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Fredrik Reinfeldt

John Fredrik Reinfeldt (pronounced ; born 4 August 1965) is a Swedish economist, lecturer, former Prime Minister of Sweden from 2006 to 2014 and chairman of the liberal conservative Moderate Party from 2003 to 2015. He was the last rotating President of the European Council in 2009. He is chairman of the Swedish Football Association since 25 March 2023.

A native of Stockholm County, Reinfeldt joined the Moderate Youth League in 1983. By 1992 he rose to the rank of chairman, a position he held until 1995. He served as Member of Parliament from 1991 to 2014, representing his home constituency. Reinfeldt was elected party leader on 25 October 2003, succeeding Bo Lundgren. Under his leadership, the Moderate Party has transformed its policies and oriented itself closer to the political centre, branding itself "the New Moderates" (Nya moderaterna). In 2010, under Reinfeldt's leadership, the Moderate Party got its highest share of the vote since the introduction of universal suffrage in 1921.

Following the 2006 general election, Reinfeldt was elected Prime Minister on 6 October. Along with the three other political parties in the centre-right Alliance for Sweden, Reinfeldt presided over a coalition government with the support of a narrow majority in parliament. At the age of 41, he was the third-youngest person to become Prime Minister of Sweden.

Reinfeldt's first term in office was marked by the late-2000s financial crisis and recession. His popularity fell until the economy of Sweden emerged as one of the strongest in Europe; this brought a resurgence of support for him, resulting in his government's re-election in 2010. Reinfeldt's second government was reduced to a minority government, owing to the rise of Sweden Democrats; he remained in power as the first centre-right Prime Minister since the Swedish-Norwegian Union to be re-elected..

His premiership was characterised by "Arbetslinjen" (English: Working line), a focus on getting more people into the workforce, and by management of the late-2000s financial crisis and recession, which resulted in one of the world's strongest public finances and top rankings in climate and health care.

He is the longest-serving non-Social Democratic Prime Minister since Erik Gustaf Boström's first spell in office between 1891 and 1900. After his defeat in the 2014 election Reinfeldt announced that he would step down from leading the party, which he did on 10 January 2015.

Early life and education
John Fredrik Reinfeldt was born in 1965 in Allmänna BB hospital in Stockholm, the eldest of three brothers to his parents Bruno (1938–2016) and Birgitta Reinfeldt. At the time of his birth his parents lived in an apartment in Österhaninge, in the south of Stockholm County, but a short time afterwards the family moved to London, where his father worked as a consultant for Shell. Upon returning to Sweden, the family first lived in an apartment in Handen before moving to a terraced house in Bromsten in northwestern Stockholm. The Reinfeldt family was living in Bromsten when Fredrik's younger brothers, Magnus and Henrik, were born in 1969 and 1973. In 1976, the family moved into a single-family home in Täby in northeastern Stockholm County. His mother Birgitta was a leadership and management consultant, and some of her professional skills might have inspired and impressed the young Fredrik.

At the age of 11, Reinfeldt became chairman of the student council (elevrådet) in his school, and became a fan of the football club Djurgårdens IF, a passion he maintains to this day. He started playing basketball for the "Tensta Tigers" while living in Bromsten (which is located adjacent to Tensta), and continued to play for them after his family moved to Täby. At his secondary school, Åva gymnasium, he studied natural science for three years. He also enjoyed setting up and performing revues and cabarets. After school, Reinfeldt completed his military service as a ranger (lapplandsjägare) at Lapland Ranger Regiment and finished first in his class as a cadet in Umeå. It was during this time that he became interested in politics, as a representative for his regiment in the congress of conscripts in the Swedish military (värnpliktsriksdagen). He graduated from Stockholm University School of Business with a degree in Business and Economics (civilekonomexamen) in 1990.

Political career
Reinfeldt joined the Moderate Youth League—the youth wing of the Swedish Moderate Party —in 1983 at the age of 18. As a member of the Moderate Youth League in Täby, he challenged the leaders of the local league, who preferred to use the premises as a place to drink beer and wine rather than engage in discussions about politics. Reinfeldt, who is said to dislike hard liquor and to consume wine and beer in moderate amounts, started "Conservative Youth" (Konservativ ungdom) and formed a bond with the mother party, eventually taking over the youth league in 1987. In 1988 he became a secretary (borgarrådssekreterare) in the Stockholm Municipality Council.

He was active in student politics while studying at Stockholm University, eventually becoming chairman of the student party "Borgerliga Studenter – Opposition '68" between 1988 and 1989. He became chairman of the Moderate Youth League's Stockholm branch in 1990, and the following year was elected a member of the Riksdag (the Swedish Parliament). In the Swedish general election of 1991 the Moderate Party and its allies had considerable success, leading to the formation of a centre-right coalition government under Moderate Party leader and Prime Minister Carl Bildt. The 1991 government was the first centre-right government in Sweden since 1982.

Leader of the Moderate Youth League
From 1992 to 1995 Reinfeldt was the chairman of the Moderate Youth League. He ousted the former chairman Ulf Kristersson at the controversial congress known as the Battle of Lycksele, securing 58 of the delegates' votes where Kristersson gained only 55. The congress was controversial because it was the culmination of a long ideological battle within the Moderate Youth League between the conservatives and the libertarians; Reinfeldt represented the conservatives and Kristersson the libertarians. Reinfeldt later stated that although the effects of that deep ideological division and battle in the party lingered on within the Moderate Youth League, he also felt that it was a defining moment in his life. Had he lost the battle he would most likely not be in politics today. In 1993 Reinfeldt wrote the book Det sovande folket, Transl:"The sleeping people", where he criticized the Swedish welfare state and argues for a liberal societal system. With phrases such as: "We don't want to see a society where people starve, but other than that no standard rights should be financed by taxes." The book later haunted Reinfeldt, when he faced criticism for phrases such as "The swedes are mentally handicapped and indoctrinated to believe that politicians can create and guarantee welfare."

From 1995 to 1997 he was chairman of the Democrat Youth Community of Europe.

Following the defeat of the Bildt government in the general election of 1994 he publicly criticized the Moderate Party leader Bildt, who he believed had become too dominant in the party.

In 1995 Reinfeldt co-authored the book "Nostalgitrippen" (The Nostalgic Trip), which described several persons in the Moderate Party leadership, including Gunnar Hökmark and Bo Lundgren, as "Carl Bildt-lookalikes." Bildt was described as being the perfect leader for the opposition to satirize; a nobleman living in the affluent Östermalm with a boyish expression and a better-than-you attitude. As for the other high party officials, the book stated that "If everyone appears similar to Carl it confirms peoples misconceptions about the Moderate Party. It becomes a party for Carl Bildt-copies."

This provoked swift reaction from the Moderate Party leadership, who believed that Reinfeldt's criticisms had gone too far. On 14 February 1995 Reinfeldt was called to a meeting of the Moderate Party's Riksdag group, which took place in the former second chamber (andrakammarsalen) of the Swedish parliament building, a meeting where Bildt apparently scolded him for hours. After this, Reinfeldt toned down his criticism, but was ostracized within the Moderate Party and not given any important posts until after the change of leadership when Lundgren succeeded Bildt in 1999. At that time he was elected into a high party group, the förtroenderåd. From 2001 to 2002 Reinfeldt was chairman of the justice committee of the Riksdag. During this time he traveled around the country gathering impressions and support at the local level of the Moderate Party.

Leader of the Moderate Party
In the general election of 2002 the Moderate Party gained 15.3 percent of the votes—its lowest share of the vote in a general election since 1973. Following the loss, Lundgren was forced to resign his position as leader of the Moderate Party. After the 2002 election Reinfeldt was elected as leader of the Moderate Party parliamentary group, spokesman for economic policy and vice chairman of the parliament's finance committee. On 25 October 2003 he was unanimously elected as the new leader of the Moderate Party.

"The New Moderates"
Under Reinfeldt's leadership, the Moderate Party adjusted its position in the political spectrum, moving towards the centre. To reflect these changes, the party's unofficial name was altered to "The New Moderates" (De nya Moderaterna) in order to emphasize the break with the past. The Moderate Party started to focus more on calls for tax cuts for low- and middle-income groups, rather than on major tax cuts that would more benefit high-income earners.

As leader of the Moderate Party, Reinfeldt tended to be less forceful in his criticism of the Swedish welfare state than his predecessors. He instead proposed reforms to Sweden's welfare state, which included cutting taxes for the lowest income earners and reducing unemployment benefits, in order to encourage the jobless to return to work. He toned down calls within the party for dismantling large portions of the Swedish welfare state, stating that change must come gradually from the bottom up and not be dictated from the top down. His goal was said to be to fine-tune the welfare state, by focusing on getting people off welfare benefits and into employment. He worked to shift the conservatives toward the middle ground by convincing voters that he would fix rather than dismantle the public welfare system.

Reinfeldt even extended an invitation to the Swedish Trade Union Confederation, traditional supporter of the Social Democrats and opponent of the Moderate Party. He also changed the Moderate Party's traditional stance towards the Swedish Labour and employment laws, stating that he prefers small changes instead of any radical reform.

People both within and outside the party differ on their analysis of Reinfeldt's transformation of the Moderate Party, with some arguing that the party was mainly honing the way it describes its visions, and others suggesting that it constituted a substantial policy change towards the centre. As a consequence of Reinfeldt's shift of the Moderate Party to the centre, the differences between the Moderate Party and their traditional opponents the Social Democratic Party have become harder to discern. In a series of radio and television debates, the then-Social Democrat leader and Prime Minister Göran Persson portrayed his opponent as a classic conservative in disguise. Persson stated that, if put into power, the conservatives would tamper with Sweden's successful formula of high taxes, a large public sector and generous benefits. There was also some criticism within the party; former Moderate Youth League chairman Christofer Fjellner called Reinfeldt's political reform "leftist rhetoric" (vänsterretorik).

Alliance for Sweden
In the run-up to the general election of 2006, Reinfeldt, as leader of the Moderate Party, participated in the creation of the Alliance for Sweden. It united the centre-right in a coalition of the Moderate Party, the Centre Party, the Liberal People's Party and the Christian Democrats. Reinfeldt is said to have been instrumental in uniting the four parties, which previously were known for being notoriously divided, in order to present a powerful alternative to the Social Democrats. The parties presented a joint election manifesto for the alliance.

2006 Swedish general election

During the run-up to the 2006 Swedish general election, Reinfeldt was subjected to a smear campaign. Mats Lindström, a staff member in the Social Democratic Party headquarters, admitted to sending e-mails accusing Reinfeldt of tax fraud, false financial declarations and only attaining his position because of his father's influence. The IP address used in the e-mails was traced to the Social Democratic Party headquarters. Social Democratic Party Secretary Marita Ulvskog apologized and said that such behavior was completely unacceptable. A short time after the e-mail campaign, images that depicted Reinfeldt and the Moderate Party in an unflattering light were spread internally within the Social Democratic Party and subsequently leaked to the media. Social Democratic Party spokeswoman Carina Persson confirmed that the material came from the Social Democratic Youth League, but denied the existence of an official smear campaign and stated that the material was not meant to be released or spread to a wider audience.

At the general election on 17 September 2006 the Alliance for Sweden won a majority of the votes after the first count, defeating the Social Democratic Party. The Moderates gained 26.1 percent of the votes, a new record for the party and over 10 percentage points higher than in 2002. The election result was also historic in being the worst result for the Social Democrats ever (34.6 percent) in a general election under universal suffrage (introduced in 1921).

Looking back at the defeat of the incumbent Social Democrats, the opinion among several members of the defeated incumbents was that the election was lost because the previous government failed to bring down unemployment, and failed to campaign on it as an issue. Ardalan Shekarabi, the former chairman for the Swedish Social Democratic Youth League, stated that "the Moderates were right strategically to focus on unemployment". Former Social Democratic minister Leif Pagrotsky stated that internal fighting, authoritarianism and perceived aggressiveness as well as a loss of appeal to the middle class and city inhabitants contributed to the election loss.

2010 Swedish general election
In the 2010 general election held on 19 September 2010 the Alliance for Sweden were reduced to a minority government, but also becoming the first centre-right government to be re-elected since before World War II. The Moderate Party gained 30.06% of the votes, which was the highest election result in over one hundred years.

The Alliance for Sweden received a plurality of votes, but not full majority in Parliament. But because of the fragmented opposition, after the entrance of the Sweden Democrats in parliament, the government could continue.

Prime Minister (2006–2014)
Reinfeldt became the Prime Minister of Sweden on 6 October 2006 when he was confirmed by king Carl XVI Gustaf having been approved by the Riksdag the previous day, serving concurrently as Leader of the Moderate Party. The 41-year old Reinfeldt became the youngest person to become Prime Minister since Rickard Sandler became Prime Minister at the age of 40 in 1925. With victories in 2006 and in 2010, Reinfeldt was the Moderate Party's longest-serving prime minister and the only person to lead the party to two consecutive general election victories. His Government compromised four parties (including his own) which prior to the election had formed a coalition named Alliance for Sweden, later turned into the Alliance.

At a press conference prior to his appointment, Reinfeldt commented that "this feels historic in many ways" partly because it was the first time in 36 years there would be a majority government in Sweden.

2008 Financial Crisis
A global financial crisis was triggered in 2008, beginning in the United States. The financial crisis of 2008 which continued into 2009, had a major impact on the Swedish economy. Reinfeldt's Government emphasized that a balanced budget was a priority, combined with income tax cuts to stimulate domestic production and commerce. The Cabinet received criticism for holding to hard in the public finances, with limited investments, and the support of Reinfeldt's policies dropped to one of the lowest ever seen for an incumbent Government.

From 2009, the Swedish economy emerged as one of the world's fastest recovering economies with high competitiveness. Sweden was noted for having proved to overcome the crisis better than any other developed countries, and this was highlighted by the Government as a force in the run-up to 2010 general election. As Sweden emerged as the best country on several areas after the financial crisis it brought a resurgence of support, which eventually resulted in his re-election in 2010. This was the first time ever that the Moderate Party was re-elected after completing a full first term.

President of the European Council
Reinfeldt became President of the European Council on 1 July 2009, as Sweden took over the Presidency of the Council of the European Union from the Czech Republic. His slogan was "taking on the challenge". Reinfeldt immediately requested the European Union to do more to combat climate change. Days earlier, he had been interviewed by Reuters and said he spoke of his worry about increased European public debt. He spoke of his wish for Turkey to join the European Union. He also spoke of his other views, such as his hope that a second term would be possible quickly for the President of the European Commission and his desire that the European Union should not sanction Iran immediately following its election protests.

Second term (2010–2014)

In the 2010 general election, the Moderate Party increased its share of the vote to 30.06%. The Alliance got a plurality of votes cast, but with 173 seats no absolute majority in parliament. With the opposition divided mainly by the Sweden Democrats, Reinfeldt could remain in government, but with a greater need to seek consensus on matters of substance with the opposition parties.

The second term compromised a slow recovery from the 2008-2009 financial crisis and consolidation of policies from the first term. The political debate came from 2013 to be highly dominated by issues where the Government came in a defense mode, in particular for the poor performance of Swedish pupils in the international study of school performance, the Programme for International Student Assessment, and profits gained in private welfare, especially after the economic collapse that had preceded the closure of school group JB Education AB and questions of how key people in the Government, including himself, acted in the N.V. Nuon Energy affair.

Reinfeldt had during his second term, in contrast to his first term, no major international engagement. Contacts with other politicians, however, remained good, which was also marked by Barack Obama's visit to Stockholm in September 2013.

Immigration policy
After the nationalist Sweden Democrats entered the Riksdag, Reinfeldt wanted to seek bipartisan consensus on immigration policy in an attempt to undercut and isolate the Sweden Democrats on their main issue. In early 2011 an agreement between the Alliance and the Green Party was reached, which would among other things, give undocumented immigrants access to universal healthcare and lessen the requirements for family reunification. During the last year of Reinfeldt's time in office Sweden faced the biggest influx of immigrants it had ever seen up until that point. During a press conference in the run-up to the 2014 election campaign Reinfeldt urged the Swedish people to "open their hearts" (öppna era hjärtan) to people fleeing wars, stating that he wouldn't promise much in the upcoming campaign considering the costs that the immigration would bring. The Sweden Democrats perceived the press conference as confirming their belief that asylum immigration is in conflict with the Swedish welfare state.

Economic policy
He adopted a liberal roadmap, leading in particular to a modification of the tax system (including the abandonment of inheritance tax), a tightening of the conditions of access to unemployment benefits or sick pay, and the reduction of public spending.

It privatised much of the health sector from 2006, with mixed results. While the number of specialists has increased, reducing waiting times for appointments, privatisation has also led to higher costs for the government (to make a profit, private institutions have to increase the number of consultations and interventions) and increased inequalities in access to health care, with specialists tending to leave the regions for the big cities and the suburbs for wealthier areas.

In early 2013, the liberal British magazine The Economist praised the Reinfeldt government's reforms, pointing out that the country could become "the next liberal supermodel".

Foreign policy
The Moderate Party has a pro-European Union policy stance —including support for exchanging the SEK for the Euro —and also supports Sweden joining NATO. During the 2000 United States presidential election, Reinfeldt visited the United States to support the campaign of George W. Bush. Prior to the 2004 United States presidential election, Reinfeldt again expressed his support for Bush. In an interview with the newspaper Stockholm City on 8 March 2004, Reinfeldt said that he preferred Bush over the Democratic Party contender John Kerry, and in a poll conducted by the newspaper Svenska Dagbladet in April 2004, Reinfeldt like a large majority of his party favoured Bush over Kerry.

Despite this, he has compared his government's actions and policies to those of Bill Clinton's administration, and supported Barack Obama in the 2008 United States presidential election.

Reinfeldt visited Washington, D.C., on 15 May 2007, meeting with President Bush. His trip also included meetings with others, including United Nations Secretary-General Ban Ki-moon and California Governor Arnold Schwarzenegger. This is his first visit to the United States since becoming Prime Minister in 2006. Bush and Reinfeldt mostly discussed climate change and free trade, focusing on the Doha Round. He visited President Barack Obama at first the White House and then in the Metropolitan Museum of Art on 23 September 2009.

Reinfeldt was President of the European Council from 1 July to 1 December 2009. The signing of the Treaty of Lisbon was Reinfeldt's role as President of the Council, which also occurred on 13 December 2009. Reinfeldt was also responsible in this role to put EU's efforts to get into a binding agreement at the United Nations Climate Change Conference in Copenhagen in 2009 but this did not succeed.

Post-premiership (2014–present)
After defeat in 2014, Reinfeldt announced he would step down as both Prime Minister of Sweden and as party leader of the Moderate Party. He stepped down from the office of Prime Minister on 3 October 2014, being succeeded by Stefan Löfven. He resigned from the Riksdag on 31 December 2014 and stepped down as party leader on 10 January 2015, being succeeded by Anna Kinberg Batra.

On 19 January 2015, Reinfeldt announced that he had formed his own business Fredrik Reinfeldt AB where he will serve as an advisor and lecturer. He will also continue to promote his "job line", which was a key part of his premiership, in a continued community deed. On 1 September 2015 he launched his autobiography, titled Halfway, where he reflects over his 25 years in Swedish and international politics.

On 11 December 2015, Reinfeldt was nominated to become the next chairman of the Extractive Industries Transparency Initiative. He will be formally appointed in February 2016.

In January 2016, Reinfeldt was awarded H. M. The King's Medal, 12th size with chain, for extraordinary efforts as Prime Minister. On 15 March 2016 it was announced that Reinfeldt had been hired by Bank of America Merrill Lynch as a senior adviser for its business in Europe, the Middle East and Africa.

On 25 March 2023, he was elected chairman of the Swedish Football Association.

Public perception
Reinfeldt has been called a "Swedish David Cameron," insofar as he succeeded in shifting the public perception of the Moderate Party from a clear right-wing position to a more centrist one. On the other hand, he is thought to have influenced Cameron, since Reinfeldt was elected party leader in 2003—two years before Cameron took control of the British Conservative Party in 2005. Reinfeldt has also been described as a communitarian.

In a study by Sifo, a Swedish polling institute, Reinfeldt was the "most admired man in Sweden" in 2006. Reinfeldt's approval rating reached its highest measured point yet in December 2006, at 57% approval in an Aftonbladet/Sifo poll. Approval ratings for Reinfeldt as a person remained overall good but fluctuating through most of the period 2006–2010, but did not always seem to translate into support for the cabinet.

Reinfeldt has been perceived as a controlled and harmonious person. He was described, already before he became prime minister, as "gentle, pensive and a good listener" and his "cool, soft-spoken approach" is said to go down well with Swedish voters; it also fits well with the promotion of the policies of his cabinet as being not ideological, but motivated by non-political reason and common sense, in implicit contrast to the "ideological excesses" of the Social Democrats and their allies. Aware of this perception, Reinfeldt has said "I am by nature confident and calm. But that does not mean I am not passionate and wouldn't feel strongly about things." Regarding his family life, Reinfeldt has cultivated the image of a good family man who enjoys housework.

Criticism
Reinfeldt has been criticized for supposedly anti-Swedish commentary such as "The native Swedish culture is only barbaric" which referred to the positive effect the inflow of people and influences had on the development of Sweden. Reinfeldt was also criticized for his book "Det sovande folket" ("The sleeping nation"), of which he initially denied authorship, but later confessed calling it a "sin of the youth". VLT published an article stating that Reinfeldt was 28 years old, a business and economics graduate and had been in parliament for two years and that he "knew fully what he was doing". The book has also received criticism for proposing radical neoliberalism. Reinfeldt has been called "one of Sweden's most dangerous leaders" in an article by Social Democrat Daniel Suhonen. Reinfeldt has also been criticized for having sold out parts of elderly care, privatized some primary and secondary schools and pharmacies. Reinfeldt received heavy criticism for having proposed in a deputy report, authored by himself, that Swedes should work to the age of 75 and further if possible. SVT published an article of Reinfeldt's commentary on Twitter speaking of low unemployment among "ethnic swedes" for which he received severe criticism. Blekinge Läns Tidning published an article criticizing Reinfeldt for being narrow minded stating that "migration can save the pension system". Henrik Lilja of conspiracy oriented Facebook group ProjektSanning criticized Reinfeldt for having "destroyed Sweden". Breakit criticized Reinfeldt after the "Ipred-lagen" (online piracy law) was passed in Sweden, since he stated that young file-share users would not be chased by the authorities but failed to mention that private corporates could force ISPs to release data. Reinfeldt asked the Swedish public to "open their hearts" towards refugees which he was criticized for by some political opponents. He also received criticism for not having provided the financial prerequisites during his eight years in power. Leftist anarchist leaning website AktuelltFokus published an article criticizing Reinfeldt, after leaving politics, for receiving a government pension with monthly payments of 156 000 SEK from Swedish tax money while his own corporate declared a profit of 22 million SEK in 2016. Jimmie Åkesson, party leader of the nationalist Sweden Democrats, has often called Reinfeldt "swede-phobic".

Personal life

In 1992, Fredrik Reinfeldt married Filippa Holmberg, the daughter of Senior Captain Cay Holmberg and Ulla Molin. Holmberg was a Stockholm County municipal politician for the Moderate Party. During Fredrik's tenure as prime minister, Filippa Reinfeldt was County Councillor for healthcare issues (sjukvårdslandstingsråd) in Stockholm. After being elected Prime Minister in 2006, Reinfeldt moved into the prime minister's official residence, the Sager House, together with his wife and their three children, Ebba, Gustaf and Erik. On 7 March 2012 it became known that the couple had separated. On 11 July 2012 the couple signed their divorce papers with consideration of 6 months. On 20 February 2013 they signed the last papers which conducted their divorce.

His father Bruno Reinfeldt was also formerly involved in local politics for the Moderate Party in Täby, but left all his political posts in February 2009 after having been arrested and later convicted for drunk driving.

On 23 February 2015, Reinfeldt confirmed that he was now in a relationship with Roberta Alenius. Alenius served as Head of Communications (Chief of the Press Secretaries) at the Cabinet Office from 2006 to 2014, while Reinfeldt served as Prime Minister. On 2 May 2017, Alenius gave birth to Reinfeldt's fourth child and second daughter. The couple announced in 2022 that they had separated.

During the 2006 election, it was brought to attention that Reinfeldt's paternal great-great-grandfather was an African American circus director from New York, John Hood, who had a son with Emma Dorotea Reinfeld, a maid from Eckau (now Iecava in present-day Latvia). Emma Dorotea Reinfeld later married the Swede Anders Karlsson, but her illegitimate son John kept his mother's surname. The spelling was later changed to Reinfeldt. He also has Italian ancestry, via his paternal grandmother.

Personal opinions
He has revealed that his personal distaste for the anti-immigration Sweden Democrats party is based on his partly African ancestry.

Reinfeldt has said that he left the Church of Sweden when he was eighteen years old, critical of the left-leaning perspectives of the church. In an interview as Prime Minister he however said that he could not state if he believed in God, discussing his belief "that something exist that is not just about the scientific explanation for how the Earth was created. But exactly what it is I don't have an answer for, I am both searching and wondering." He was however married, and had his children baptized in the Church of Sweden.

He has lately also attracted some attention as a political science fiction writer. His social dystopia "Det sovande folket" (The Sleeping People) was in 2013 featured as a play at Teater Alma in Stockholm.

National honours

 * Commemorative Ruby Jubilee Medal of His Majesty The King (15092013).png 🇸🇪 Recipient of the King Carl XVI Gustaf's Jubilee Commemorative Medal II (23 August 2013)
 * Noribbon.svg 🇸🇪 H. M. The King's Medal, 12th size with chain (4 February 2016)

Foreign honours

 * EST Order of the Cross of Terra Mariana - 1st Class BAR.svg 🇪🇪 Estonia: Order of the Cross of Terra Mariana, 1st Class (18 January 2011)

title: Fredrik Reinfeldt


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Byron Dorgan

Byron Leslie Dorgan (born May 14, 1942) is an American author, businessman and former politician who served as a United States Representative (1981–1992) and United States Senator (1992–2011) from North Dakota. He is a member of the Democratic Party.

, he serves as a senior policy advisor for the Washington, DC law firm Arent Fox LLP. He was a member of the Senate Democratic leadership for 16 years, first as Assistant Democratic Floor Leader and then as Chairman of the Democratic Policy Committee and Chairman of the Committee on Indian Affairs. Dorgan announced that he would not seek re-election in 2010.

In addition to his work at Arent Fox, Dorgan serves as a senior fellow at the Bipartisan Policy Center, where he focuses on energy policy issues as co-chair of BPC's Energy Project and is also a member of the ReFormers Caucus of Issue One. He is an adjunct professor at Georgetown University; he also serves on several boards of directors, including the Board of Governors of Argonne National Laboratory and on the National Advisory Board of the Center for Arms Control and Non-Proliferation.

Dorgan is also a New York Times best-selling author of five books, including two on economic and political issues, two novels described as eco-thrillers and the latest book titled “The Girl in the Photograph” a true story about a Native American girl living on an Indian Reservation.

Early life, education, and business career
Dorgan was born in Dickinson, North Dakota, the son of Dorothy and Emmett Patrick Dorgan, and was raised in Regent, North Dakota. His father's family was of Irish and Swedish ancestry, while his mother's was German and Norwegian. He graduated from Regent High School and earned a Bachelor of Science from the University of North Dakota and a Master of Business Administration from the University of Denver. Dorgan worked for Boeing and the Martin-Marietta Corporation in the aerospace industry.

Early political career
Dorgan's public service career began at age 26, when he was appointed North Dakota State Tax Commissioner to a fill a vacancy opened upon the death of the incumbent tax commissioner. He was the youngest constitutional officer in North Dakota's history. He was re-elected to that office by large margins in 1972 and 1976, and was chosen one of "Ten Outstanding State Officials" in the United States by the Washington Monthly magazine. His future Senate colleague Kent Conrad worked in the same office before succeeding Dorgan at this post. Dorgan ran unsuccessfully for a seat in Congress in 1974. He was elected to the United States House of Representatives in his second bid in 1980. He was a member from 1981 until 1992, being re-elected five times.

Elections
In 1992, the Democratic incumbent, Kent Conrad opted not to run for re-election because of a campaign promise. Dorgan won the election for the seat. However, that September the state's other senator, Quentin Burdick, died and Conrad ran for the seat in the special election. Conrad took the new seat in 1992 and Dorgan assumed Conrad's old seat a few weeks early. Dorgan was re-elected in 1998 and 2004. Conrad later was elected for a full term from North Dakota's other Senate seat.

Tenure
When Dorgan was chairman of the Democratic Policy Committee, he was one of the most powerful Democrats in the Senate. He was considered "something of a liberal hero." In the later years of his Senate career, he had been increasingly sought by the national media for comment on political issues. He was a strong opponent of continuing the U.S. embargo toward Cuba. He was instrumental in passing legislation to remove the embargo as it applied to the sale of food and medicine to Cuba. He introduced, with varying levels of success, several amendments to end the U.S. prohibition on travel to Cuba, and to terminate funds for anti-Castro broadcasting. Dorgan has also opposed most bills "liberalizing" trade policies between the United States and other countries, maintaining that most trade agreements resulted in higher trade deficits and shipping U.S. jobs overseas. He has a mixed record on tort reform issues, voting against the Private Securities Litigation Reform Act and the Class Action Fairness Act, but voting in favor of the vetoed Common Sense Product Liability and Legal Reform Act and the Protection of Lawful Commerce in Arms Act.

Chairman of Senate Energy Panel
Dorgan was Chairman of the Senate Energy and Water Appropriations Subcommittee and was also senior member of the Senate Energy Committee. He was an early supporter of renewable energy, sponsoring measures on the production tax credit for wind energy and creating a Renewable Fuels Standard (RFS) mandate to help build a renewable fuels industry. He also persuaded the U.S. Geological Survey to conduct and release the first official estimate of recoverable oil in the Bakken Formation in North Dakota. That estimate concluded that there was up to 4.3 billion barrels of recoverable oil from the shale deposits in North Dakota.

Chairman of Senate Aviation Panel
Dorgan was Chairman of the Aviation Subcommittee of the Senate Commerce Committee and worked extensively on aviation issues. He has served as co-chairman of the Eno Center for Transportation project exploring ways to reorganize the Air Traffic Control function at the Federal Aviation Administration (FAA) in order to accelerate the movement to the next generation air traffic control system using GPS as a replacement for ground-based radar.

Red River Valley Research Corridor
As a member of the Senate Appropriations Committee, Dorgan earmarked substantial funds to create a Red River Valley Research Corridor to bring new high-tech jobs to that region. The Research Corridor was anchored by North Dakota State University and the University of North Dakota, which became magnets for new economic opportunities and new jobs in materials science, micro and nano-technology research, unmanned aviation vehicle research, among others.

Financial Regulation and the Global Financial Crisis
As early as 1994, Dorgan was sounding the warning about the speculation in unregulated financial derivatives, which would later be a central issue in the subprime mortgage crisis and subsequent 2007–2012 global financial crisis, by U.S. banks on their proprietary accounts. He wrote the cover story for the Washington Monthly magazine titled "Very Risky Business" warning of the danger to the economy of the wagers that large financial institutions were making by trading in unlimited derivatives.

In 1999, Dorgan voiced continuing concern over lack of regulation of derivatives.

"We are moving towards greater risk. We must do something to address the regulation of hedge funds and especially derivatives in this country, $33 trillion, a substantial amount of it held by the 25 largest banks in this country, a substantial amount being traded in proprietary accounts of those banks. That kind of risk overhanging the financial institutions of this country one day, with a thud, will wake everyone up."

Senator Dorgan was one of only eight members of the Senate to vote against the repeal of key provisions of the Glass-Steagall Act (contained in the Gramm–Leach–Bliley Act) in 1999. During debate on that 1999 legislation, in a speech on the Senate floor, he said that, "it will in my judgement raise the likelihood of future massive taxpayer bailouts" (cited in John Lanacaster, Whoops, London, 2010, p. 161). On September 26, 2008, against a backdrop of growing economic turmoil caused by the Credit Crunch, David Leonhardt of The New York Times singled out a quotation made by Dorgan in 1999 during the US Senate's repeal of the Glass–Steagall Act. "I think we will look back in 10 years' time and say we should not have done this, but we did because we forgot the lessons of the past, and that that which is true in the 1930s is true in 2010."

On January 23, 2008, Dorgan was one of the first politicians to speak of the oncoming economic downturn in a speech to the Senate given in response to then-President Bush's economic stimulus package.

Additional Senate history
In 2007, Dorgan was a major supporter of net neutrality legislation in the Senate, seeing it as essential to keeping the Internet open and democratic.

In 2007, he was a major opponent of the McCain-Kennedy Comprehensive Immigration Reform Act of 2007 (S. 1639) saying that the legislation's guest worker provision would continue the downward push of illegal aliens on the wages of American workers.

In 2009, he voted along with all 39 voting Republican senators and 12 Democrats against an amendment to the Helping Families Save Their Homes Act of 2009.

Three times, Dorgan introduced a bill to form a new committee modeled after the 1940s Truman Committee to oversee Government waste, fraud, and corruption in the awarding of government contracts.

In 2009, Dorgan voted to approve the $838 billion stimulus package. The Senate voted 61–37 to pass this legislation.

In 2009, Dorgan sided with fellow Democrats to make funds available to modify or build facilities to allow Guantanamo detainees to be brought to the United States. This was a reversal from his previous vote to not allow federal funds to be used to transfer or incarcerate Guantanamo inmates.

Although Dorgan had indicated in early 2008 he would seek a fourth term in the Senate, on January 5, 2010, he issued a statement announcing he would not run for re-election. In it, he insisted that the "...decision [was] not a reflection of any dissatisfaction with my work in the Senate, nor [was] it connected to a potential election contest [in the fall of 2010] (frankly, I believe if I were to run for another term I would be reelected)." He gave his Senate farewell speech on December 9, 2010.

Committee assignments

 * 2009-2010
 * Committee on Appropriations
 * Subcommittee on Agriculture, Rural Development, Food and Drug Administration, and Related Agencies
 * Subcommittee on Commerce, Justice, Science, and Related Agencies
 * Subcommittee on Defense
 * Subcommittee on Energy and Water Development (chairman)
 * Subcommittee on Interior, Environment, and Related Agencies
 * Subcommittee on Transportation, Housing and Urban Development, and Related Agencies
 * Committee on Commerce, Science, and Transportation
 * Subcommittee on Aviation Operations, Safety, and Security (chairman)
 * Subcommittee on Communications, Technology, and the Internet
 * Subcommittee on Competitiveness, Innovation, and Export Promotion
 * Subcommittee on Consumer Protection, Product Safety, and Insurance
 * Subcommittee on Surface Transportation and Merchant Marine Infrastructure, Safety, and Security
 * Committee on Energy and Natural Resources
 * Subcommittee on Energy
 * Subcommittee on National Parks
 * Subcommittee on Water and Power
 * Committee on Indian Affairs (chairman)

Center for Native American Youth
Following his departure from the Senate, Dorgan announced the creation of a non-profit organization to help Native American youth living on Indian Reservations. He donated $1 million of unused campaign funds to create the Center for Native American Youth (CNAY), which is housed as a separate program at the Aspen Institute. The center works on teen suicide prevention, providing educational opportunities, and additional issues with Indian youth in the United States. CNAY sponsors a Champions of Change program that recognizes outstanding Native American youth and develops mentors for other youth. Dorgan serves as the unpaid chairman of the Board of CNAY.

Personal life
Dorgan is married to the former Kimberly Olson, who was formerly an Executive Vice President and lobbyist for The American Council of Life Insurers. Together they have two children, Brendon and Haley. From his first marriage, Dorgan has a son Scott who has two children, Mason and Madison, and he also had a daughter Shelly, who is deceased.

Campaign contribution controversy
In November 2005, Dorgan was accused of receiving campaign contributions from people who worked for companies connected to lobbyist Jack Abramoff. Because Dorgan was the top Democrat on the committee investigating corruption charges against Abramoff, questions were raised about a possible conflict of interest. In a statement released on November 28, 2005, Dorgan responded by asserting that he has never personally met Jack Abramoff, nor has he ever received money from Abramoff. Dorgan did acknowledge receiving money from Abramoff's clients, but the donations began prior to their involvement with Abramoff. Dorgan's statement went on to say that he has supported the programs that benefited Abramoff's clients years prior to the contribution. On December 13, 2005, Dorgan announced that he was returning all donations from Abramoff's clients as a precaution to avoid any impropriety as the contributions may have been directed or requested by Abramoff.

Nonfiction

 * Electric Transmission Infrastructure and Investment Needs: Hearing Before the Committee on Energy and Natural Resources, U.S. Senate (editor). Diane Pub Co., 2003 ISBN 0-7567-2997-1.
 * Take This Job and Ship It: How Corporate Greed and Brain-Dead Politics Are Selling Out America. Thomas Dunne Books (2006) ISBN 0-312-35522-X. (appeared on The New York Times Best Seller list)
 * Reckless!: How Debt, Deregulation, and Dark Money Nearly Bankrupted America (And How We Can Fix It!). Thomas Dunne Books (2009) ISBN 0-312-38303-7.
 * The Girl in the Photograph: The True Story of a Native American Child, Lost and Found in America. Thomas Dunne Books, 2019. ISBN 9781250173645.

Fiction

 * Blowout (with David Hagberg). Forge, 2012. ISBN 978-0-7653-2737-6
 * Gridlock (with David Hagberg). Forge, 2013. ISBN 978-0-7653-2738-3

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

title: Byron Dorgan


text:
Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form $$a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^{(n)} = b(x)$$ where $a_{0}(x)$, ..., $a_{n}(x)$ and $b(x)$ are arbitrary differentiable functions that do not need to be linear, and $y′, ..., y^{(n)}$ are the successive derivatives of an unknown function $y$ of the variable $x$.

Such an equation is an ordinary differential equation (ODE). A linear differential equation may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives.

Types of solution
A linear differential equation or a system of linear equations such that the associated homogeneous equations have constant coefficients may be solved by quadrature, which means that the solutions may be expressed in terms of integrals. This is also true for a linear equation of order one, with non-constant coefficients. An equation of order two or higher with non-constant coefficients cannot, in general, be solved by quadrature. For order two, Kovacic's algorithm allows deciding whether there are solutions in terms of integrals, and computing them if any.

The solutions of homogeneous linear differential equations with polynomial coefficients are called holonomic functions. This class of functions is stable under sums, products, differentiation, integration, and contains many usual functions and special functions such as exponential function, logarithm, sine, cosine, inverse trigonometric functions, error function, Bessel functions and hypergeometric functions. Their representation by the defining differential equation and initial conditions allows making algorithmic (on these functions) most operations of calculus, such as computation of antiderivatives, limits, asymptotic expansion, and numerical evaluation to any precision, with a certified error bound.

Basic terminology
The highest order of derivation that appears in a (linear) differential equation is the order of the equation. The term $b(x)$, which does not depend on the unknown function and its derivatives, is sometimes called the constant term of the equation (by analogy with algebraic equations), even when this term is a non-constant function. If the constant term is the zero function, then the differential equation is said to be homogeneous, as it is a homogeneous polynomial in the unknown function and its derivatives. The equation obtained by replacing, in a linear differential equation, the constant term by the zero function is the . A differential equation has constant coefficients if only constant functions appear as coefficients in the associated homogeneous equation.

A  of a differential equation is a function that satisfies the equation. The solutions of a homogeneous linear differential equation form a vector space. In the ordinary case, this vector space has a finite dimension, equal to the order of the equation. All solutions of a linear differential equation are found by adding to a particular solution any solution of the associated homogeneous equation.

Linear differential operator
A basic differential operator of order $i$ is a mapping that maps any differentiable function to its $i$th derivative, or, in the case of several variables, to one of its partial derivatives of order $i$. It is commonly denoted $$\frac{d^i}{dx^i}$$ in the case of univariate functions, and $$\frac{\partial^{i_1+\cdots +i_n}}{\partial x_1^{i_1}\cdots \partial x_n^{i_n}}$$ in the case of functions of $n$ variables. The basic differential operators include the derivative of order 0, which is the identity mapping.

A linear differential operator (abbreviated, in this article, as linear operator or, simply, operator) is a linear combination of basic differential operators, with differentiable functions as coefficients. In the univariate case, a linear operator has thus the form $$a_0(x)+a_1(x)\frac{d}{dx} + \cdots +a_n(x)\frac{d^n}{dx^n},$$ where $a_{0}(x), ..., a_{n}(x)$ are differentiable functions, and the nonnegative integer $n$ is the order of the operator (if $a_{n}(x)$ is not the zero function).

Let $L$ be a linear differential operator. The application of $L$ to a function $f$ is usually denoted $Lf$ or $Lf(X)$, if one needs to specify the variable (this must not be confused with a multiplication). A linear differential operator is a linear operator, since it maps sums to sums and the product by a scalar to the product by the same scalar.

As the sum of two linear operators is a linear operator, as well as the product (on the left) of a linear operator by a differentiable function, the linear differential operators form a vector space over the real numbers or the complex numbers (depending on the nature of the functions that are considered). They form also a free module over the ring of differentiable functions.

The language of operators allows a compact writing for differentiable equations: if $$L = a_0(x)+a_1(x)\frac{d}{dx} + \cdots +a_n(x)\frac{d^n}{dx^n},$$ is a linear differential operator, then the equation $$a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^{(n)}=b(x)$$ may be rewritten $$Ly=b(x).$$

There may be several variants to this notation; in particular the variable of differentiation may appear explicitly or not in $y$ and the right-hand and of the equation, such as $Ly(x) = b(x)$ or $Ly = b$.

The kernel of a linear differential operator is its kernel as a linear mapping, that is the vector space of the solutions of the (homogeneous) differential equation $Ly = 0$.

In the case of an ordinary differential operator of order $n$, Carathéodory's existence theorem implies that, under very mild conditions, the kernel of $L$ is a vector space of dimension $n$, and that the solutions of the equation $Ly(x) = b(x)$ have the form $$S_0(x) + c_1S_1(x) + \cdots + c_n S_n(x),$$ where $c_{1}, ..., c_{n}$ are arbitrary numbers. Typically, the hypotheses of Carathéodory's theorem are satisfied in an interval $I$, if the functions $b, a_{0}, ..., a_{n}$ are continuous in $I$, and there is a positive real number $k$ such that $|a_{n}(x)| > k$ for every $x$ in $I$.

Homogeneous equation with constant coefficients
A homogeneous linear differential equation has constant coefficients if it has the form $$a_0y + a_1y' + a_2y'' + \cdots + a_n y^{(n)} = 0$$ where $a_{1}, ..., a_{n}$ are (real or complex) numbers. In other words, it has constant coefficients if it is defined by a linear operator with constant coefficients.

The study of these differential equations with constant coefficients dates back to Leonhard Euler, who introduced the exponential function $e^{x}$, which is the unique solution of the equation $f′ = f$ such that $f(0) = 1$. It follows that the $n$th derivative of $e^{cx}$ is $c^{n}e^{cx}$, and this allows solving homogeneous linear differential equations rather easily.

Let $$a_0y + a_1y' + a_2y'' + \cdots + a_ny^{(n)} = 0$$ be a homogeneous linear differential equation with constant coefficients (that is $a_{0}, ..., a_{n}$ are real or complex numbers).

Searching solutions of this equation that have the form $e^{αx}$ is equivalent to searching the constants $α$ such that $$a_0e^{\alpha x} + a_1\alpha e^{\alpha x} + a_2\alpha^2 e^{\alpha x}+\cdots + a_n\alpha^n e^{\alpha x} = 0.$$ Factoring out $e^{αx}$ (which is never zero), shows that $α$ must be a root of the characteristic polynomial $$a_0 + a_1t + a_2 t^2 + \cdots + a_nt^n$$ of the differential equation, which is the left-hand side of the characteristic equation $$a_0 + a_1t + a_2 t^2 + \cdots + a_nt^n = 0.$$

When these roots are all distinct, one has $n$ distinct solutions that are not necessarily real, even if the coefficients of the equation are real. These solutions can be shown to be linearly independent, by considering the Vandermonde determinant of the values of these solutions at $x = 0, ..., n – 1$. Together they form a basis of the vector space of solutions of the differential equation (that is, the kernel of the differential operator). In the case where the characteristic polynomial has only simple roots, the preceding provides a complete basis of the solutions vector space. In the case of multiple roots, more linearly independent solutions are needed for having a basis. These have the form $$x^ke^{\alpha x},$$ where $i$ is a nonnegative integer, $k$ is a root of the characteristic polynomial of multiplicity $α$, and $−i$. For proving that these functions are solutions, one may remark that if $m$ is a root of the characteristic polynomial of multiplicity $α$, the characteristic polynomial may be factored as $1$. Thus, applying the differential operator of the equation is equivalent with applying first $m$ times the operator $ \frac{d}{dx} - \alpha $, and then the operator that has $m$ as characteristic polynomial. By the exponential shift theorem, $$\left(\frac{d}{dx}-\alpha\right)\left(x^ke^{\alpha x}\right)= kx^{k-1}e^{\alpha x},$$

and thus one gets zero after $k < m$ application of $ \frac{d}{dx} - \alpha $.

As, by the fundamental theorem of algebra, the sum of the multiplicities of the roots of a polynomial equals the degree of the polynomial, the number of above solutions equals the order of the differential equation, and these solutions form a base of the vector space of the solutions.

In the common case where the coefficients of the equation are real, it is generally more convenient to have a basis of the solutions consisting of real-valued functions. Such a basis may be obtained from the preceding basis by remarking that, if $P(t)(t − α)^{m}$ is a root of the characteristic polynomial, then $k + 1$ is also a root, of the same multiplicity. Thus a real basis is obtained by using Euler's formula, and replacing $$x^ke^{(a+ib)x}$$ and $$x^ke^{(a-ib)x}$$ by $$x^ke^{ax} \cos(bx)$$ and $$x^ke^{ax} \sin(bx)$$.

Second-order case
A homogeneous linear differential equation of the second order may be written $$y'' + ay' + by = 0,$$ and its characteristic polynomial is $$r^2 + ar + b.$$

If $P$ and $a$ are real, there are three cases for the solutions, depending on the discriminant $a + ib$. In all three cases, the general solution depends on two arbitrary constants $a – ib$ and $D = a^{2} − 4b$.

 * If $c_{1}$, the characteristic polynomial has two distinct real roots $b$, and $α$. In this case, the general solution is $$c_1 e^{\alpha x} + c_2 e^{\beta x}.$$
 * If $c_{2}$, the characteristic polynomial has a double root $D > 0$, and the general solution is $$(c_1 + c_2 x) e^{-ax/2}.$$
 * If $D = 0$, the characteristic polynomial has two complex conjugate roots $−a/2$, and the general solution is $$c_1 e^{(\alpha + \beta i)x} + c_2 e^{(\alpha - \beta i)x},$$ which may be rewritten in real terms, using Euler's formula as $$ e^{\alpha x} (c_1\cos(\beta x) + c_2 \sin(\beta x)).$$

Finding the solution $D < 0$ satisfying $α ± βi$ and $y(x)$, one equates the values of the above general solution at $y(0) = d_{1}$ and its derivative there to $y′(0) = d_{2}$ and $0$, respectively. This results in a linear system of two linear equations in the two unknowns $d_{1}$ and $d_{2}$. Solving this system gives the solution for a so-called Cauchy problem, in which the values at $c_{1}$ for the solution of the DEQ and its derivative are specified.

Non-homogeneous equation with constant coefficients
A non-homogeneous equation of order $β$ with constant coefficients may be written $$y^{(n)}(x) + a_1 y^{(n-1)}(x) + \cdots + a_{n-1} y'(x)+ a_ny(x) = f(x),$$ where $c_{2}$ are real or complex numbers, $n$ is a given function of $f$, and $x$ is the unknown function (for sake of simplicity, "$0$" will be omitted in the following).

There are several methods for solving such an equation. The best method depends on the nature of the function $y$ that makes the equation non-homogeneous. If $f$ is a linear combination of exponential and sinusoidal functions, then the exponential response formula may be used. If, more generally, $f$ is a linear combination of functions of the form $a_{1}, ..., a_{n}$, $(x)$, and $x^{n}e^{ax}$, where $f$ is a nonnegative integer, and $n$ a constant (which need not be the same in each term), then the method of undetermined coefficients may be used. Still more general, the annihilator method applies when $a$ satisfies a homogeneous linear differential equation, typically, a holonomic function.

The most general method is the variation of constants, which is presented here.

The general solution of the associated homogeneous equation $$y^{(n)} + a_1 y^{(n-1)} + \cdots + a_{n-1} y'+ a_ny = 0$$ is $$y=u_1y_1+\cdots+ u_ny_n,$$ where $x^{n} cos(ax)$ is a basis of the vector space of the solutions and $x^{n} sin(ax)$ are arbitrary constants. The method of variation of constants takes its name from the following idea. Instead of considering $(y_{1}, ..., y_{n})$ as constants, they can be considered as unknown functions that have to be determined for making $f$ a solution of the non-homogeneous equation. For this purpose, one adds the constraints $$\begin{align} 0 &= u'_1y_1 + u'_2y_2 + \cdots+u'_ny_n \\ 0 &= u'_1y'_1 + u'_2y'_2 + \cdots + u'_n y'_n \\ &\;\;\vdots \\ 0 &= u'_1y^{(n-2)}_1+u'_2y^{(n-2)}_2 + \cdots + u'_n y^{(n-2)}_n, \end{align}$$ which imply (by product rule and induction) $$y^{(i)} = u_1 y_1^{(i)} + \cdots + u_n y_n^{(i)}$$ for $u_{1}, ..., u_{n}$, and $$y^{(n)} = u_1 y_1^{(n)} + \cdots + u_n y_n^{(n)} +u'_1y_1^{(n-1)}+u'_2y_2^{(n-1)}+\cdots+u'_ny_n^{(n-1)}.$$

Replacing in the original equation $y$ and its derivatives by these expressions, and using the fact that $u_{1}, ..., u_{n}$ are solutions of the original homogeneous equation, one gets $$f=u'_1y_1^{(n-1)} + \cdots + u'_ny_n^{(n-1)}.$$

This equation and the above ones with $i = 1, ..., n – 1$ as left-hand side form a system of $y$ linear equations in $y_{1}, ..., y_{n}$ whose coefficients are known functions ($n$, the $0$, and their derivatives). This system can be solved by any method of linear algebra. The computation of antiderivatives gives $u′_{1}, ..., u′_{n}$, and then $yi$.

As antiderivatives are defined up to the addition of a constant, one finds again that the general solution of the non-homogeneous equation is the sum of an arbitrary solution and the general solution of the associated homogeneous equation.

First-order equation with variable coefficients
The general form of a linear ordinary differential equation of order 1, after dividing out the coefficient of $u_{1}, ..., u_{n}$, is: $$y'(x) = f(x) y(x) + g(x).$$

If the equation is homogeneous, i.e. $y = u_{1}y_{1} + ⋯ + u_{n}y_{n}$, one may rewrite and integrate: $$\frac{y'}{y}= f, \qquad \log y = k +F, $$ where $f$ is an arbitrary constant of integration and $$F=\textstyle\int f\,dx$$ is any antiderivative of $k$. Thus, the general solution of the homogeneous equation is $$y=ce^F,$$ where $y′(x)$ is an arbitrary constant.

For the general non-homogeneous equation, it is useful to multiply both sides of the equation by the reciprocal $g(x) = 0$ of a solution of the homogeneous equation. This gives $$y'e^{-F}-yfe^{-F}= ge^{-F}.$$ As $f$ the product rule allows rewriting the equation as $$\frac{d}{dx}\left(ye^{-F}\right)= ge^{-F}.$$ Thus, the general solution is $$y=ce^F + e^F\int ge^{-F}dx,$$ where $-fe^{-F} = \tfrac{d}{dx} \left(e^{-F}\right),$ is a constant of integration, and $c$ is any antiderivative of $F$ (changing of antiderivative amounts to change the constant of integration).

Example
Solving the equation $$y'(x) + \frac{y(x)}{x} = 3x.$$ The associated homogeneous equation $$y'(x) + \frac{y(x)}{x} = 0$$ gives $$\frac{y'}{y}=-\frac{1}{x},$$ that is $$y=\frac{c}{x}.$$

Dividing the original equation by one of these solutions gives $$xy'+y=3x^2.$$ That is $$(xy)'=3x^2,$$ $$xy=x^3 +c,$$ and $$y(x)=x^2+c/x.$$ For the initial condition $$y(1)=\alpha,$$ one gets the particular solution $$y(x)=x^2+\frac{\alpha-1}{x}.$$

System of linear differential equations
A system of linear differential equations consists of several linear differential equations that involve several unknown functions. In general one restricts the study to systems such that the number of unknown functions equals the number of equations.

An arbitrary linear ordinary differential equation and a system of such equations can be converted into a first order system of linear differential equations by adding variables for all but the highest order derivatives. That is, if $f$ appear in an equation, one may replace them by new unknown functions $y', y'', \ldots, y^{(k)}$ that must satisfy the equations $y_1, \ldots, y_k$ and $y'=y_1$ for $c = e^{k}$.

A linear system of the first order, which has $y_i'=y_{i+1},$ unknown functions and $n$ differential equations may normally be solved for the derivatives of the unknown functions. If it is not the case this is a differential-algebraic system, and this is a different theory. Therefore, the systems that are considered here have the form $$\begin{align} y_1'(x) &= b_1(x) +a_{1,1}(x)y_1+\cdots+a_{1,n}(x)y_n\\[1ex] &\;\;\vdots\\[1ex] y_n'(x) &= b_n(x) +a_{n,1}(x)y_1+\cdots+a_{n,n}(x)y_n, \end{align}$$ where $n$ and the $b_n$ are functions of $a_{i,j}$. In matrix notation, this system may be written (omitting "$e^{−F}$") $$\mathbf{y}' = A\mathbf{y}+\mathbf{b}.$$

The solving method is similar to that of a single first order linear differential equations, but with complications stemming from noncommutativity of matrix multiplication.

Let $$\mathbf{u}' = A\mathbf{u}.$$ be the homogeneous equation associated to the above matrix equation. Its solutions form a vector space of dimension $x$, and are therefore the columns of a square matrix of functions $n$, whose determinant is not the zero function. If $y′ − fy = g$, or $U(x)$ is a matrix of constants, or, more generally, if $A$ commutes with its antiderivative $A$, then one may choose $\textstyle B=\int Adx$ equal the exponential of $U$. In fact, in these cases, one has $$\frac{d}{dx}\exp(B) = A\exp (B).$$ In the general case there is no closed-form solution for the homogeneous equation, and one has to use either a numerical method, or an approximation method such as Magnus expansion.

Knowing the matrix $B$, the general solution of the non-homogeneous equation is $$\mathbf{y}(x) = U(x)\mathbf{y_0} + U(x)\int U^{-1}(x)\mathbf{b}(x)\,dx,$$ where the column matrix $$\mathbf{y_0}$$ is an arbitrary constant of integration.

If initial conditions are given as $$\mathbf y(x_0)=\mathbf y_0,$$ the solution that satisfies these initial conditions is $$\mathbf{y}(x) = U(x)U^{-1}(x_0)\mathbf{y_0} + U(x)\int_{x_0}^x U^{-1}(t)\mathbf{b}(t)\,dt.$$

Higher order with variable coefficients
A linear ordinary equation of order one with variable coefficients may be solved by quadrature, which means that the solutions may be expressed in terms of integrals. This is not the case for order at least two. This is the main result of Picard–Vessiot theory which was initiated by Émile Picard and Ernest Vessiot, and whose recent developments are called differential Galois theory.

The impossibility of solving by quadrature can be compared with the Abel–Ruffini theorem, which states that an algebraic equation of degree at least five cannot, in general, be solved by radicals. This analogy extends to the proof methods and motivates the denomination of differential Galois theory.

Similarly to the algebraic case, the theory allows deciding which equations may be solved by quadrature, and if possible solving them. However, for both theories, the necessary computations are extremely difficult, even with the most powerful computers.

Nevertheless, the case of order two with rational coefficients has been completely solved by Kovacic's algorithm.

Cauchy–Euler equation
Cauchy–Euler equations are examples of equations of any order, with variable coefficients, that can be solved explicitly. These are the equations of the form $$x^n y^{(n)}(x) + a_{n-1} x^{n-1} y^{(n-1)}(x) + \cdots + a_0 y(x) = 0,$$ where $U$ are constant coefficients.

Holonomic functions
A holonomic function, also called a D-finite function, is a function that is a solution of a homogeneous linear differential equation with polynomial coefficients.

Most functions that are commonly considered in mathematics are holonomic or quotients of holonomic functions. In fact, holonomic functions include polynomials, algebraic functions, logarithm, exponential function, sine, cosine, hyperbolic sine, hyperbolic cosine, inverse trigonometric and inverse hyperbolic functions, and many special functions such as Bessel functions and hypergeometric functions.

Holonomic functions have several closure properties; in particular, sums, products, derivative and integrals of holonomic functions are holonomic. Moreover, these closure properties are effective, in the sense that there are algorithms for computing the differential equation of the result of any of these operations, knowing the differential equations of the input.

Usefulness of the concept of holonomic functions results of Zeilberger's theorem, which follows.

A holonomic sequence is a sequence of numbers that may be generated by a recurrence relation with polynomial coefficients. The coefficients of the Taylor series at a point of a holonomic function form a holonomic sequence. Conversely, if the sequence of the coefficients of a power series is holonomic, then the series defines a holonomic function (even if the radius of convergence is zero). There are efficient algorithms for both conversions, that is for computing the recurrence relation from the differential equation, and vice versa.

It follows that, if one represents (in a computer) holonomic functions by their defining differential equations and initial conditions, most calculus operations can be done automatically on these functions, such as derivative, indefinite and definite integral, fast computation of Taylor series (thanks of the recurrence relation on its coefficients), evaluation to a high precision with certified bound of the approximation error, limits, localization of singularities, asymptotic behavior at infinity and near singularities, proof of identities, etc.

title: Linear differential equation


text:
Talk:Nizkor Project

Usenet posts
This page seems only to exist to host a set of links to anti-Ken McVay Usenet posts. Can someone please write either write an NPOV encylopedia article here, or delete this? -- —Preceding unsigned comment added by 217.158.106.233 (talk • contribs)

 * There's not a single allegation in the McVay Files that isn't supported by public sources. If McVay and his cyber-Stasi goons find the contents of those files embarassing...too bad. The article is a stub. Feel free to balance it by adding more information, but deleting the article because it's not flattering to Nizkor/McVay...sounds suspiciously like censorship. -- Anon. 2

 * Notice that all those claiming that Ken McVay is a 'cyber-Stasi goon' post anonymously. That should give you a clue as to their credibility.

Just go to http://www.nizkor.org and see for yourself.
 * Only a denier would say that! Autarch 15:33, 14 December 2005 (UTC)

To anonymous user/LaylaD:

Please read up on NPOV again. Rhetoric like this:

 * . . .the maintainers of the web site display only those messages and material that are friendly to their ultra-Zionist agenda. . .

 * Google has also been instrumental in documenting the anti-Arab sentiments on the anti-revisionist side of the debate.

 * The Nizkor web site has been accused by revisionists and various Web sites as being funded by Israel and other Zionist sources. There is a good deal of evidence to support these accusations. ..

 * Regardless of McVay's strenuous denials, extremism clearly taints both sides of the debate. Ken McVay has been criticized for his obvious anti-Arab, anti-Black prejudices and ties with the ultra-Zionist fringe. For example, McVay has befriended racists who refer to Arabs as 'diaperheads' and tends to take a hard pro-Israel line matched only by Christian fundamentalists and others on the extreme right.

 * Unsurprisingly, McVay is uncritical of racists who happen to be Jewish and/or Zionist.

 *  Nizkor itself is increasingly seen as a hate group, since it aggressively supports the Israeli Holocaust against the Palestinian people.

does not fit the policy. And I'm not even a Zionist, so your allegations of "extremist-Zionist censorship" are rather silly. — No-One Jones (talk) 09:10, 21 Jan 2004 (UTC)

 * That kind of smears you cited are alas, all too typical of denier tactics. Autarch 15:33, 14 December 2005 (UTC)

 * What we're seeing here is a micro-thumbprint of what's been happening on alt.revisionism itself for at least the past ten years. And it hasn't even begun to get nasty...and hopefully it never will. --Modemac 10:30, 21 Jan 2004 (UTC)

 * Hopefully we won't - some of the deniers just don't seem organised enough to sustain such an attack on Wikipedia - those that are, don't seem too inclined to try, possibly because their lies will be pointed out very quickly, IMHO. Autarch 19:41, 10 January 2007 (UTC)

Other Site of Story:
Material Refuting Nizkor claims can be found at: http://www.vho.org/GB/Books/dth/found.html http://www.vho.org/GB/Books/trr/

George

 * In other words, more revisionist stuff. Nizkor already has a counterpoint to this guy, Germar Rudolf: http://www.nizkor.org/features/techniques-of-denial/forensic.html

--Modemac 12:55, 7 Mar 2004 (UTC)

Name
What does the name mean? Mikkalai 00:54, 13 Mar 2004 (UTC)

"Nizkor", as far as I recall, means "we will remember" in Hebrew. A fitting title. [[User:DO'Neil|DO'Иeil]] 07:35, Sep 9, 2004 (UTC)

Zinkor
Metzer seems to refer to Nizkor as Zinkor. Sholud Metzger speak German, then this could be a wordplay on the German word 'zinken' (verb) or 'Zinken' (noun) -- the verb describes a number of criminal activities, such as marking game cards, while the noun refers to the signs left in old days by hobos or gypsies on houses or other places to communicate with each other.

However, this is only if Metzger speaks German well enough to actually be aware of those meanings. Thought it might be interesting.

Dietwald 22:26, 17 September 2005 (UTC)

Spurious claims
I note that Matt Giwer denied posting anti-semitic statements - this is laughable, as I distinctly remember him posting such statements over the last decade to alt.revisionism. Indeed, he became something of an embarrassment to the denier cause, given that they were pretending to be objective historians and Giwers' support clearly showed the appeal of their nonsense to its' true audience. Autarch 15:38, 14 December 2005 (UTC)

The Trial Of Adolf Eichmann
There is a number of youtube posted the Eichmann trial sessions. McVay published the Record of Proceedings in the District Court of Jerusalem of The Trial Of Adolf Eichmann. It's disappointing to see how unprofessionally it was done. I spent some time listening the Session no 46. Both witnesses H. Salz and A. Arnon spoke German. Comparing the original of the testimonies to the ones recorded by McVay it is not possible to recognise McVay's toponyms in his Volume II: Session no 46: Licca (actually Lika), Ossetz (Osijek), Peniek (Tenje), Zarzecze (?) etc. McVay recorded in the same session "in Jasenovac, where 60,000 people perished", but Arnon said "in Jasenovac, where 600,000 people perished". Long ago, on some internet forum, McVay was warned about this wrong number but he refused admit it and correct it.--Taribuk (talk) 10:12, 30 August 2017 (UTC)

Malware?
Browsers such as Chrome, Firefox and Seamonkey are warning that nizkor.org is infected with malware. I think it is probably a false positive and my guess is that the site has been falsely reported by its enemies as I can't see anything obviously suspicious in its HTML. That said, it is best not to take any risks (It is possible that a compromised site might serve malware only to users running vulnerable browser versions so my check is not 100% conclusive) so I am about to edit the article and comment out all the URLs for nizkor.org. Please feel free to undo this once the matter is resolved and the site is no longer flagged as unsafe by browsers. --DanielRigal (talk) 22:34, 26 December 2018 (UTC)

 * OK. I have done that now. It has made a bit of a mess of the references in the reflist but I think this is better than sending people to a site that might be a risk to them. As I said before, please revert my changes once the site is no longer flagged as dangerous. --DanielRigal (talk) 22:41, 26 December 2018 (UTC)

I have fixed the url in the template then. — Preceding unsigned comment added by Zezen (talk • contribs)

 * I can't see any problems now so I've uncommented the remaining commented out URLs. Not all of them work, as the site has been reorganised. If anybody wants to have a go at fixing them then please go ahead. --DanielRigal (talk) 10:40, 25 November 2021 (UTC)

title: Talk:Nizkor Project


text:
Conversation analysis

Conversation analysis (CA) is an approach to the study of social interaction that empirically investigates the mechanisms by which humans achieve mutual understanding. It focuses on both verbal and non-verbal conduct, especially in situations of everyday life. CA originated as a sociological method, but has since spread to other fields. CA began with a focus on casual conversation, but its methods were subsequently adapted to embrace more task- and institution-centered interactions, such as those occurring in doctors' offices, courts, law enforcement, helplines, educational settings, and the mass media, and focus on multimodal and nonverbal activity in interaction, including gaze, body movement and gesture. As a consequence, the term conversation analysis has become something of a misnomer, but it has continued as a term for a distinctive and successful approach to the analysis of interactions. CA and ethnomethodology are sometimes considered one field and referred to as EMCA.

Conversation analysis should not be confused with other methods of analyzing conversation or interaction, such as other areas of pragmatics and discourse analysis.

History
Conversation analysis was developed in the late 1960s and early 1970s principally by the sociologist Harvey Sacks and his close associates Emanuel Schegloff and Gail Jefferson. Sacks was inspired by Harold Garfinkel's ethnomethodology and Erving Goffman's conception of what came to be known as the interaction order, but also a number of minor sources of contemporary influences such as the generativism of Noam Chomsky and its focus on building an apparatus. The speech act theory of John Searle was a parallel development rather than influencing or influenced by CA. Today CA is an established method used in sociology, anthropology, linguistics, speech-communication and psychology, and has developed subfields such as interactional sociolinguistics and interactional linguistics, discourse analysis and discursive psychology.

Method
The method consists of detailed qualitative analysis of stretches of interaction between a number of people, often with accompanied by a detailed transcription. Most studies rely on a collection of cases, often from different interactions with different people, but some studies also focus on a single-case analysis. Crucially, the method uses the fact that interaction consists of multiple participants and that they make sense of each other, so the method proceeds by considering e.g. how one turn by a specific participant displays an understanding of the previous turn by another participant (or other earlier interaction). This is commonly referred to as the next-turn proof procedure even though proof is not to be taken literally. Research questions revolve around participants' orientation, that is, what features (linguistic or other) that cues people to respond in certain ways and influence the trajectory of an interaction. A key part of the method are deviant cases in collections, as they show that when a participant does not follow a norm, the interaction is affected in a way that reveals the existence of the norm in focus.

The data used in CA is in the form of video- or audio-recorded conversations, collected with or without researchers' involvement, typically from a video camera or other recording device in the space where the conversation takes place (e.g. a living room, picnic, or doctor's office). The researchers construct detailed transcriptions from the recordings, containing as much detail as is possible.

The transcription often contains additional information about nonverbal communication and the way people say things. Jeffersonian transcription is a commonly used method of transcription and nonverbal details are often transcribed according to Mondadan conventions by Lorenza Mondada.

After transcription, the researchers perform inductive data-driven analysis aiming to find recurring patterns of interaction. Based on the analysis, the researchers identify regularities, rules or models to describe these patterns, enhancing, modifying or replacing initial hypotheses. While this kind of inductive analysis based on collections of data exhibits is basic to fundamental work in CA, it has been more common in recent years to also use statistical analysis in applications of CA to solve problems in medicine and elsewhere.

While conversation analysis provides a method of analysing conversation, this method is informed by an underlying theory of what features of conversation are meaningful and the meanings that are likely implied by these features. Additionally there is a body of theory about how to interpret conversation.

Basic structures
Conversation analysis provides a model that can be used to understand interactions, and offers a number of concepts to describe them. The following section contains important concepts and phenomena identified in the conversation analytical literature, and will refer to articles that are centrally concerned with the phenomenon. A conversation is viewed as a collection of turns of speaking; errors or misunderstandings in speech are addressed with repairs, and turns may be marked by the delay between them or other linguistic features.

Turn-taking organization
The analysis of turn-taking started with the description in a model in the paper known as the Simplest Systematics, which was very programmatic for the field of Conversation analysis and one of the most cited papers published in the journal Language.

The model is designed to explain that when people talk in conversation, they do not always talk all at the same time, but generally, one person speaks at a time, and then another person can follow. Such a contribution to a conversation by one speaker is then a turn. A turn is created through certain forms or units that listeners can recognize and count on, called turn construction units (TCUs), and speakers and listeners will know that such forms can be a word or a clause, and use that knowledge to predict when a speaker is finished so that others can speak, to avoid or minimize both overlap and silence. A listener will look for the places where they can start speaking - so-called transition relevant places (TRPs) - based on how the units appear over time. Turn construction units can be created or recognized via four methods, i.e. types of unit design:
 * Grammatical methods, i.e. morphosyntactic structures.
 * Prosodic methods, e.g. pitch, speed and changes in pronunciation.
 * Pragmatic methods: turns perform actions, and at the point where listeners have heard enough and know enough, a turn can be pragmatically complete.
 * Visual methods: Gesture, gaze and body movement is also used to indicate that a turn is over. For example, a person speaking looks at the next speaker when their turn is about to end.

Each time a turn is over, speakers also have to decide who can talk next, and this is called turn allocation. The rules for turn allocation is commonly formulated in the same way as in the original Simplest Systematics paper, with 2 parts where the first consists of 3 elements:

 * 1) * a. If the current speaker selects a next one to speak at the end of current TCU (by name, gaze or contextual aspects of what is said), the selected speaker has the right and obligation to speak next.
 * 2) * b. If the current speaker does not select a next speaker, other potential speakers have the right to self-select (the first starter gets the turn)
 * 3) * c. If options 1a and 1b have not been implemented, current speaker may continue with another TCU.
 * 4) At the end of that TCU, the option system applies again.

Based on the turn-taking system, three types of silence may be distinguished:
 * Pause: A period of silence within a speaker's TCU, i.e. during a speaker's turn when a sentence is not finished.
 * Gap: A period of silence between turns, for example after a question has been asked and not yet answered
 * Lapse: A period of silence when no sequence or other structured activity is in progress: the current speaker stops talking, does not select a next speaker, and no one self selects. Lapses are commonly associated with visual or other forms of disengagement between speakers, even if these periods are brief.

Some types of turns may require extra work before they can successfully take place. Speakers wanting a long turn, for example to tell a story or describe important news, must first establish that others will not intervene during the course of the telling through some form of preface and approval by the listener (a so-called go-ahead). The preface and its associated go-ahead comprise a pre-sequence. Conversations cannot be appropriately ended by 'just stopping', but require a special closing sequence.

The model also leaves puzzles to be solved, for example concerning how turn boundaries are identified and projected, and the role played by gaze and body orientation in the management of turn-taking. It also establishes some questions for other disciplines: for example, the split second timing of turn-transition sets up a cognitive 'bottle neck' in which potential speakers must attend to incoming speech while also preparing their own contribution - something which imposes a heavy load of human processing capacity, and which may impact the structure of languages.

However, the original formulation in Sacks et al.1974 is designed to model turn-taking only in ordinary and informal conversation, and not interaction in more specialized, institutional environments such as meetings, courts, news interviews, mediation hearings, which have distinctive turn-taking organizations that depart in various ways from ordinary conversation. Later studies have looked at institutional interaction and turn-taking in institutional contexts. Interruptions have also been examined and analyzed.

Adjacency pairs
Talk tends to occur in responsive pairs; however, the pairs may be split over a sequence of turns. Adjacency pairs divide utterance types into first pair parts and second pair parts to form a pair type. There are many examples of adjacency pairs including Questions-Answers, Offer-Acceptance/Refusal and Compliment-Response.

Sequence expansion
Sequence expansion allows talk which is made up of more than a single adjacency pair to be constructed and understood as performing the same basic action and the various additional elements are as doing interactional work related to the basic action underway. Sequence expansion is constructed in relation to a base sequence of a first pair part (FPP) and a second pair part (SPP) in which the core action underway is achieved. It can occur prior to the base FPP, between the base FPP and SPP, and following the base SPP.
 * Pre-expansion: an adjacency pair that may be understood as preliminary to the main course of action. A generic pre-expansion is a summon-answer adjacency pair, as in "Mary?"/ "Yes?".It is generic in the sense that it does not contribute to any particular types of base adjacency pair, such as request or suggestion. There are other types of pre-sequence that work to prepare the interlocutors for the subsequent speech action. For example, "Guess what!"/"What?" as preliminary to an announcement of some sort, or "What are you doing?"/"Nothing" as preliminary to an invitation or a request.
 * Insert expansion: an adjacency pair that comes between the FPP and SPP of the base adjacency pair. Insert expansions interrupt the activity under way, but are still relevant to that action. Insert expansion allows a possibility for a second speaker, the speaker who must produce the SPP, to do interactional work relevant to the projected SPP. An example of this would be a typical conversation between a customer and a shopkeeper:
 * Customer: I would like a turkey sandwich, please. (FPP base)
 * Server: White or wholegrain? (Insert FPP)
 * Customer: Wholegrain. (Insert SPP)
 * Server: Okay. (SPP base)

 * Post-expansion: a turn or an adjacency pair that comes after, but is still tied to, the base adjacency pair. There are two types: minimal and non-minimal. Minimal expansion is also termed sequence closing thirds, because it is a single turn after the base SPP (hence third) that does not project any further talk beyond their turn (hence closing). Examples of sequence closing thirds include "oh", "I see", "okay", etc.

Preference organization
CA may reveal structural (i.e. practice-underwritten) preferences in conversation for some types of actions (within sequences of action) over others, as responses in certain sequential environments. For example, responsive actions which agree with, or accept, positions taken by a first action tend to be performed more straightforwardly and faster than actions that disagree with, or decline, those positions. The former is termed a preferred turn shape, meaning the turn is not preceded by silence nor is it produced with delays, mitigation and accounts. The latter is termed a dispreferred turn shape, which describes a turn with opposite characteristics. One consequence of this is that agreement and acceptance are promoted over their alternatives, and are more likely to be the outcome of the sequence. Pre-sequences are also a component of preference organization and contribute to this outcome.

Repair
Repair organization describes how parties in conversation deal with problems in speaking, hearing, or understanding, and there are various mechanisms through which certain "troubles" in interaction are dealt with. Repair segments are classified by who initiates repair (self or other), by who resolves the problem (self or other), and by how it unfolds within a turn or a sequence of turns. The organization of repair is also a self-righting mechanism in social interaction. Participants in conversation seek to correct the trouble source by initiating and preferring self repair, the speaker of the trouble source, over other repair. Self repair initiations can be placed in three locations in relation to the trouble source, in a first turn, a transition space or in a third turn.

Action formation
Turns in interaction implement actions, and a specific turn may perform one (or more) specific actions. The study of action focuses on the description of how turns at talk are composed and positioned so as to realize one or more actions. This could include questions, assessments, storytelling, and complaints. Focus is both on how those actions are formed through linguistic or other activity (the formation of action) and how they are understood (the ascription of action to turns). The study of action also concerns the ways in which the participants’ knowledge, relations, and stances towards the ongoing interactional projects are created, maintained, and negotiated, and thus the intersubjectivity of how people interact. The concept of action within CA resembles, but is different from the concept of speech act in other fields of pragmatics.

Jeffersonian transcription
Gail Jefferson developed a system of transcription while working with Harvey Sacks. In this system, speakers are introduced with a name followed by a colon, as conventionally used in scripts. It is designed to use typographical and orthographical conventions used elsewhere, rather than a strict phonetic system such as the International Phonetic Alphabet. The transcription conventions take into account overlapping speech, delays between speech, pitch, volume and speed based on research showing that these features matter for the conversation in terms of action, turn-taking and more. Transcripts are typically written in a monospaced font to ease the alignment of overlap symbols. There are various transcription systems based on the jeffersonian conventions with slight differences. Galina Bolden has designed a system for transcribing Russian conversations while Samtalegrammatik.dk uses their own system for Danish. GAT2 (Gesprächsanalytisches Transskriptionssystem 2) was also designed originally for German and to systematize the way some of the prosodic features are handled. The TalkBank also has its own system designed for use with its CLAN (CHILDES Language Analyzer) software.

Interactional linguistics
Interactional linguistics (IL) is Conversation analysis when the focus is on linguistic structure. While CA has worked with language in its data since the beginning, the interest in the structure of it, and possible relations to grammatical theory, was sometimes secondary to sociological (or ethnomethodological) research questions. The field developed during the 90's and got its name with the publication of the 2001 Studies in Interactional Linguistics and is inspired by West Coast functional grammar which is sometimes considered to have effectively merged with IL since then, but has also gained inspiration from British phoneticians doing prosodic analysis. Levinson's former department on Language and Cognition at the Max Planck Institute for Psycholinguistics has been important in connecting CA and IL with linguistic typology. Interactional linguistics has studied topics within syntax, phonetics and semantics as they relate to e.g. action and turn-taking. There is a journal called Interactional Linguistics.

Discursive psychology
Discursive psychology (DP) is the use of CA on psychological themes, and studies how psychological phenomena are attended to, understood and construed in interaction. The subfield formed through studies by Jonathan Potter and Margaret Wetherell, most notably their 1987 book Discourse and social psychology: Beyond attitudes and behaviour.

Membership categorization analysis
Membership categorization analysis (MCA) was influenced by the work of Harvey Sacks and his work on Membership Categorization Devices (MCD). Sacks argues that members' categories comprise part of the central machinery of organization and developed the notion of MCD to explain how categories can be hearably linked together by native speakers of a culture. His example that is taken from a children's storybook (The baby cried. The mommy picked it up) shows how "mommy" is interpreted as the mother of the baby by speakers of the same culture. In light of this, categories are inference rich – a great deal of knowledge that members of a society have about the society is stored in terms of these categories. Stokoe further contends that members’ practical categorizations form part of ethnomethodology's description of the ongoing production and realization of ‘facts’ about social life and including members’ gendered reality analysis, thus making CA compatible with feminist studies.

Contrasts to other theories about language
In contrast to the use of introspection in linguistics, conversation analysis studies naturally-occurring talk in a strongly empirical fashion through the use of recordings In contrast to the theory developed by John Gumperz, CA maintains it is possible to analyze talk-in-interaction by examining its recordings alone (audio for telephone, video for copresent interaction). CA researchers do not believe that the researcher needs to consult with the talk participants or members of their speech community.

It is distinct from discourse analysis in focus and method. (i) Its focus is on processes involved in social interaction and does not include written texts or larger sociocultural phenomena (for example, 'discourses' in the Foucauldian sense). (ii) Its method, following Garfinkel and Goffman's initiatives, is aimed at determining the methods and resources that the interacting participants use and rely on to produce interactional contributions and make sense of the contributions of others. Thus CA is neither designed for, nor aimed at, examining the production of interaction from a perspective that is external to the participants' own reasoning and understanding about their circumstances and communication. Rather the aim is to model the resources and methods by which those understandings are produced.

In considering methods of qualitative analysis, Braun and Clarke distinguish thematic analysis from conversation analysis and discourse analysis, viewing thematic analysis to be theory agnostic while conversation analysis and discourse analysis are considered to be based on theories.

Applied conversation analysis
Conversation analysis is used in various contexts leading to a number of different fields benefitting from conversation analytic findings. This includes the study of doctor-patient interactions, media interviews, second-language acquisition, and various institutional settings. For instance, Tanya Stivers studied the pressures that lead to doctors prescribing antibiotics. A focus on interaction in professional contexts was established by the 1992 book Talk at Work by Paul Drew and John Heritage, but earlier studies had also focused on specific institutional contexts, mostly one at a time. More recently, conversation analysis has also been used in the development of conversational user interfaces and chatbots.

Criticism
Conversation analysis has been criticized for not being able to address issues of power and inequality in society at large. Another point of critique is the focus on single-case analysis and the generalizability of collection-based descriptions has been questioned.

title: Conversation analysis