foreign Minister Gustav Stresemann for the realization of the Locarno Treaties, which aimed at reconciliation between France and Germany after the First World War. To avoid another worldwide conflict, he was instrumental in the agreement known as the Kellogg–Briand Pact of 1928, as well to establish a "European Union" in 1929. However, all his efforts were compromised by the rise of nationalistic and revanchist ideas like Nazism and fascism following the Great Depression.

Early life
He was born in Nantes, Loire-Inférieure (now Loire-Atlantique) of a petit bourgeois family. He attended the Nantes Lycée, where, in 1877, he developed a close friendship with Jules Verne. He studied law at the Faculty of Law of Paris, and soon went into politics, associating himself with the most advanced movements, writing articles for the syndicalist journal Le Peuple, and directing the Lanterne for some time. From this he passed to the Petite République, leaving it to found L'Humanité, in collaboration with Jean Jaurès.

Activism
At the same time he was prominent in the movement for the formation of trade unions, and at the congress of workers at Nantes in 1894, he secured the adoption of the labor union idea against the adherents of Jules Guesde. From that time, Briand was one of the leaders of the French Socialist Party. In 1902, after several unsuccessful attempts, he was elected deputy. He declared himself a strong partisan of the union of the left in what was known as the Bloc, to check the reactionary deputies of the right.

From the beginning of his career in the Chamber of Deputies, Briand was occupied with the question of the separation of church and state. He was appointed the reporter of the commission charged with the preparation of the 1905 law on separation, and his report at once marked him out as one of the coming leaders. He succeeded in carrying his project through with but slight modifications, and without dividing the parties upon whose support he relied.

He was the principal author of the law of separation, but, not content with preparing it; he wished to apply it as well. The ministry of Maurice Rouvier was allowing disturbances during the taking of inventories of church property, a clause of the law for which Briand was not responsible. Consequently, he accepted the portfolio of Public Instruction and Worship in the Sarrien ministry (1906). So far as the chamber was concerned, his success was complete. But the acceptance of a position in a bourgeois ministry led to his exclusion from the Unified Socialist Party (March 1906). As opposed to Jaurès, he contended that the Socialists should co-operate actively with the Radicals in all matters of reform, and not stand aloof to await the complete fulfillment of their ideals. He himself was atheist.

He became a freemason in the lodge Le Trait d'Union in July 1887 while the lodge did not record his name in spite of his repeated requests. Le Trait d'Union Orient de Saint-Nazaire lodge had declared him "unworthy of belonging to the great masonic family on 6 September 1889". In 1895 he joined the lodge Les Chevaliers du Travail that was established in 1893.

Pre-war
Briand served as Minister of Justice under Clemenceau in 1908–9, before succeeding Clemenceau as Prime Minister on 24 July 1909, serving until 2 March 1911. In social policy, Briand's first ministry was notable for the passage of a bill in April 1910 for workers' and farmers' pensions. That same year, compulsory sickness and old-age insurance was introduced for 8 million rural and urban workers. However, a law court decision in 1912 that questioned the legality of compulsion "enabled a large proportion of employers and workers to evade the law."

Briand again served as Minister of Justice 1912-13 under the premiership of the rightwinger Raymond Poincaré (soon to become president of the Republic), before again becoming Prime Minister for a few months from 21 January 1913 until 22 March 1913.

1914–15
At the end of August 1914, following the outbreak of the First World War, Briand again became Minister of Justice when René Viviani reconstructed his ministry. In the winter of 1914–15 Briand was one of those who pushed for an expedition to Salonika, in the hope of helping Serbia, and perhaps bringing Greece, Romania, Bulgaria and Italy into the war as a pro-French bloc, which would also act as a barrier to future Russian expansion in the Balkans. He got on well with Lloyd George, who was also, contrary to military advice, keen for operations in the Balkans, and had a long talk with him on 4 February 1915. Briand was the main mover in persuading Maurice Sarrail to accept the Salonika command in August 1915.

In October 1915 following an unsuccessful French offensive and the entry of Bulgaria, Briand again became Prime Minister (29 October 1915), succeeding René Viviani. He also became Foreign Minister for the first time, a post held by Théophile Delcassé until the final weeks of the previous government. He was also pledged to "unité de front", not just between the military and Parliament but also closer links with the other Allies, a pledge met with "prolonged, thunderous applause" by the deputies.

Draft proposals for Allied cooperation, prepared by Lord Esher and Maurice Hankey were on the table by the time British Prime Minister H. H. Asquith visited Paris on 17 November (mainly to discuss Greece, and only his second wartime talks with France; the first had been with Viviani in July 1915).

The opening weeks of Briand's ministry required him to broker an agreement between General Gallieni, the new War Minister, and General Joffre, newly (2 December) promoted to "Commander-in-Chief of the French Armies" (generalissimo) over all theatres apart from North Africa.

1916
In the poisonous atmosphere after the opening of the German attack at Verdun (21 February 1916), Gallieni read an angry report at the Council of Ministers on 7 March criticising Joffre's conduct of operations over the last eighteen months and demanding ministerial control, then resigned. He was falsely suspected of wanting to launch a military takeover of the government. Briand knew that publication of the report would damage morale and might bring down the government. Gallieni was persuaded to remain in office until a replacement had been agreed. General Roques was appointed after it had been ensured that Joffre had no objections.

The first formal Allied conference met in Paris on 26 March 1916 (Italy did not participate) but initially made little impact, perhaps because Briand had vetoed the British suggestion of a permanent secretariat, or perhaps because there had been three informal sets of Anglo-French talks in the last quarter of 1915, one of which, the Chantilly meeting, had already seen strategy plans drawn up.

Late in March 1916 Joffre and Briand blocked the withdrawal of five British divisions from Salonika. Briand was widely suspected of wanting to make his mistress Princess George of Greece, who was born a Bonaparte. In the spring of 1916 Briand urged Sarrail to take the offensive in the Balkans to take some of the heat off Verdun, although the British, preoccupied with the upcoming Somme offensive, declined to send further troops and Sarrail's offensive that summer was not a success. Briand also attended the conference at Saleux on 31 May 1916 about the upcoming Anglo-French offensive on the Somme, with President Poincaré (on whose train it was held), General Foch (commander, Army Group North) and the British Commander-in-Chief General Haig.

The first Secret Session of the Chamber of Deputies was held in June 1916 to discuss the shortcomings of the defence at Verdun. The government won a vote of confidence but with a clause demanding "effective supervision" of the army. The Parliamentary Army Commission elected Abel Ferry as a commissioner (1 August). By October Ferry was presenting his fourth report on army railways, to Joffre's fury.

Late in 1916 Roques had been sent on a fact-finding mission to Salonika after Britain, Italy and Russia had pushed for the dismissal of the theatre commander Sarrail. To Briand's and Joffre's surprise, Roques returned recommending that Sarrail be reinforced and that Sarrail no longer report to Joffre. Coming on the back of the disappointing results of the Somme campaign and the defeat of Romania, Roques' report further discredited Briand and Joffre and added to the Parliamentary Deputies' demands for a closed session. In November Ferry presented a report on the shortage of manpower. A secret session was held on 21 November about calling up the Class of 1918 followed by another a week later.

On 27 November Briand proposed that Joffre be effectively demoted to commander-in-chief in northern France, with both he and Sarrail reporting to the War Minister, although he withdrew this proposal after Joffre threatened resignation. The Closed Session began on 28 November and lasted until 7 December. Briand had little choice but to make concessions to preserve his government, and in a speech of 29 November he promised to repeal Joffre's promotion of December 1915 and in vague terms to appoint a general as technical adviser to the government. Briand survived a confidence vote by 344-160 (six months earlier he had won a confidence vote 440-80).

Reconstructed government
On 13 December Briand formed a new government, reducing the size of the Council of Ministers from 23 to 10 and replacing Roques with General Lyautey. That day his government survived a vote of confidence by 30 votes, and Joffre was appointed "general-in-chief of the French armies, technical adviser to the government, consultative member of the War Committee" (he was persuaded to accept by Briand, but soon found that he had been stripped of real power and asked to be relieved altogether on 26 December), with Nivelle replacing him as commander-in-chief of the Armies of the North and Northeast.

A Senate Secret Session on 21 December attacked Briand's plans for a smaller war cabinet as "yet another level of bureaucracy"; on 23 December Briand pledged that he would continue to push for a "permanent Allied bureau" to secure constant cooperation between the Allied nations. Briand's reduced War Cabinet was formed in imitation of the small executive body formed by Lloyd George, just appointed Prime Minister of Britain, but in practice Briand's often met just prior to meetings of the main Cabinet. Painlevé declined the job of War Minister as he would have preferred Petain as commander-in-chief rather than the inexperienced Nivelle. Like President Poincaré Briand had thought Petain too cautious to be suitable.

Nivelle's appointment caused great friction between the British and French high commands, after Lloyd George attempted to have Haig placed under Nivelle's command at the Calais Conference in January. Briand only reluctantly agreed to attend another allied conference in London (12–13 March 1917) to resolve the matter. Briand resigned as Prime Minister on 20 March 1917 as a result of disagreements over the prospective Nivelle Offensive, to be succeeded by Alexandre Ribot.

1920s
Briand returned to power in 1921. He supervised the French role in the Washington Naval Conference of 1921–22. Three factors guided the French strategy and necessitated a Mediterranean focus: the French navy needed to carry a great many goods, the Mediterranean was the axis of chief interest, and a supply of oil was essential. The primary goal was to defend French North Africa, and Briand made practical choices, for naval policy was a reflection of overall foreign policy. The Conference agreed on the American proposal that capital ships be limited to a ratio of 5 to 5 to 3 for the United States, Britain, and Japan, with Italy and France allocated 1.7 each. France's participation reflected its need to deal with its diminishing power and reduced human, material, and financial resources.

Briand's efforts to come to an agreement over reparations with the Germans failed in the wake of German intransigence. The immediate cause of Briand's forced resignation was a seemingly trivial incident during the Cannes Conference of 1922. Pressured into a game of golf by David Lloyd George he played so badly that opposition factions in the National Assembly were able to portray him as both inept and a British sycophant. He was succeeded by the more bellicose Raymond Poincaré. In the wake of the Ruhr Crisis, however, Briand's more conciliatory style became more acceptable, and he returned to the Quai d'Orsay in 1925. He would remain foreign minister until his death in 1932. During this time, he was a member of 14 cabinets, four of which he headed himself in 1925–1926 and 1929.

Briand negotiated the Briand-Ceretti Agreement with the Vatican, giving the French government a role in the appointment of Catholic bishops.

Kellogg–Briand Pact
Aristide Briand received the 1926 Nobel Peace Prize together with Gustav Stresemann of Germany for the Locarno Treaties (Austen Chamberlain of the United Kingdom had received a share of the Peace Prize a year earlier for the same agreement ).

A 1927 proposal by Briand and United States Secretary of State Frank B. Kellogg for a universal pact outlawing war led the following year to the Pact of Paris, aka the Kellogg–Briand Pact.

Briand plan for European federation
As foreign minister Briand formulated an original proposal for a new economic union of Europe. Described as Briand's Locarno diplomacy and as an aspect of Franco-German rapprochement, it was his answer to Germany's quick economic recovery and future political power. Briand made his proposals in a speech in favor of a European Union in the League of Nations on 5 September 1929, and in 1930, in his "Memorandum on the Organization of a Regime of European Federal Union" for the Government of France.

The idea was to provide a framework to contain France's former enemy while preserving as much of the 1919 Versailles settlement as possible. The Briand plan entailed the economic collaboration of the great industrial areas of Europe and the provision of political security to Eastern Europe against Soviet threats. The basis was economic cooperation, but his fundamental concept was political, for it was political power that would determine economic choices. The plan, under the Memorandum on the Organization of a System of European Federal Union, was in the end presented as a French initiative to the League of Nations. With the death of his principal supporter, German foreign minister Gustav Stresemann, and the onset of the Great Depression in 1929, Briand's plan was never adopted but it suggested an economic framework for developments after World War II that eventually resulted in the European Union.

In evaluating his internationalism, historian Douglas Houston concludes: Briand's internationalism is easy to deride; nothing he achieved was durable, and his aim seemed no more than old-fashioned security fired by a personal ambition he made little effort to hide. Yet no one worked harder or more imaginatively to give the new international system life. His internationalism sprang from the realization that France could not be secure until everyone else was. He may have embraced principle for reasons of Realpolitik, but there is little doubt that he became convinced of the justice of his cause.

Briand's first Government, 24 July 1909 – 3 November 1910

 * Aristide Briand – President of the Council and Minister of the Interior and Worship
 * Stéphen Pichon – Minister of Foreign Affairs
 * Jean Brun – Minister of War
 * Georges Cochery – Minister of Finance
 * René Viviani – Minister of Labour and Social Security Provisions
 * Louis Barthou – Minister of Justice
 * Auguste Boué de Lapeyrère – Minister of Marine
 * Gaston Doumergue – Minister of Public Instruction and Fine Arts
 * Joseph Ruau – Minister of Agriculture
 * Georges Trouillot – Minister of Colonies
 * Alexandre Millerand – Minister of Public Works, Posts, and Telegraphs
 * Jean Dupuy – Minister of Commerce and Industry

Briand's second Government, 3 November 1910 – 2 March 1911

 * Aristide Briand – President of the Council and Minister of the Interior and Worship
 * Stéphen Pichon – Minister of Foreign Affairs
 * Jean Brun – Minister of War
 * Louis Lucien Klotz – Minister of Finance
 * Louis Lafferre – Minister of Labour and Social Security Provisions
 * Théodore Girard – Minister of Justice
 * Auguste Boué de Lapeyrère – Minister of Marine
 * Maurice Faure – Minister of Public Instruction and Fine Arts
 * Maurice Raynaud – Minister of Agriculture
 * Jean Morel – Minister of Colonies
 * Louis Puech – Minister of Public Works, Posts, and Telegraphs
 * Jean Dupuy – Minister of Commerce and Industry

Changes
 * 23 February 1911 – Briand succeeds Brun as interim Minister of War.

Briand's third and fourth Governments, 21 January – 22 March 1913

 * Aristide Briand – President of the Council and Minister of the Interior
 * Charles Jonnart – Minister of Foreign Affairs
 * Eugène Étienne – Minister of War
 * Louis Lucien Klotz – Minister of Finance
 * René Besnard – Minister of Labour and Social Security Provisions
 * Louis Barthou – Minister of Justice
 * Pierre Baudin – Minister of Marine
 * Théodore Steeg – Minister of Public Instruction and Fine Arts
 * Fernand David – Minister of Agriculture
 * Jean Morel – Minister of Colonies
 * Jean Dupuy – Minister of Public Works, Posts, and Telegraphs
 * Gabriel Guist'hau – Minister of Commerce and Industry

Briand's fifth Government, 29 October 1915 – 12 December 1916

 * Aristide Briand – President of the Council and Minister of Foreign Affairs
 * Joseph Galliéni – Minister of War
 * Louis Malvy – Minister of the Interior
 * Alexandre Ribot – Minister of Finance
 * Albert Métin – Minister of Labour and Social Security Provisions
 * René Viviani – Minister of Justice
 * Lucien Lacaze – Minister of Marine
 * Paul Painlevé – Minister of Public Instruction and Fine Arts
 * Jules Méline – Minister of Agriculture
 * Gaston Doumergue – Minister of Colonies
 * Marcel Sembat – Minister of Public Works
 * Étienne Clémentel – Minister of Commerce, Industry, Posts, and Telegraphs
 * Léon Bourgeois – Minister of State
 * Denys Cochin – Minister of State
 * Émile Combes – Minister of State
 * Charles de Freycinet – Minister of State
 * Jules Guesde – Minister of State

Changes
 * 15 November 1915 – Paul Painlevé becomes Minister of Inventions for the National Defense in addition to being Minister of Public Instruction and Fine Arts.
 * 16 March 1916 – Pierre Auguste Roques succeeds Galliéni as Minister of War

Briand's sixth Government, 12 December 1916 – 20 March 1917

 * Aristide Briand – President of the Council and Minister of Foreign Affairs
 * Hubert Lyautey – Minister of War
 * Albert Thomas – Minister of Armaments and War Manufacturing
 * Louis Malvy – Minister of the Interior
 * Alexandre Ribot – Minister of Finance
 * Étienne Clémentel – Minister of Commerce, Industry, Labour, Social Security Provisions, Agriculture, Posts, and Telegraphs
 * René Viviani – Minister of Justice, Public Instruction, and Fine Arts
 * Lucien Lacaze – Minister of Marine
 * Édouard Herriot – Minister of Supply, Public Works, and Transport
 * Gaston Doumergue – Minister of Colonies

Changes
 * 15 March 1917 – Lucien Lacaze succeeds Lyautey as interim Minister of War.

Briand's seventh Government, 16 January 1921 – 15 January 1922

 * Aristide Briand – President of the Council and Minister of Foreign Affairs
 * Louis Barthou – Minister of War
 * Pierre Marraud – Minister of the Interior
 * Paul Doumer – Minister of Finance
 * Charles Daniel-Vincent – Minister of Labour
 * Laurent Bonnevay – Minister of Justice
 * Gabriel Guist'hau – Minister of Marine
 * Léon Bérard – Minister of Public Instruction and Fine Arts
 * André Maginot – Minister of War Pensions, Grants, and Allowances
 * Edmond Lefebvre du Prey – Minister of Agriculture
 * Albert Sarraut – Minister of Colonies
 * Yves Le Trocquer – Minister of Public Works
 * Georges Leredu – Minister of Hygiene, Welfare Work, and Social Security Provisions
 * Lucien Dior – Minister of Commerce and Industry
 * Louis Loucheur – Minister of Liberated Regions

Briand's eighth Government, 28 November 1925 – 9 March 1926

 * Aristide Briand – President of the Council and Minister of Foreign Affairs
 * Paul Painlevé – Minister of War
 * Camille Chautemps – Minister of the Interior
 * Louis Loucheur – Minister of Finance
 * Antoine Durafour – Minister of Labour, Hygiene, Welfare Work, and Social Security Provisions
 * René Renoult – Minister of Justice
 * Georges Leygues – Minister of Marine
 * Édouard Daladier – Minister of Public Instruction and Fine Arts
 * Paul Jourdain – Minister of Pensions
 * Jean Durand – Minister of Agriculture
 * Léon Perrier – Minister of Colonies
 * Anatole de Monzie – Minister of Public Works
 * Charles Daniel-Vincent – Minister of Commerce and Industry

Changes
 * 16 December 1925 – Paul Doumer succeeds Loucheur as Minister of Finance.

Briand's ninth Government, 9 March – 23 June 1926

 * Aristide Briand – President of the Council and Minister of Foreign Affairs
 * Paul Painlevé – Minister of War
 * Louis Malvy – Minister of the Interior
 * Raoul Péret – Minister of Finance
 * Antoine Durafour – Minister of Labour, Hygiene, Welfare Work, and Social Security Provisions
 * Pierre Laval – Minister of Justice
 * Georges Leygues – Minister of Marine
 * Lucien Lamoureux – Minister of Public Instruction and Fine Arts
 * Paul Jourdain – Minister of Pensions
 * Jean Durand – Minister of Agriculture
 * Léon Perrier – Minister of Colonies
 * Anatole de Monzie – Minister of Public Works
 * Charles Daniel-Vincent – Minister of Commerce and Industry

Changes
 * 10 April 1926 – Jean Durand succeeds Malvy as Minister of the Interior. François Binet succeeds Durand as Minister of Agriculture.

Briand's tenth Government, 23 June – 19 July 1926

 * Aristide Briand – President of the Council and Minister of Foreign Affairs
 * Adolphe Guillaumat – Minister of War
 * Jean Durand – Minister of the Interior
 * Joseph Caillaux – Minister of Finance, Vice President of the Council
 * Antoine Durafour – Minister of Labour, Hygiene, Welfare Work, and Social Security Provisions
 * Pierre Laval – Minister of Justice
 * Georges Leygues – Minister of Marine
 * Bertrand Nogaro – Minister of Public Instruction and Fine Arts
 * Paul Jourdain – Minister of Pensions
 * François Binet – Minister of Agriculture
 * Léon Perrier – Minister of Colonies
 * Charles Daniel-Vincent – Minister of Public Works
 * Fernand Chapsal – Minister of Commerce and Industry

Briand's eleventh Government, 29 July – 3 November 1929

 * Aristide Briand – President of the Council and Minister of Foreign Affairs
 * Paul Painlevé – Minister of War
 * André Tardieu – Minister of the Interior
 * Henry Chéron – Minister of Finance
 * Louis Loucheur – Minister of Labour, Hygiene, Welfare Work, and Social Security Provisions
 * Louis Barthou – Minister of Justice
 * Georges Leygues – Minister of Marine
 * Laurent Eynac – Minister of Air
 * Pierre Marraud – Minister of Public Instruction and Fine Arts
 * Louis Antériou – Minister of Pensions
 * Jean Hennessy – Minister of Agriculture
 * André Maginot – Minister of Colonies
 * Pierre Forgeot – Minister of Public Works
 * Georges Bonnefous – Minister of Commerce and Industry

title: Aristide Briand


text:
USS Rhode Island

There have been three ships of the United States Navy named USS Rhode Island, after the American state.

 * USS Rhode Island (1860), a wooden sidewheel steamer previously named John P. King and Eagle, and later renamed Charleston that saw action in the Civil War.
 * USS Rhode Island (BB-17), a Virginia-class battleship, sailed on the first leg of the Great White Fleet's voyage, and provided anti-submarine services during World War I.
 * USS Rhode Island (SSBN-730), an Ohio-class submarine, laid down in 1981, and renamed USS Henry M. Jackson soon after.
 * USS Rhode Island (SSBN-740), an Ohio-class submarine launched in 1993

title: USS Rhode Island


text:
Trace class

In mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent of the choice of basis used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear algebra. All trace-class operators are compact operators.

In quantum mechanics, mixed states are described by density matrices, which are certain trace class operators.

Trace-class operators are essentially the same as nuclear operators, though many authors reserve the term "trace-class operator" for the special case of nuclear operators on Hilbert spaces and use the term "nuclear operator" in more general topological vector spaces (such as Banach spaces).

Note that the trace operator studied in partial differential equations is an unrelated concept.

Definition
Let $$H$$ be a separable Hilbert space, $$\left\{e_k\right\}_{k=1}^{\infty}$$ an orthonormal basis and $$A : H \to H$$ a positive bounded linear operator on $$H$$. The trace of $$A$$ is denoted by $$\operatorname{Tr} (A)$$ and defined as
 * $$\operatorname{Tr} (A) = \sum_{k=1}^{\infty} \left\langle A e_k, e_k \right\rangle,$$

independent of the choice of orthonormal basis. A (not necessarily positive) bounded linear operator $$T:H\rightarrow H$$ is called trace class if and only if
 * $$\operatorname{Tr}( |T|) < \infty,$$

where $$|T| := \sqrt{T^* T}$$ denotes the positive-semidefinite Hermitian square root.

The trace-norm of a trace class operator $T$ is defined as $$\|T\|_1 := \operatorname{Tr} (|T|).$$ One can show that the trace-norm is a norm on the space of all trace class operators $$B_1(H)$$ and that $$B_1(H)$$, with the trace-norm, becomes a Banach space.

When $$H$$ is finite-dimensional, every (positive) operator is trace class and this definition of trace of $$A$$ coincides with the definition of the trace of a matrix. If $$H$$ is complex, then $$A$$ is always self-adjoint (i.e. $$A=A^*=|A|$$) though the converse is not necessarily true.

Equivalent formulations
Given a bounded linear operator $$T : H \to H$$, each of the following statements is equivalent to $$T$$ being in the trace class:
 * $\operatorname{Tr} (|T|) =\sum_k \left\langle |T| \, e_k, e_k \right\rangle$ is finite for every orthonormal basis $$\left(e_k\right)_{k}$$ of $H$.
 * $T$ is a nuclear operator
 * There exist two orthogonal sequences $$\left(x_i\right)_{i=1}^{\infty}$$ and $$\left(y_i\right)_{i=1}^{\infty}$$ in $$H$$ and positive real numbers $$\left(\lambda_i\right)_{i=1}^{\infty}$$ in $\ell^1$ such that $\sum_{i=1}^{\infty} \lambda_i < \infty$ and
 * $$x \mapsto T(x) = \sum_{i=1}^{\infty} \lambda_i \left\langle x, x_i \right\rangle y_i, \quad \forall x \in H,$$
 * where $$\left(\lambda_i\right)_{i=1}^{\infty}$$ are the singular values of $T$ (or, equivalently, the eigenvalues of $$|T|$$), with each value repeated as often as its multiplicity.

 * $T$ is a compact operator with $$\operatorname{Tr}(|T|)<\infty.$$
 * If $T$ is trace class then
 * $$\|T\|_1 = \sup \left\{ |\operatorname{Tr} (C T)| : \|C\| \leq 1 \text{ and } C : H \to H \text{ is a compact operator } \right\}.$$

 * $T$ is an integral operator.
 * $T$ is equal to the composition of two Hilbert-Schmidt operators.
 * $\sqrt{|T|}$ is a Hilbert-Schmidt operator.

Spectral theorem
Let $$T$$ be a bounded self-adjoint operator on a Hilbert space. Then $$T^2$$ is trace class if and only if $$T$$ has a pure point spectrum with eigenvalues $$\left\{\lambda_i(T)\right\}_{i=1}^{\infty}$$ such that
 * $$\operatorname{Tr}(T^2) = \sum_{i=1}^{\infty}\lambda_i(T^2) < \infty.$$

Mercer's theorem
Mercer's theorem provides another example of a trace class operator. That is, suppose $$K$$ is a continuous symmetric positive-definite kernel on $$L^2([a,b])$$, defined as
 * $$ K(s,t) = \sum_{j=1}^\infty \lambda_j \, e_j(s) \, e_j(t) $$

then the associated Hilbert–Schmidt integral operator $$T_K$$ is trace class, i.e.,
 * $$\operatorname{Tr}(T_K) = \int_a^b K(t,t)\,dt = \sum_i \lambda_i.$$

Finite-rank operators
Every finite-rank operator is a trace-class operator. Furthermore, the space of all finite-rank operators is a dense subspace of $$B_1(H)$$ (when endowed with the trace norm).

Given any $$x, y \in H,$$ define the operator $$ x \otimes y : H \to H$$ by $$(x \otimes y)(z) := \langle z, y \rangle x.$$ Then $$x \otimes y$$ is a continuous linear operator of rank 1 and is thus trace class; moreover, for any bounded linear operator A on H (and into H), $$\operatorname{Tr}(A(x \otimes y)) = \langle A x, y \rangle.$$

Properties
 If $$A : H \to H$$ is a non-negative self-adjoint operator, then $$A$$ is trace-class if and only if $$\operatorname{Tr} A < \infty.$$ Therefore, a self-adjoint operator $$A$$ is trace-class if and only if its positive part $$A^{+}$$ and negative part $$A^{-}$$ are both trace-class. (The positive and negative parts of a self-adjoint operator are obtained by the continuous functional calculus.)

The trace is a linear functional over the space of trace-class operators, that is, $$\operatorname{Tr}(aA + bB) = a \operatorname{Tr}(A) + b \operatorname{Tr}(B).$$ The bilinear map $$\langle A, B \rangle = \operatorname{Tr}(A^* B)$$ is an inner product on the trace class; the corresponding norm is called the Hilbert–Schmidt norm. The completion of the trace-class operators in the Hilbert–Schmidt norm are called the Hilbert–Schmidt operators.

$$\operatorname{Tr} : B_1(H) \to \Complex$$ is a positive linear functional such that if $$T$$ is a trace class operator satisfying $$T \geq 0 \text{ and }\operatorname{Tr} T = 0,$$ then $$T = 0.$$

If $$T : H \to H$$ is trace-class then so is $$T^*$$ and $$\|T\|_1 = \left\|T^*\right\|_1.$$

If $$A : H \to H$$ is bounded, and $$T : H \to H$$ is trace-class, then $$AT$$ and $$TA$$ are also trace-class (i.e. the space of trace-class operators on H is an ideal in the algebra of bounded linear operators on H), and $$\|A T\|_1 = \operatorname{Tr}(|A T|) \leq \|A\| \|T\|_1, \quad \|T A\|_1 = \operatorname{Tr}(|T A|) \leq \|A\| \|T\|_1.$$ Furthermore, under the same hypothesis, $$\operatorname{Tr}(A T) = \operatorname{Tr}(T A)$$ and $$|\operatorname{Tr}(A T)| \leq \|A\| \|T\|.$$ The last assertion also holds under the weaker hypothesis that A and T are Hilbert–Schmidt.

If $$\left(e_k\right)_{k}$$ and $$\left(f_k\right)_{k}$$ are two orthonormal bases of H and if T is trace class then $\sum_{k} \left| \left\langle T e_k, f_k \right\rangle \right| \leq \|T\|_{1}.$

If A is trace-class, then one can define the Fredholm determinant of $$I + A$$: $$\det(I + A) := \prod_{n \geq 1}[1 + \lambda_n(A)],$$ where $$\{\lambda_n(A)\}_n$$ is the spectrum of $$A.$$ The trace class condition on $$A$$ guarantees that the infinite product is finite: indeed, $$\det(I + A) \leq e^{\|A\|_1}.$$ It also implies that $$\det(I + A) \neq 0$$ if and only if $$(I + A)$$ is invertible.

If $$A : H \to H$$ is trace class then for any orthonormal basis $$\left(e_k\right)_{k}$$ of $$H,$$ the sum of positive terms $\sum_k \left| \left\langle A \, e_k, e_k \right\rangle \right|$ is finite.

If $$A = B^* C$$ for some Hilbert-Schmidt operators $$B$$ and $$C$$ then for any normal vector $$e \in H,$$ $|\langle A e, e \rangle| = \frac{1}{2} \left(\|B e\|^2 + \|C e\|^2\right)$ holds.

Lidskii's theorem
Let $$A$$ be a trace-class operator in a separable Hilbert space $$H,$$ and let $$\{\lambda_n(A)\}_{n=1}^{N\leq \infty}$$ be the eigenvalues of $$A.$$ Let us assume that $$\lambda_n(A)$$ are enumerated with algebraic multiplicities taken into account (that is, if the algebraic multiplicity of $$\lambda$$ is $$k,$$ then $$\lambda$$ is repeated $$k$$ times in the list $$\lambda_1(A), \lambda_2(A), \dots$$). Lidskii's theorem (named after Victor Borisovich Lidskii) states that $$\operatorname{Tr}(A)=\sum_{n=1}^N \lambda_n(A)$$

Note that the series on the right converges absolutely due to Weyl's inequality $$\sum_{n=1}^N \left|\lambda_n(A)\right| \leq \sum_{m=1}^M s_m(A)$$ between the eigenvalues $$\{\lambda_n(A)\}_{n=1}^N$$ and the singular values $$\{s_m(A)\}_{m=1}^M$$ of the compact operator $$A.$$

Relationship between common classes of operators
One can view certain classes of bounded operators as noncommutative analogue of classical sequence spaces, with trace-class operators as the noncommutative analogue of the sequence space $$\ell^1(\N).$$

Indeed, it is possible to apply the spectral theorem to show that every normal trace-class operator on a separable Hilbert space can be realized in a certain way as an $$\ell^1$$ sequence with respect to some choice of a pair of Hilbert bases. In the same vein, the bounded operators are noncommutative versions of $$\ell^{\infty}(\N),$$ the compact operators that of $$c_0$$ (the sequences convergent to 0), Hilbert–Schmidt operators correspond to $$\ell^2(\N),$$ and finite-rank operators to $$c_{00}$$ (the sequences that have only finitely many non-zero terms). To some extent, the relationships between these classes of operators are similar to the relationships between their commutative counterparts.

Recall that every compact operator $$T$$ on a Hilbert space takes the following canonical form: there exist orthonormal bases $$(u_i)_i $$ and $$(v_i)_i$$ and a sequence $$\left(\alpha_i\right)_{i}$$ of non-negative numbers with $$\alpha_i \to 0$$ such that $$T x = \sum_i \alpha_i \langle x, v_i\rangle u_i \quad \text{ for all } x\in H.$$ Making the above heuristic comments more precise, we have that $$T$$ is trace-class iff the series $\sum_i \alpha_i$ is convergent, $$T$$ is Hilbert–Schmidt iff $\sum_i \alpha_i^2$  is convergent, and $$T$$ is finite-rank iff the sequence $$\left(\alpha_i\right)_{i}$$ has only finitely many nonzero terms. This allows to relate these classes of operators. The following inclusions hold and are all proper when $$H$$ is infinite-dimensional:$$\{ \text{ finite rank } \} \subseteq \{ \text{ trace class } \} \subseteq \{ \text{ Hilbert--Schmidt } \} \subseteq \{ \text{ compact } \}.$$

The trace-class operators are given the trace norm $\|T\|_1 = \operatorname{Tr} \left[\left(T^* T\right)^{1/2}\right] = \sum_i \alpha_i.$ The norm corresponding to the Hilbert–Schmidt inner product is $$\|T\|_2 = \left[\operatorname{Tr} \left(T^* T\right)\right]^{1/2} = \left(\sum_i \alpha_i^2\right)^{1/2}.$$ Also, the usual operator norm is $\| T \| = \sup_{i} \left(\alpha_i\right).$ By classical inequalities regarding sequences, $$\|T\| \leq \|T\|_2 \leq \|T\|_1$$ for appropriate $$T.$$

It is also clear that finite-rank operators are dense in both trace-class and Hilbert–Schmidt in their respective norms.

Trace class as the dual of compact operators
The dual space of $$c_0$$ is $$\ell^1(\N).$$ Similarly, we have that the dual of compact operators, denoted by $$K(H)^*,$$ is the trace-class operators, denoted by $$B_1.$$ The argument, which we now sketch, is reminiscent of that for the corresponding sequence spaces. Let $$f \in K(H)^*,$$ we identify $$f$$ with the operator $$T_f$$ defined by $$\langle T_f x, y \rangle = f\left(S_{x,y}\right),$$ where $$S_{x,y}$$ is the rank-one operator given by $$S_{x,y}(h) = \langle h, y \rangle x.$$

This identification works because the finite-rank operators are norm-dense in $$K(H).$$ In the event that $$T_f$$ is a positive operator, for any orthonormal basis $$u_i,$$ one has $$\sum_i \langle T_f u_i, u_i \rangle = f(I) \leq \|f\|,$$ where $$I$$ is the identity operator: $$I = \sum_i \langle \cdot, u_i \rangle u_i.$$

But this means that $$T_f$$ is trace-class. An appeal to polar decomposition extend this to the general case, where $$T_f$$ need not be positive.

A limiting argument using finite-rank operators shows that $$\|T_f\|_1 = \|f\|.$$ Thus $$K(H)^*$$ is isometrically isomorphic to $$B_1.$$

As the predual of bounded operators
Recall that the dual of $$\ell^1(\N)$$ is $$\ell^{\infty}(\N).$$ In the present context, the dual of trace-class operators $$B_1$$ is the bounded operators $$B(H).$$ More precisely, the set $$B_1$$ is a two-sided ideal in $$B(H).$$ So given any operator $$T \in B(H),$$ we may define a continuous linear functional $$\varphi_T$$ on $$B_1$$ by $$\varphi_T(A) = \operatorname{Tr} (AT).$$ This correspondence between bounded linear operators and elements $$\varphi_T$$ of the dual space of $$B_1$$ is an isometric isomorphism. It follows that $$B(H)$$ the dual space of $$B_1.$$ This can be used to define the weak-* topology on $$B(H).$$

title: Trace class