title: Mongolian People's Party

text: In the 2009 Mongolian presidential election, Democratic Party candidate Tsakhiagiin Elbegdorj defeated MPRP candidate and incumbent president Nambaryn Enkhbayar. In January 2012, the Democratic Party decided to leave the coalition government before the June parliamentary elections. In the 2012 parliamentary elections, the Democratic Party defeated the MPP; the MPP became the opposition, with 26 seats in parliament. In the 2012 local elections in Ulaanbaatar, the provinces and districts, the MPP was defeated for the first time in Mongolia's history. In the 2013 Mongolian presidential election, the Democratic Party candidate and incumbent president Tsakhiagiin Elbegdorj again defeated the MPP candidate.


title: Mongolian People's Party

text: The MPP returned to power in 2016, winning an 85-percent majority of parliamentary seats. Prime Minister Chimed Saikhanbileg and parliament chairman Zandaakhuu Enkhbold were defeated, with the MPP's Jargaltulga Erdenebat elected to succeed Saikhanbileg.


title: Mongolian People's Party

text: The restoration of the party name to the Mongolian People’s Party had been at the core of discussions among party members and at party congresses since 1990. In 2010, it was extensively deliberated at all party levels, resulting on 81.3 percent of the membership supporting the restoration of the Mongolian People’s Party name and 10.7 percent of the membership wanting to deliberate the matter during the 26th party congress. The decision to restore the party's original name was approved by 99.3 percent of the delegates to the 26th party congress. At the congress, the party’s political ideology was refocused from democratic socialism to social democracy.


title: Mongolian People's Party

text: After the MPRP restored its original name, former Mongolian president and MPRP chairman Nambaryn Enkhbayar founded a new political party in 2010. Enkhbayar received permission to use the name Mongolian People's Revolutionary Party for his new party from the Supreme Court of Mongolia on 24 June 2011.


title: Mongolian People's Party

text: The MPP won a landslide victory in the 2020 parliamentary election. The party's election platform had six chapters and addresses population income, economic policy, governance, green development policy, Ulaanbaatar city development, and regional development policy. The election result marked the first time a single party has retained an absolute majority in consecutive elections. Previously the Mongolian People's Party and the Democratic Party had taken turns wielding a majority in the State Great Khural or were compelled to form coalition governments.


title: Mongolian People's Party

text: In June 2021, former prime minister Ukhnaa Khurelsukh of the MPP became the country's sixth democratically elected president after winning the presidential election, further consolidating the party's power in the Mongolian government.


title: Sergey Naryshkin

text: Sergey Yevgenyevich Naryshkin (; born 27 October 1954) is a Russian politician and businessman who has served as the director of the Foreign Intelligence Service since 2016. Previously, he was Chairman of the State Duma (2011–2016) and Kremlin Chief of Staff (2008–2012); he was also chairman of the Historical Truth Commission in May 2009 until it was dissolved in February 2012.


title: Sergey Naryshkin

text: Sergei Yevgenyevich Naryshkin was born in Leningrad and graduated from Leningrad Institute of Mechanics with a degree in engineering in 1978, and, in 1978, he was the first secretary of its Komsomol which was the Communist Party's youth wing. From 1978, Naryshkin studied at the Moscow Higher School of the KGB () for two years in the French section while Nikolay Tokarev also studied at the Higher School of the KGB at the same time. In the 1990s he also graduated from International Management Institute of Saint Petersburg with a degree in economics.


title: Sergey Naryshkin

text: In 2015, Naryshkin's dissertation in economics was exposed as fraudulent in an investigation by Dissernet, with more than half of the text plagiarized from other publications.


title: Sergey Naryshkin

text: In 1982, Naryshkin was appointed Deputy Vice-Rector of the Leningrad Polytechnical Institute. From 1988 to 1992, he worked in the Soviet Embassy in Brussels as an expert in the State Committee on Science and Technologies in the office of the economic adviser, but Alexei Pastyukhov, a childhood friend, stated that Naryshkin worked as third secretary. Some sources suggest that while there he began to work for the KGB after he had been at a group of the KGB Higher School where he and Vladimir Putin were fellow students.


title: Sergey Naryshkin

text: From 1992 until 1995, he worked in the Committee for Economy and Finance of Saint Petersburg Mayor Office. After he left, he became the chief of the external investment department of Promstroybank—a position he would hold until 1997. From 1997 until 1998, Naryshkin led the Investment Department of the Leningrad Oblast government. From 1998 until 2004, he was the Chairman of the Committee for External Economic and International Relations of the government of Leningrad Oblast.


title: Sergey Naryshkin

text: In early 2004, he was a deputy head of the economic department of the Russian presidential administration. From March through September 2004, Naryshkin was a deputy chief of staff of the Russian government.


title: Sergey Naryshkin

text: Since 2004, he has been a member of the board of directors of Sovkomflot and a deputy chairman of the board of directors of Rosneft. Since 31 August 2004, Naryshkin has also been Chairman of the Board of Directors of Channel One of the Russian television.


title: Sergey Naryshkin

text: Since 13 September 2004, he has been a Minister, Chief of Staff of the Government of Russia. On 15 February 2007, President Vladimir Putin announced that Naryshkin had been appointed Deputy Prime Minister of Russia for external economic activity, focusing on collaboration with the Commonwealth of Independent States.


title: Sergey Naryshkin

text: Naryshkin was elected to the State Duma, the lower house of the Russian parliament in December 2011. When the Duma began meeting for its new term on 21 December 2011, Naryshkin was elected as Chairman of the State Duma; he received 238 votes in favor of his candidacy, while 88 deputies opposed him.


title: Sergey Naryshkin

text: In June 2012, Naryshkin signed a resolution on setting up a culture council under the State Duma speaker. The council is “a standing advisory body”. The tasks of the council are “the examination and drafting of initiatives on topical problems of legislative regulations in culture and associated industries, the development of recommendations on culture for the use in lawmaking”.


title: Sergey Naryshkin

text: Since the rise of tensions between European Union and Russia in 2014, Naryshkin was perceived as one of the main coordinators of contacts with European far-right and far-left parties supporting Russian foreign policy in Europe.


title: Sergey Naryshkin

text: As a result of the 2014 Crimean crisis, the federal government of the United States under Barack Obama blacklisted Naryshkin and other close friends of the Russian president, including Sergei Ivanov and Gennadi Timchenko. Nevertheless, he officially visited the U.S., along with other Russian top security chiefs, at the end of January 2018.


title: Sergey Naryshkin

text: In November 2021, Naryshkin dismissed reports of a possible invasion of Ukraine asserting that it was "malicious propaganda by the US State Department".


title: Sergey Naryshkin

text: Days before Russia invaded Ukraine in February 2022, Naryshkin received widespread attention in the global press for visibly trembling and "stutter[ing] uncomfortably" as Putin humiliated him publicly for "fumbling" his response to the Russian President's questioning during a Security Council of Russia meeting concerning recognizing the Russian-backed separatist regions of Donetsk and Luhansk.


title: Sergey Naryshkin

text: On 6 April 2022 in response to the 2022 Russian invasion of Ukraine, the Office of Foreign Assets Control of the United States Department of the Treasury added Naryshkin to its list of persons sanctioned pursuant to .


title: Sergey Naryshkin

text: Naryshkin is the Chairman of the Board of Trustees of the Russian Presidential Academy of National Economy and Public Administration (RANEPA).


title: Dan Patrick (politician)

text: Dan Goeb Patrick (born Dannie Scott Goeb; April 4, 1950) is an American radio talk show host, television broadcaster, and politician. He has been serving as the 42nd lieutenant governor of Texas since January 2015, under Greg Abbott.


title: Dan Patrick (politician)

text: Originally from Baltimore, Maryland, Patrick began his career as a radio and television broadcaster. After forming a chain of sports bars and subsequently going bankrupt, he became a radio host again, this time becoming a conservative commentator. From 2007 to 2015, Patrick was a Republican member of the Texas Senate for the 7th District, which included a small portion of the city of Houston and several Houston-area suburbs located mostly in northwest Harris County.


title: Dan Patrick (politician)

text: Patrick defeated three-term incumbent David Dewhurst in the primary runoff for lieutenant governor on May 27, 2014. He then won the position in the fall general election. He was re-elected in 2018 and 2022, defeating Democratic nominee Mike Collier.


title: Dan Patrick (politician)

text: Patrick was born Dannie Scott Goeb in Baltimore on April 4, 1950. He was raised in a blue-collar neighborhood in East Baltimore. He is the only child of the former Vilma Jean Marshall (1926–2016) and Charles Anthony Goeb (1926–2002), who worked at "The Baltimore Sun" for thirty-one years as a newspaper vendor, before he retired in 1984.


title: Dan Patrick (politician)

text: Patrick graduated with a Bachelor of Arts in English from the University of Maryland, Baltimore County. He is the first member of his family to graduate from college. After graduating and embarking on a broadcasting career, he changed his name from "Dannie Scott Goeb" to "Dan Goeb Patrick" – informally in 1977 and legally in 2004 – to honor his wife's family and brother-in-law.


title: Dan Patrick (politician)

text: Patrick started his first radio job in 1968 at the age of 18. After college, in 1977, he became a television broadcaster at WNEP-TV in Scranton, Pennsylvania. Patrick later held a similar position at WTTG in Washington, D.C., before he became the lead sportscaster with KHOU-TV in Houston.


title: Dan Patrick (politician)

text: As a broadcaster, Patrick was able to get attention through various stunts, such as painting himself blue in support for the Houston Oilers and wearing a large cowboy hat. He became the second most popular TV personality in Houston by 1983, as well as one of the most well-known, though surveys also found that he was one of the most disliked. Patrick's public speaking skills caused him to be nicknamed "the Silver-tongued Devil." Patrick left his job at KHOU in the mid-1980s after failing to reach an agreement with Belo Corporation (which bought KHOU-TV in 1984) for a long-term contract.


title: Dan Patrick (politician)

text: In November 1983, Patrick and several investors opened one of the first sports bars in the U.S., which they named Dan and Nick's Sportsmarket. The bar did well for a time, due to "the strength of Patrick's personality" and an oil boom in Houston at the time, and they eventually took ownership of five sports bars in the city. Patrick's mother was the company bookkeeper. Questions later arose during the 2014 lieutenant governor's race about the immigration status of one of Patrick's employees, Miguel "Mike" Andrade. Patrick and Andrade offered different recollections about Andrade's employment. The matter was raised by one of Patrick's opponents, Jerry Patterson, who questioned Patrick's declared commitment to halt illegal immigration.


title: Dan Patrick (politician)

text: When the oil boom of the mid-80s ended, Houston's economy fell and fiscally damaged Patrick's sports bar chain. In 1986, after the sports bars failed, Patrick filed for personal bankruptcy and in October 1992, discharged several hundred thousand dollars of debt obligation. Patrick, who stated it took him 10 years for him and his family "to regain financial equilibrium," has frequently and openly discussed the ordeal and stated how it shaped him as an individual and conservative.


title: Dan Patrick (politician)

text: Following bankruptcy, Patrick reinvented himself as a conservative talk radio host in the 1990s. He began by buying a four-hour timeslot at AM 700 KSEV (then called KTBT) in the summer of 1987. He originally was a sports radio host, operating out of his remaining sports bar. However, he was able to take over the radio station in 1988, and he switched to politics shortly afterward. He hosted a conservative radio talk show. The program, "Dan Patrick & Friends", was broadcast in the Houston radio market on KSEV and in Dallas on AM 1160 KVCE. Initially he broadcast under the pseudonym "Dan Scott" as a radio host, later changing to the current name at the request of his employer to avoid confusion of Patrick with another anchor at a competing station with the last name of Scott.


title: Dan Patrick (politician)

text: Patrick grew successful and influential through his talk radio career. He earned high name recognition. As a talk radio host, Patrick advocated for fiscal conservatism, evangelical Christian values on social issues, and he became a vocal opponent of illegal immigration. He was also known as a populist. Patrick's talk radio career was instrumental to his political rise, including his election and influence in the State Senate and his eventual election as lieutenant governor. One notable decision Patrick made as the owner of a talk radio station was to sign relative unknown Rush Limbaugh for airing on KSEV in 1989 via radio syndication. Limbaugh's success as a national talk show host helped increase ratings of Patrick's radio station.


title: Dan Patrick (politician)

text: In addition to radio, Patrick anchored "The Patrick Report", a half-hour news program which aired on Houston television station KTBU during 2001. Patrick was also general manager of KTBU. By February 2006, Patrick already owned one radio station. In 2006, Patrick signed a deal to purchase radio station KMGS AM 1160 in Highland Park, Texas (now KBDT). By 2013, Patrick was the majority owner of two radio stations, in Houston and Dallas radio markets. Patrick continued broadcasting after his election as a State Senator, and he continued to own KSEV after his election as lieutenant governor.


title: Dan Patrick (politician)

text: In November 2008, Patrick began work to produce "The Heart of Texas", a movie based on a real-life story of two families in Simonton, a small Houston-area city. The movie was released the next year on DVD.


title: Dan Patrick (politician)

text: Patrick proposed a boycott of Bill Maher's television show "Politically Incorrect" over controversial statements made by the comedian following the 9/11 terrorist attacks. Patrick is also frequently at odds with the "Houston Chronicle" and announced a boycott of that newspaper in April 2004. He owned a blog called "Chronically Biased", which criticized the newspaper.


title: Dan Patrick (politician)

text: Patrick was first elected to Texas State Senate's seventh district in 2006, winning the primary election with 68.8% of the vote and the general election with 69.2% of the vote. His term began on January 9, 2007 with the convening of the Eightieth Texas Legislature.


title: Dan Patrick (politician)

text: In the 2010 general election, Patrick was reelected with 86.4% of the vote. He also endorsed Rick Perry for re-election in the 2010 election. Soon after winning re-election, Patrick announced, and subsequently created, a Tea Party Caucus in the Texas state legislature, which at its creation had 48 legislative members.


title: Dan Patrick (politician)

text: Patrick obtained passage of three Senate bills during his first session. In the Senate, Patrick actively advocated for a "fiercely conservative agenda." At the time, few of his proposals passed.


title: Dan Patrick (politician)

text: W. Gardner Selby, editor of the "Austin American-Statesman"'s "PolitiFact Texas", listed Patrick as third among the top 10 Republican political influencers in Texas. Patrick is also listed in "Texas Monthly" as one of the state's most powerful players.


title: Dan Patrick (politician)

text: During his first month as a legislator, Patrick introduced to make abortion in Texas illegal should the Supreme Court overturn "Roe v. Wade".


title: Dan Patrick (politician)

text: In May 2012, acrimony between Patrick and fellow Republican state senator John Carona was widely reported throughout Texas. In an email exchange, Patrick accused Carona of spreading false rumors about Patrick's marriage. Carona denied that, and additionally denied having commented on Patrick's sexuality. Carona further said to Patrick: "I've never been shy about sharing my dislike and distrust of you. Put bluntly, I believe you are a snake oil salesman, a narcissist that would say anything to draw attention to himself." News reports suggest that the feud was motivated by positioning to succeed David Dewhurst as lieutenant governor should Dewhurst have won a seat as U.S. senator, in 2012.


title: Dan Patrick (politician)

text: On June 26, 2013, Patrick announced he would challenge incumbent David Dewhurst in the Republican primary for lieutenant governor in 2014. This challenge came despite Patrick's enthusiastic endorsement of Dewhurst in his failed 2012 bid for the U.S. Senate. Patrick stated that while he had been planning on retiring from politics after his Senate term ended, he decided to run for lieutenant governor after Dewhurst failed to end fellow State Senator Wendy Davis's filibuster of Texas Senate Bill 5 and after Senator Jane Nelson refused to run herself.


title: Dan Patrick (politician)

text: In his race for lieutenant governor, Patrick was endorsed in July 2013 by Mike Huckabee, the former governor of Arkansas who ran unsuccessfully for the 2008 Republican presidential nomination. In 2012, Huckabee had also endorsed David Dewhurst for the U.S. Senate nomination for the seat vacated by Kay Bailey Hutchison. Victory went, however, to the Republican Ted Cruz.


title: Dan Patrick (politician)

text: At a candidate forum in College Station in January 2014, Patrick said that he and two other challengers to Dewhurst, Jerry E. Patterson and Todd Staples, could have sought re-election in their current positions as Land Commissioner and Texas Commissioner of Agriculture, respectively, but were instead "putting our positions on the line because we need new leadership. ... An energetic, passionate conservative to lead the Senate."


title: Dan Patrick (politician)

text: At the candidate forum, Patrick described education as a key issue in his campaign because of the 25 percent statewide high school drop-out rate, rising to 40 to 50 percent in the inner cities. He stated that "we do not have a future in the state of Texas if we have half of the next adult population – majority being Hispanic – don't have a high school degree." Patrick said that as lieutenant governor, he would work to secure the border with Mexico and to abolish sanctuary cities and in-state tuition for illegal immigrants. He also called for lowering property taxes.


title: Dan Patrick (politician)

text: Patrick led the four-candidate field in the primary with 550,769 votes (41.5%). Dewhurst followed with 376,196 (28.3%); Staples, with 235,981 (17.8%), and Patterson, 165,787 (12.5%). Election watchers did not expect Patrick to get first place. In the runoff election on May 27, Patrick won with 487,829 votes (65.1%), defeating Dewhurst, who had 262,086 votes (34.9%). Patrick's victory was one of several notable primary victories by Tea Party movement-aligned Republicans in the election runoff.


title: Dan Patrick (politician)

text: According to Ross Ramsey of "The Texas Tribune", Patrick did not shift to the political middle as the general election approached, contrary to what political candidates typically do. On November 4, 2014, Patrick won the general election against his state Senate colleague, Democrat Leticia Van de Putte of San Antonio, to become the lieutenant governor-elect of Texas. He was swept into office in a Republican landslide that saw the party retain all statewide elected offices for the fifth consecutive election.


title: Dan Patrick (politician)

text: On January 9, 2017, the day before the 85th Texas Legislature began its session, Patrick announced he would run for re-election in 2018. He stated his early announcement was in order to dispel rumors that he would challenge Governor Greg Abbott or U.S. Senator Ted Cruz. Patrick easily won the Republican primary on March 6, 2018, defeating Rockwall City Council Member Scott Milder.


title: Dan Patrick (politician)

text: In addition to his own campaign, Patrick was active in endorsing and assisting Republican primary candidates in the Texas Senate, including some challengers to GOP incumbents. Patrick's favored candidates won nearly all the races where Patrick made intraparty endorsements. Later in the year, Patrick donated nearly $175,000 to Texas Senate candidate Pete Flores in a special election; Flores won the election in an upset, increasing Patrick's chances of keeping a three-fifths GOP majority in the Senate after the 2018 elections. Patrick succeeded in maintaining a three-fifths majority in the Senate, though Republican Senator Kel Seliger was considered a possible swing-vote.


title: Dan Patrick (politician)

text: In the November 6 general election, Patrick won re-election to a second term, defeating Democratic challenger Mike Collier. He won about 51% of the vote against Collier's 46%.


title: Dan Patrick (politician)

text: In the 2022 general election, Patrick again defeated Democratic challenger Mike Collier, winning about 53.8% of the vote to Collier's 43.5%.


title: Dan Patrick (politician)

text: Patrick was sworn in on January 20, 2015. Soon after assuming office, the Texas Senate voted to drop the threshold needed to consider a bill from two-thirds to three-fifths, something that Patrick had long supported. Under Patrick, the Senate enforced procedural rules that had long been ignored.


title: Dan Patrick (politician)

text: Major legislation that Patrick helped pass during his tenure as lieutenant governor include legalization of campus carry and open carry, a bill allowing pastors to refuse marrying couples if it violates their beliefs, and expanded border security and enforcement measures.


title: Dan Patrick (politician)

text: Patrick made legislation prohibiting state or local governments from issuing subpoenas on pastors' sermons a priority in the 2017 session. Governor Abbott signed the bill into law on May 21, 2017.


title: Dan Patrick (politician)

text: Patrick made legislation requiring the U.S. national anthem at state-funded events a priority for the 2021 session, along with legislation to protect "election integrity" in Texas. Otherwise, Patrick assumed a low-key profile at the beginning of the legislative session. Following the regular 2021 session, "The New York Times" described Patrick and Governor Abbott as "the driving force behind one of the hardest right turns in recent state history," with Patrick the more conservative of the two. According to the "Houston Chronicle", Patrick "uniquely grasped and wielded the power of the growing right-wing movement in Texas," allowing him to become influential in the state.


title: Dan Patrick (politician)

text: Patrick actively endorsed candidates in the 2022 Republican primaries for the Texas Senate, something described as "unusual" for a lieutenant governor. He reportedly had an influential role in former president Donald Trump's endorsements in Texas elections.


title: Dan Patrick (politician)

text: Patrick opposes abortion and supported Texas' "Mandatory Ultrasound Bill", a bill signed into law in May 2011 by Governor Perry, which requires women seeking abortion to have a sonogram of the fetus taken at least twenty-four hours before the abortion is performed.


title: Dan Patrick (politician)

text: Patrick opposes abortion in cases of incest and rape. In January 2014, when he was asked about exceptions to outlawing abortion, Patrick said, "The only exception would be if the life of the mother was truly in danger…but that is rare."


title: Dan Patrick (politician)

text: In February 2011, Patrick, who at the time was vice chairman of the Texas senate's Committee on Education, spoke in favor of cutting an unspecified number of non-teaching positions from the state's public school districts, citing positions such as "math department supervisors" or "curriculum experts". At the time, Patrick cited a statistic later determined to be misleading by PolitiFact that Texas's 1,200+ public school districts, considered as a group, are the fifth-largest employer in the world.


title: Dan Patrick (politician)

text: Patrick has supported placing creationism within the public school curriculum in Texas, despite court rulings that such a policy would violate the First Amendment to the United States Constitution.


title: Dan Patrick (politician)

text: In 2021, Patrick supported legislation to prevent public schools from requiring that students read writings by prominent civil rights figures, such as Susan B. Anthony, Cesar Chavez, and Martin Luther King Jr., when covering women’s suffrage and the civil rights movement in social studies classes.


title: Dan Patrick (politician)

text: In 2022, Patrick pledged to end tenure for new hires at Texas public universities. He also said that he intended to revoke tenure for faculty who teach critical race theory.


title: Dan Patrick (politician)

text: In 2019, Patrick called for requiring background checks for gun sales between two strangers. Patrick later backed away from this position, instead throwing his support behind legislation to expand gun rights, including constitutional carry.


title: Dan Patrick (politician)

text: Patrick opposes illegal immigration. As a talk radio host, he reserved some of his "most hard-edged oratory for illegal immigrants." Patrick expressed support for Arizona's SB 1070 immigration enforcement law, and supports passing a similar law in Texas that would allow local law enforcement to ask lawfully-stopped individuals about their immigration status and would make it a state misdemeanor to be present in Texas as an illegal immigrant.


title: Dan Patrick (politician)

text: As Lieutenant Governor, Patrick moved to keep National Guard troops sent to the Texas-Mexico border during the illegal immigration surge of 2014 indefinitely, rather than until March 2015, as originally planned. Patrick's 2015 budget in the Texas Senate called for spending $815 million on border security, which he said was more than the previous seven years combined. Governor Greg Abbott signed the measure—for about $800 million—into law. In a June 2018 interview on Fox Business Network, Patrick estimated that 30 million illegal immigrants lived in the U.S.


title: Dan Patrick (politician)

text: In 2014, after a federal court ruled that Texas' ban on same-sex marriage was unconstitutional, Patrick expressed his opposition to same-sex marriage, and vowed to fight such court decisions should he be elected to the Lt. Governor's office. Patrick argued that if the Texas ban was removed, then it would lead to the legalization of bigamy, pedophilia and incest.


title: Dan Patrick (politician)

text: Patrick strongly opposed HERO, an unsuccessful Houston ordinance intended to establish legal protections for gay and transgender residents along with some other classes, as he claimed that the ordinance would lead to sexual predators being freely able to enter women's restrooms. Patrick has stated that if necessary, he would support legislation to require people to use the bathroom that corresponds to the gender listed on their birth certificates.


title: Dan Patrick (politician)

text: Hours after the 2016 Orlando nightclub shooting, Patrick tweeted a picture of the Bible verse, "Do not be deceived: God cannot be mocked. A man reaps what he sows. Galatians 6:7." An adviser released a statement that the tweet had been pre-scheduled, and the tweet was later deleted. Patrick issued a statement on the incident, again stating that the tweet was pre-planned and that "I didn't pull down the FB post & tweet because God's word is wrong. His word is never wrong ... I took it down to stop the hateful comments and the misinformation being spread of God's message to all of us- straight or gay."


title: Dan Patrick (politician)

text: In May 2016, Patrick criticized the Obama administration after it released a directive stating that all public schools must allow transgender students to use the bathroom and locker facilities that correspond with their identified gender, stating that, on the prospect of the federal government withholding funding for Texas schools for not following the directive, "he can keep his 30 pieces of silver [and that w]e will not yield to blackmail from the president of the United States." In 2017, Patrick strongly advocated for a bathroom bill that would prohibit transgender students at public schools from using any restroom other than that of their biological sex. Patrick described the legislation as a "legislative priority." Patrick encouraged state Senator Lois Kolkhorst of Brenham to introduce a bathroom bill similar to a previous law adopted in 2016 in North Carolina, and strongly pushed for it at its proposal on January 5, 2017. Texas House Speaker Joe Straus of San Antonio, a moderate Republican, said that the measure is not an important matter for lower chamber.


title: Dan Patrick (politician)

text: In April 2019, Patrick called Democratic presidential candidate Beto O'Rourke "light in the loafers", a slur often used to insinuate someone as gay, though O'Rourke is heterosexual. Patrick also called O'Rourke a "moron." Patrick later stated that while he stood by his comments, the insinuation was unintentional.


title: Dan Patrick (politician)

text: In 2020, Patrick referred to vote-by-mail expansion efforts during the COVID-19 pandemic as a "scam by Democrats to steal the election."


title: Dan Patrick (politician)

text: In 2021, Patrick presided over the passage of legislation in the Texas Senate that restricted voting rights, including prohibiting local boards from sending applications for mail-in ballots to voters.


title: Dan Patrick (politician)

text: In 2022, Patrick's campaign sent out a mass mailing to Republican voters across Texas with inaccurate instructions on how to send requests for absentee ballots. The mailing included return envelopes that were addressed to the Texas secretary of state's address when they should have been to local election offices. Patrick's campaign defended the inaccurate instructions, saying it "gave voters an added layer of comfort" not to have to mail sent to "Blue County election officials."


title: Dan Patrick (politician)

text: In 2019, Patrick opposed a bill that would have decriminalized simple possession of cannabis in Texas. After the Texas House passed the bill, he announced that it was dead on arrival in the Senate.


title: Dan Patrick (politician)

text: In 2021, during an interview, Patrick expressed that he was open to some medical cannabis changes, while he downplayed the more ambitious efforts. He said: "We're not gonna turn this into California where anybody can get a slip from a doctor and go down to some retail store and say 'You know, I got a headache today so I need marijuana,' because that's just a veil for legalizing it for recreational use." In fact, on the date of the statement, it was already legal to sell recreational cannabis to adults in California, under proposition 64.


title: Dan Patrick (politician)

text: In November 2012, Patrick asked Texas attorney general Greg Abbott's office to issue an opinion on the constitutionality of government entities providing domestic partner insurance benefits. An amendment to the Texas Constitution in 2005 limits marriage to heterosexual relationships and prohibits similar, alternative legal arrangements. Patrick did not disclose his own views on same-sex marriage or civil unions for same-sex couples. He told the "Houston Chronicle" that his request was prompted by Dallas County's November 2012 decision and an Austin-area public school districts' October 2012 decision to join other Texas cities and counties in extending benefits to their unmarried employees' heterosexual or homosexual partners.


title: Dan Patrick (politician)

text: Patrick was interviewed extensively on ABC's "20/20" segment "The Age of Consent: When Young Love Is a Sex Crime," defending his position on the strict Texas statutory rape laws. "While it seems unfair, he was 19, she was 15," says Patrick, "That's the price you pay. Even if you end up getting married."


title: Dan Patrick (politician)

text: Patrick is a strong supporter of maintaining Confederate monuments on public display, despite opposition from civil rights groups who consider the statues as a defense of the institution of slavery and of the Civil War. As one of six members of the board that oversees the Texas State Capitol grounds, Patrick described the need: "to learn from history all of our history, including events and times that many would like to forget. ... Our goal should be to have a meaningful dialogue for future generations so those moments in our history are not repeated."


title: Dan Patrick (politician)

text: In an interview with Fox News host Tucker Carlson on March 23, 2020, Patrick stated that he was willing to risk his life from the COVID-19 pandemic if it would avoid an economic shutdown, which he stated would negatively impact subsequent generations. Patrick also stated that he thought many grandparents agreed with him on this. Patrick later moderated his rhetoric while continuing to show skepticism of shutting down the economy.


title: Dan Patrick (politician)

text: Patrick worked to increase access to hydroxychloroquine, an unproven drug to treat the coronavirus which President Trump promoted. On April 7, 2020, Patrick announced the creation of a task force to make recommendations on how to re-open Texas's economy.


title: Dan Patrick (politician)

text: Patrick again garnered controversy on April 21, when he defended his previous comments on the pandemic by saying "And what I said when I was with you that night, there are more important things than living. And that's saving this country for my children, and my grandchildren and saving this country for all of us. And I don't want to die, nobody wants to die, but man, we got to take some risks and get back in the game, and get this country back up and running."


title: Dan Patrick (politician)

text: In May 2020, Patrick paid a $7,000 fine imposed on a Dallas businesswoman after she defied Texas's lockdown orders in order to keep her hair salon open. He said, "Seven days in jail, no bail and a $7,000 fine is outrageous."


title: Dan Patrick (politician)

text: After the 2019 El Paso shooting, Patrick listed factors that he believed contributed to the shooting, starting off with video games, saying, "We've always had guns, always had evil, but I see a video game industry that teaches young people to kill."


title: Dan Patrick (politician)

text: Patrick endorsed Texas Senator Ted Cruz for the 2016 Republican presidential primaries and served as his Texas campaign chairman. After businessman Donald Trump became the Republican nominee, Patrick endorsed Trump and eventually became the Texas state chairman for his campaign. Trump won Texas by 9 percentage points, the closest result since 1996. In January 2018, Patrick stated that he considered Presidents Trump and Ronald Reagan as the two greatest presidents in his lifetime, and the "Austin American-Statesman" described Patrick as an "ardent defender" of Trump.


title: Dan Patrick (politician)

text: At a political rally for President Trump on October 17, 2019, Patrick told a crowd of 20,000 that liberals "are not our opponents, they are our enemy."


title: Dan Patrick (politician)

text: After Joe Biden won the 2020 election and Trump made false claims of fraud, Patrick backed Trump as he refused to concede. Patrick said he would pay up to $1 million for reports of voter fraud across the country. In October 2021, Patrick paid the first reward of $25,000 to a Pennsylvania poll worker who reported a man that voted twice.


title: Dan Patrick (politician)

text: Patrick's first marriage ended in divorce. His second wife is Janetlea "Jan" Patricia Rankin, a former teacher. The couple was married in 1975 and lives in the Houston suburb of Cypress. They have two children, Ryan and Shane. Ryan served as a district judge from Harris County, Texas, and swore in his father in 2015, for his term as lieutenant governor of Texas. In July 2017, Ryan Patrick was chosen to be U.S. Attorney for the Southern District of Texas by U.S. President Donald Trump, and the United States Senate subsequently confirmed him.


title: Dan Patrick (politician)

text: While growing up, Patrick and his family were "not very religious." After moving to Houston, he and his wife attended a Catholic church, but he joined a Baptist church soon after learning about it. Though Patrick was a member of the Second Baptist Church Houston since 1992, he stated he was not truly a Christian until March 1994, when, on a television-and-radio convention in Las Vegas, he repented of his sins, committed his life to God, and was saved. After this, Patrick's faith became an important part of his life, and he considered going into Christian ministry for a time.


title: Dan Patrick (politician)

text: Patrick, an evangelical Christian, is a member of various Christian organizations, including Fellowship of Christian Athletes and the International Bible Society, and has served as guest pastor of his church, the Second Baptist Church Houston. He is very outspoken about his Christian faith, and he stated in his inauguration speech upon becoming lieutenant governor that "I respect all faiths and religions, but I am a Christian first, a conservative second and a Republican third, and I praise Jesus for this moment and this day." Patrick was baptized in the Jordan River during a trip to Israel in 2016.


title: Lake Karachay

text: Lake Karachay (), sometimes spelled Karachai or Karachaj, was a small lake in the southern Ural mountains in central Russia. Starting in 1951, the Soviet Union used Karachay as a dumping site for radioactive waste from Mayak, the nearby nuclear waste storage and reprocessing facility, located near the town of Ozyorsk (then called Chelyabinsk-40). Today the lake is completely infilled, acting as "a near-surface permanent and dry nuclear waste storage facility."


title: Lake Karachay

text: The radioactivity of the lake is comparable to the Chernobyl disaster, the worst nuclear accident of all time.


title: Lake Karachay

text: The name "karachay" means "black water" or "black creek" in several Northwestern Turkic languages, including Tatar.


title: Lake Karachay

text: Built in total secrecy between 1946 and 1948, the Mayak plant was the first reactor used to create plutonium for the Soviet atomic bomb project. In accordance with Stalinist procedure and supervised by NKVD Chief Lavrenti Beria, it was the utmost priority to produce enough weapons-grade material to match the U.S. nuclear superiority following the atomic bombings of Hiroshima and Nagasaki. Little to no consideration was paid to worker safety or responsible disposal of waste materials, and the reactors all were optimized for plutonium production, producing many tons of contaminated materials and utilizing open-cycle cooling systems which directly contaminated every liter of the thousands of liters of cooling water the reactors used every day.


title: Lake Karachay

text: Lake Kyzyltash was the largest natural lake capable of providing cooling water to the reactors; it was rapidly contaminated because of their use of the open-cycle system. Lake Karachay was even closer; however the lake was too small to provide sufficient cooling water. Lake Karachay was then designated a close-by and convenient dumping ground for large quantities of high-level radioactive waste too "hot" to store in the facility's underground storage vats. The original plan was to use the lake to store highly radioactive material until it could be returned to the Mayak facility's underground concrete storage vats, but this proved impossible due to the lethal levels of radioactivity. The lake was used for this purpose until the Kyshtym Disaster in 1957, in which the underground vats exploded due to a faulty cooling system. This incident caused widespread contamination of the entire Mayak area (as well as a large swath of territory to the northeast). This led to greater caution among the administration, fearing international attention, and caused the dumping grounds to be spread out over a variety of areas (including several lakes and the Techa River, along which many villages lay).


title: Lake Karachay

text: In the 1960s, the lake began to dry out; its area dropped from 0.5 km in 1951 to 0.15 km by the end of 1993. In 1968, following a drought in the region, the wind carried 185 PBq (5 MCi) of radioactive dust away from the dried area of the lake, irradiating half a million people.


title: Lake Karachay

text: Between 1978 and 1986, the lake was filled with almost 10,000 hollow concrete blocks to prevent sediments from shifting. Conservation of the affected area continued into the 2000s via the federal target program "Nuclear and Radiation Safety in 2008 and for the period up to 2015", with the rest of the lake finally being backfilled in November 2015. Conservation work was completed in December 2016 with the final layer of rock and soil being added, effectively making the former lake "a near-surface permanent and dry nuclear waste storage facility."


title: Lake Karachay

text: According to a report by the Worldwatch Institute on nuclear waste, Karachay is the most polluted (open-air) place on Earth from a radiological point of view. The lake accumulated some 4.44 exabecquerels (EBq) of radioactivity over less than one square mile of water, including 3.6 EBq of caesium-137 and 0.74 EBq of strontium-90. For comparison, the Chernobyl disaster released 0.085 EBq of caesium-137, a much smaller amount and over thousands of square miles. (The total Chernobyl release is estimated between 5 and 12 EBq of radioactivity, however essentially only caesium-134/137 [and to a lesser extent, strontium-90] contribute to land contamination because the rest is too short-lived). The sediment of the lake bed is estimated to be composed almost entirely of high level radioactive waste deposits to a depth of roughly .


title: Lake Karachay

text: In 1990, the radiation level in the region near where radioactive effluent was discharged into the lake was 600 röntgens per hour (approximately 6 Sv/h) according to the Natural Resources Defense Council, sufficient to give a lethal dose to a human within less than an hour.


title: Lake Karachay

text: , the lake's status is completely infilled, using special concrete blocks, rock, and dirt. It had been completely backfilled in November 2015, then monitored before placing the final layer of rock and dirt. Monitoring data showed "clear reduction of the deposition of radionuclides on the surface" after 10 months. A decades-long monitoring program for underground water was expected to be implemented shortly after.


title: Generating function

text: In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series, the "formal" power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem. One can generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers.


title: Generating function

text: There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions and examples are given below. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require indices to start at 1 rather than 0), but the ease with which they can be handled may differ considerably. The particular generating function, if any, that is most useful in a given context will depend upon the nature of the sequence and the details of the problem being addressed.


title: Generating function

text: Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations defined for formal series. These expressions in terms of the indeterminate  may involve arithmetic operations, differentiation with respect to  and composition with (i.e., substitution into) other generating functions; since these operations are also defined for functions, the result looks like a function of . Indeed, the closed form expression can often be interpreted as a function that can be evaluated at (sufficiently small) concrete values of , and which has the formal series as its series expansion; this explains the designation "generating functions". However such interpretation is not required to be possible, because formal series are not required to give a convergent series when a nonzero numeric value is substituted for . Also, not all expressions that are meaningful as functions of  are meaningful as expressions designating formal series; for example, negative and fractional powers of  are examples of functions that do not have a corresponding formal power series.


title: Generating function

text: Generating functions are not functions in the formal sense of a mapping from a domain to a codomain. Generating functions are sometimes called generating series, in that a series of terms can be said to be the generator of its sequence of term coefficients.


title: Generating function

text: When the term "generating function" is used without qualification, it is usually taken to mean an ordinary generating function.


title: Generating function

text: If is the probability mass function of a discrete random variable, then its ordinary generating function is called a probability-generating function.


title: Generating function

text: The ordinary generating function can be generalized to arrays with multiple indices. For example, the ordinary generating function of a two-dimensional array (where and are natural numbers) is


title: Generating function

text: Exponential generating functions are generally more convenient than ordinary generating functions for combinatorial enumeration problems that involve labelled objects.


title: Generating function

text: Another benefit of exponential generating functions is that they are useful in transferring linear recurrence relations to the realm of differential equations. For example, take the Fibonacci sequence that satisfies the linear recurrence relation . The corresponding exponential generating function has the form


title: Generating function

text: and its derivatives can readily be shown to satisfy the differential equation as a direct analogue with the recurrence relation above. In this view, the factorial term is merely a counter-term to normalise the derivative operator acting on .


title: Generating function

text: The main article provides several more classical, or at least well-known examples related to special arithmetic functions in number theory.


title: Generating function

text: The Bell series of a sequence is an expression in terms of both an indeterminate and a prime and is given by


title: Generating function

text: Formal Dirichlet series are often classified as generating functions, although they are not strictly formal power series. The "Dirichlet series generating function" of a sequence is


title: Generating function

text: The Dirichlet series generating function is especially useful when is a multiplicative function, in which case it has an Euler product expression in terms of the function's Bell series


title: Generating function

text: If is a Dirichlet character then its Dirichlet series generating function is called a Dirichlet -series. We also have a relation between the pair of coefficients in the Lambert series expansions above and their DGFs. Namely, we can prove that


title: Generating function

text: The idea of generating functions can be extended to sequences of other objects. Thus, for example, polynomial sequences of binomial type are generated by


title: Generating function

text: where is a sequence of polynomials and is a function of a certain form. Sheffer sequences are generated in a similar way. See the main article generalized Appell polynomials for more information.


title: Generating function

text: Polynomials are a special case of ordinary generating functions, corresponding to finite sequences, or equivalently sequences that vanish after a certain point. These are important in that many finite sequences can usefully be interpreted as generating functions, such as the Poincaré polynomial and others.


title: Generating function

text: A fundamental generating function is that of the constant sequence , whose ordinary generating function is the geometric series


title: Generating function

text: The left-hand side is the Maclaurin series expansion of the right-hand side. Alternatively, the equality can be justified by multiplying the power series on the left by , and checking that the result is the constant power series 1 (in other words, that all coefficients except the one of are equal to 0). Moreover, there can be no other power series with this property. The left-hand side therefore designates the multiplicative inverse of in the ring of power series.


title: Generating function

text: Expressions for the ordinary generating function of other sequences are easily derived from this one. For instance, the substitution gives the generating function for the geometric sequence for any constant :


title: Generating function

text: (The equality also follows directly from the fact that the left-hand side is the Maclaurin series expansion of the right-hand side.) In particular,


title: Generating function

text: One can also introduce regular gaps in the sequence by replacing by some power of , so for instance for the sequence (which skips over ) one gets the generating function


title: Generating function

text: By squaring the initial generating function, or by finding the derivative of both sides with respect to and making a change of running variable , one sees that the coefficients form the sequence , so one has


title: Generating function

text: and the third power has as coefficients the triangular numbers whose term is the binomial coefficient , so that


title: Generating function

text: one can find the ordinary generating function for the sequence of square numbers by linear combination of binomial-coefficient generating sequences:


title: Generating function

text: We may also expand alternately to generate this same sequence of squares as a sum of derivatives of the geometric series in the following form:


title: Generating function

text: so that we can form the analogous generating functions over the integral th powers generalizing the result in the square case above. In particular, since we can write


title: Generating function

text: The ordinary generating function of a sequence can be expressed as a rational function (the ratio of two finite-degree polynomials) if and only if the sequence is a linear recursive sequence with constant coefficients; this generalizes the examples above. Conversely, every sequence generated by a fraction of polynomials satisfies a linear recurrence with constant coefficients; these coefficients are identical to the coefficients of the fraction denominator polynomial (so they can be directly read off). This observation shows it is easy to solve for generating functions of sequences defined by a linear finite difference equation with constant coefficients, and then hence, for explicit closed-form formulas for the coefficients of these generating functions. The prototypical example here is to derive Binet's formula for the Fibonacci numbers via generating function techniques.


title: Generating function

text: We also notice that the class of rational generating functions precisely corresponds to the generating functions that enumerate "quasi-polynomial" sequences of the form


title: Generating function

text: In general, Hadamard products of rational functions produce rational generating functions. Similarly, if


title: Generating function

text: then this generating function's diagonal coefficient generating function is given by the well-known OGF formula


title: Generating function

text: This result is computed in many ways, including Cauchy's integral formula or contour integration, taking complex residues, or by direct manipulations of formal power series in two variables.


title: Generating function

text: Multiplication of ordinary generating functions yields a discrete convolution (the Cauchy product) of the sequences. For example, the sequence of cumulative sums (compare to the slightly more general Euler–Maclaurin formula)


title: Generating function

text: because is the ordinary generating function for the sequence . See also the section on convolutions in the applications section of this article below for further examples of problem solving with convolutions of generating functions and interpretations.


title: Generating function

text: For integers , we have the following two analogous identities for the modified generating functions enumerating the shifted sequence variants of and , respectively:


title: Generating function

text: We have the following respective power series expansions for the first derivative of a generating function and its integral:


title: Generating function

text: The differentiation–multiplication operation of the second identity can be repeated times to multiply the sequence by , but that requires alternating between differentiation and multiplication. If instead doing differentiations in sequence, the effect is to multiply by the th falling factorial:


title: Generating function

text: Using the Stirling numbers of the second kind, that can be turned into another formula for multiplying by formula_39 as follows (see the main article on generating function transformations):


title: Generating function

text: A negative-order reversal of this sequence powers formula corresponding to the operation of repeated integration is defined by the zeta series transformation and its generalizations defined as a derivative-based transformation of generating functions, or alternately termwise by and performing an integral transformation on the sequence generating function. Related operations of performing fractional integration on a sequence generating function are discussed here.


title: Generating function

text: In this section we give formulas for generating functions enumerating the sequence given an ordinary generating function where , , and (see the main article on transformations). For , this is simply the familiar decomposition of a function into even and odd parts (i.e., even and odd powers):


title: Generating function

text: More generally, suppose that and that denotes the th primitive root of unity. Then, as an application of the discrete Fourier transform, we have the formula


title: Generating function

text: For integers , another useful formula providing somewhat "reversed" floored arithmetic progressions — effectively repeating each coefficient times — are generated by the identity


title: Generating function

text: A formal power series (or function) is said to be holonomic if it satisfies a linear differential equation of the form


title: Generating function

text: where the coefficients are in the field of rational functions, . Equivalently, is holonomic if the vector space over spanned by the set of all of its derivatives is finite dimensional.


title: Generating function

text: Since we can clear denominators if need be in the previous equation, we may assume that the functions, are polynomials in . Thus we can see an equivalent condition that a generating function is holonomic if its coefficients satisfy a -recurrence of the form


title: Generating function

text: for all large enough and where the are fixed finite-degree polynomials in . In other words, the properties that a sequence be "-recursive" and have a holonomic generating function are equivalent. Holonomic functions are closed under the Hadamard product operation on generating functions.


title: Generating function

text: The functions , , , , , the dilogarithm function , the generalized hypergeometric functions and the functions defined by the power series


title: Generating function

text: Examples of -recursive sequences with holonomic generating functions include and , where sequences such as and are "not" -recursive due to the nature of singularities in their corresponding generating functions. Similarly, functions with infinitely many singularities such as , , and are "not" holonomic functions.


title: Generating function

text: Tools for processing and working with -recursive sequences in "Mathematica" include the software packages provided for non-commercial use on the RISC Combinatorics Group algorithmic combinatorics software site. Despite being mostly closed-source, particularly powerful tools in this software suite are provided by the codice_1 package for guessing "-recurrences" for arbitrary input sequences (useful for experimental mathematics and exploration) and the codice_2 package which is able to find P-recurrences for many sums and solve for closed-form solutions to -recurrences involving generalized harmonic numbers. Other packages listed on this particular RISC site are targeted at working with holonomic "generating functions" specifically.


title: Generating function

text: In calculus, often the growth rate of the coefficients of a power series can be used to deduce a radius of convergence for the power series. The reverse can also hold; often the radius of convergence for a generating function can be used to deduce the asymptotic growth of the underlying sequence.


title: Generating function

text: For instance, if an ordinary generating function that has a finite radius of convergence of can be written as


title: Generating function

text: where each of and is a function that is analytic to a radius of convergence greater than (or is entire), and where then


title: Generating function

text: Often this approach can be iterated to generate several terms in an asymptotic series for . In particular,


title: Generating function

text: The asymptotic growth of the coefficients of this generating function can then be sought via the finding of , , , , and to describe the generating function, as above.


title: Generating function

text: Similar asymptotic analysis is possible for exponential generating functions; with an exponential generating function, it is that grows according to these asymptotic formulae. Generally, if the generating function of one sequence minus the generating function of a second sequence has a radius of convergence that is larger than the radius of convergence of the individual generating functions then the two sequences have the same asymptotic growth.


title: Generating function

text: One can define generating functions in several variables for arrays with several indices. These are called multivariate generating functions or, sometimes, super generating functions. For two variables, these are often called bivariate generating functions.


title: Generating function

text: For instance, since is the ordinary generating function for binomial coefficients for a fixed , one may ask for a bivariate generating function that generates the binomial coefficients for all and . To do this, consider itself as a sequence in , and find the generating function in that has these sequence values as coefficients. Since the generating function for is


title: Generating function

text: Expansions of (formal) "Jacobi-type" and "Stieltjes-type" continued fractions ("-fractions" and "-fractions", respectively) whose th rational convergents represent -order accurate power series are another way to express the typically divergent ordinary generating functions for many special one and two-variate sequences. The particular form of the Jacobi-type continued fractions (-fractions) are expanded as in the following equation and have the next corresponding power series expansions with respect to for some specific, application-dependent component sequences, and , where denotes the formal variable in the second power series expansion given below:


title: Generating function

text: The coefficients of formula_59, denoted in shorthand by , in the previous equations correspond to matrix solutions of the equations


title: Generating function

text: For (though in practice when ), we can define the rational th convergents to the infinite -fraction, , expanded by


title: Generating function

text: Moreover, the rationality of the convergent function for all implies additional finite difference equations and congruence properties satisfied by the sequence of , "and" for if then we have the congruence


title: Generating function

text: for non-symbolic, determinate choices of the parameter sequences and when , that is, when these sequences do not implicitly depend on an auxiliary parameter such as , , or as in the examples contained in the table below.


title: Generating function

text: The next table provides examples of closed-form formulas for the component sequences found computationally (and subsequently proved correct in the cited references)


title: Generating function

text: in several special cases of the prescribed sequences, , generated by the general expansions of the -fractions defined in the first subsection. Here we define and the parameters , and to be indeterminates with respect to these expansions, where the prescribed sequences enumerated by the expansions of these -fractions are defined in terms of the -Pochhammer symbol, Pochhammer symbol, and the binomial coefficients.


title: Generating function

text: The radii of convergence of these series corresponding to the definition of the Jacobi-type -fractions given above are in general different from that of the corresponding power series expansions defining the ordinary generating functions of these sequences.


title: Generating function

text: As an example of a Lambert series identity not given in the main article, we can show that for we have that


title: Generating function

text: where we have the special case identity for the generating function of the divisor function, , given by


title: Generating function

text: Multivariate generating functions arise in practice when calculating the number of contingency tables of non-negative integers with specified row and column totals. Suppose the table has rows and columns; the row sums are and the column sums are . Then, according to I. J. Good, the number of such tables is the coefficient of


title: Generating function

text: In the bivariate case, non-polynomial double sum examples of so-termed ""double"" or ""super"" generating functions of the form


title: Generating function

text: include the following two-variable generating functions for the binomial coefficients, the Stirling numbers, and the Eulerian numbers:


title: Generating function

text: Generating functions give us several methods to manipulate sums and to establish identities between sums.


title: Generating function

text: The simplest case occurs when . We then know that for the corresponding ordinary generating functions.


title: Generating function

text: As another example of using generating functions to relate sequences and manipulate sums, for an arbitrary sequence we define the two sequences of sums


title: Generating function

text: for all , and seek to express the second sums in terms of the first. We suggest an approach by generating functions.


title: Generating function

text: Finally, it follows that we may express the second sums through the first sums in the following form:


title: Generating function

text: In this example, we reformulate a generating function example given in Section 7.3 of "Concrete Mathematics" (see also Section 7.1 of the same reference for pretty pictures of generating function series). In particular, suppose that we seek the total number of ways (denoted ) to tile a 3-by- rectangle with unmarked 2-by-1 domino pieces. Let the auxiliary sequence, , be defined as the number of ways to cover a 3-by- rectangle-minus-corner section of the full rectangle. We seek to use these definitions to give a closed form formula for without breaking down this definition further to handle the cases of vertical versus horizontal dominoes. Notice that the ordinary generating functions for our two sequences correspond to the series


title: Generating function

text: If we consider the possible configurations that can be given starting from the left edge of the 3-by- rectangle, we are able to express the following mutually dependent, or "mutually recursive", recurrence relations for our two sequences when defined as above where , , , and :


title: Generating function

text: we can use the initial conditions specified above and the previous two recurrence relations to see that we have the next two equations relating the generating functions for these sequences given by


title: Generating function

text: which then implies by solving the system of equations (and this is the particular trick to our method here) that


title: Generating function

text: Thus by performing algebraic simplifications to the sequence resulting from the second partial fractions expansions of the generating function in the previous equation, we find that and that


title: Generating function

text: for all integers . We also note that the same shifted generating function technique applied to the second-order recurrence for the Fibonacci numbers is the prototypical example of using generating functions to solve recurrence relations in one variable already covered, or at least hinted at, in the subsection on rational functions given above.


title: Generating function

text: A discrete "convolution" of the terms in two formal power series turns a product of generating functions into a generating function enumerating a convolved sum of the original sequence terms (see Cauchy product).


title: Generating function

text: Multiplication of generating functions, or convolution of their underlying sequences, can correspond to a notion of independent events in certain counting and probability scenarios. For example, if we adopt the notational convention that the probability generating function, or "pgf", of a random variable is denoted by , then we can show that for any two random variables


title: Generating function

text: if and are independent. Similarly, the number of ways to pay cents in coin denominations of values in the set {1, 5, 10, 25, 50} (i.e., in pennies, nickels, dimes, quarters, and half dollars, respectively) is generated by the product


title: Generating function

text: and moreover, if we allow the cents to be paid in coins of any positive integer denomination, we arrive at the generating for the number of such combinations of change being generated by the partition function generating function expanded by the infinite -Pochhammer symbol product of


title: Generating function

text: An example where convolutions of generating functions are useful allows us to solve for a specific closed-form function representing the ordinary generating function for the Catalan numbers, . In particular, this sequence has the combinatorial interpretation as being the number of ways to insert parentheses into the product so that the order of multiplication is completely specified. For example, which corresponds to the two expressions and . It follows that the sequence satisfies a recurrence relation given by


title: Generating function

text: which then leads to another "simple" (of form) continued fraction expansion of this generating function.


title: Generating function

text: A "fan of order " is defined to be a graph on the vertices with edges connected according to the following rules: Vertex 0 is connected by a single edge to each of the other vertices, and vertex formula_107 is connected by a single edge to the next vertex for all . There is one fan of order one, three fans of order two, eight fans of order three, and so on. A spanning tree is a subgraph of a graph which contains all of the original vertices and which contains enough edges to make this subgraph connected, but not so many edges that there is a cycle in the subgraph. We ask how many spanning trees of a fan of order are possible for each .


title: Generating function

text: As an observation, we may approach the question by counting the number of ways to join adjacent sets of vertices. For example, when , we have that , which is a sum over the -fold convolutions of the sequence for . More generally, we may write a formula for this sequence as


title: Generating function

text: from which we see that the ordinary generating function for this sequence is given by the next sum of convolutions as


title: Generating function

text: from which we are able to extract an exact formula for the sequence by taking the partial fraction expansion of the last generating function.


title: Generating function

text: Sometimes the sum is complicated, and it is not always easy to evaluate. The "Free Parameter" method is another method (called "snake oil" by H. Wilf) to evaluate these sums.


title: Generating function

text: Both methods discussed so far have as limit in the summation. When n does not appear explicitly in the summation, we may consider as a “free” parameter and treat as a coefficient of , change the order of the summations on and , and try to compute the inner sum.


title: Generating function

text: It is instructive to use the same method again for the sum, but this time take as the free parameter instead of . We thus set


title: Generating function

text: We say that two generating functions (power series) are congruent modulo , written if their coefficients are congruent modulo for all , i.e., for all relevant cases of the integers (note that we need not assume that is an integer here—it may very well be polynomial-valued in some indeterminate , for example). If the "simpler" right-hand-side generating function, , is a rational function of , then the form of this sequence suggests that the sequence is eventually periodic modulo fixed particular cases of integer-valued . For example, we can prove that the Euler numbers,


title: Generating function

text: One of the most useful, if not downright powerful, methods of obtaining congruences for sequences enumerated by special generating functions modulo any integers (i.e., not only prime powers ) is given in the section on continued fraction representations of (even non-convergent) ordinary generating functions by -fractions above. We cite one particular result related to generating series expanded through a representation by continued fraction from Lando's "Lectures on Generating Functions" as follows:


title: Generating function

text: Generating functions also have other uses in proving congruences for their coefficients. We cite the next two specific examples deriving special case congruences for the Stirling numbers of the first kind and for the partition function which show the versatility of generating functions in tackling problems involving integer sequences.


title: Generating function

text: provides an overview of the congruences for these numbers derived strictly from properties of their generating function as in Section 4.6 of Wilf's stock reference "Generatingfunctionology".


title: Generating function

text: We repeat the basic argument and notice that when reduces modulo 2, these finite product generating functions each satisfy


title: Generating function

text: Similarly, we can reduce the right-hand-side products defining the Stirling number generating functions modulo 3 to obtain slightly more complicated expressions providing that


title: Generating function

text: In this example, we pull in some of the machinery of infinite products whose power series expansions generate the expansions of many special functions and enumerate partition functions. In particular, we recall that "the" partition function is generated by the reciprocal infinite -Pochhammer symbol product (or -Pochhammer product as the case may be) given by


title: Generating function

text: This partition function satisfies many known congruence properties, which notably include the following results though there are still many open questions about the forms of related integer congruences for the function:


title: Generating function

text: We show how to use generating functions and manipulations of congruences for formal power series to give a highly elementary proof of the first of these congruences listed above.


title: Generating function

text: all of the coefficients are divisible by 5 except for those which correspond to the powers and moreover in those cases the remainder of the coefficient is 1 modulo 5. Thus,


title: Generating function

text: we may equate the coefficients of in the previous equations to prove our desired congruence result, namely that for all .


title: Generating function

text: There are a number of transformations of generating functions that provide other applications (see the main article). A transformation of a sequence's "ordinary generating function" (OGF) provides a method of converting the generating function for one sequence into a generating function enumerating another. These transformations typically involve integral formulas involving a sequence OGF (see integral transformations) or weighted sums over the higher-order derivatives of these functions (see derivative transformations).


title: Generating function

text: Generating function transformations can come into play when we seek to express a generating function for the sums


title: Generating function

text: There are also integral formulas for converting between a sequence's OGF, , and its exponential generating function, or EGF, , and vice versa given by


title: Generating function

text: Knuth's article titled ""Convolution Polynomials"" defines a generalized class of "convolution polynomial" sequences by their special generating functions of the form


title: Generating function

text: We say that a family of polynomials, , forms a "convolution family" if and if the following convolution condition holds for all , and for all :


title: Generating function

text: We see that for non-identically zero convolution families, this definition is equivalent to requiring that the sequence have an ordinary generating function of the first form given above.


title: Generating function

text: For a fixed non-zero parameter , we have modified generating functions for these convolution polynomial sequences given by


title: Generating function

text: where is implicitly defined by a functional equation of the form . Moreover, we can use matrix methods (as in the reference) to prove that given two convolution polynomial sequences, and , with respective corresponding generating functions, and , then for arbitrary we have the identity


title: Generating function

text: Examples of convolution polynomial sequences include the "binomial power series", , so-termed "tree polynomials", the Bell numbers, , the Laguerre polynomials, and the Stirling convolution polynomials.


title: Generating function

text: An initial listing of special mathematical series is found here. A number of useful and special sequence generating functions are found in Section 5.4 and 7.4 of "Concrete Mathematics" and in Section 2.5 of Wilf's "Generatingfunctionology". Other special generating functions of note include the entries in the next table, which is by no means complete.


title: Kavinsky

text: Vincent Belorgey (born 31 July 1975), known professionally as Kavinsky, is a French musician, producer, DJ, and actor. His production style is reminiscent of the electropop film soundtracks of the 1980s. Kavinsky claims that his music is inspired by thousands of movies he watched as a young boy and that he has cherry-picked the best parts from them, consolidating them into one concept. Kavinsky has been compared to many similar French house artists, including Daft Punk and Danger. He achieved greater mainstream recognition after his song "Nightcall" was featured in the 2011 film "Drive". His debut studio album, "OutRun", was released in 2013.


title: Kavinsky

text: After many years as an actor, Kavinsky's musical career started in 2005 after being inspired by his close friends Jackson Fourgeaud and Quentin Dupieux, the latter director also included Kavinsky's music in his film "Steak". During this period Kavinsky produced his first single "Testarossa Autodrive" which was inspired by the Testarossa model of Ferrari (one of which Vincent drives in real life). Kavinsky presented the single to Quentin, who in turn presented it to a record label he had access to because of his filming career, and Kavinsky signed with Record Makers.


title: Kavinsky

text: Kavinsky went on to release three EPs on the Record Makers label: "Teddy Boy" in 2006, "1986" a year later, and "Nightcall" with Lovefoxxx of CSS in 2010. Kavinsky toured alongside Daft Punk, The Rapture, Justice, and SebastiAn in 2007.


title: Kavinsky

text: The SebastiAn remix of "Testarossa Autodrive" off the "1986" EP is featured in the video games "Grand Theft Auto IV" and "Gran Turismo 5 Prologue". Kavinsky's single "Nightcall" was featured in the opening credits of the film "Drive", and became a major hit soon after.


title: Kavinsky

text: In December 2012 he released "ProtoVision" and on 25 February 2013 released his debut studio album "OutRun".


title: Kavinsky

text: In November 2021, he returned from his seven year hiatus with the lead single "Renegade" from his second studio album "Reborn". The song is produced by Gaspard Augé and Victor Le Masne.


title: Kavinsky

text: Kavinsky is a character made by Vincent Belorgey that has a striking resemblance to Vincent himself but the backstory does not follow anything in Belorgey's history. Kavinsky's story is that after crashing his Testarossa in 1986, he reappeared as a zombie in 2006 to make his own electronic music. Kavinsky's songs help tell his story; Vincent claims in an interview, "'Night Call' is just about the zombie guy [who] goes to his girlfriend's house and says okay I'm not the same, we need to talk", referring to Kavinsky going back to find his girlfriend after the crash who has already moved on with her life.


title: Kavinsky

text: In interview, Kavinsky stated that the entirety of "Teddy Boy" was written and recorded on a Yamaha DX7, which was famous and notable for the synth-pop sound of the 1980s. Kavinsky originally started making music on an old Apple computer given to him by his friend Mr. Oizo.


title: Antonov An-70

text: The Antonov An-70 (-70) is a four-engine medium-range transport aircraft, and the first aircraft to take flight powered only by propfan engines. It was developed in the late 1980s by the Antonov Design Bureau to replace the obsolete An-12 military transport aircraft. The maiden flight of the first prototype took place in December 1994 in Kyiv, now independent Ukraine. Within months the prototype had suffered a mid-air collision. A second airframe was produced to allow the flight-test programme to proceed. Both prototypes were produced by the Kyiv Aircraft Production Plant.


title: Antonov An-70

text: Following the dissolution of the Soviet Union in the early 1990s, the programme became a joint development between Russia and Ukraine. The former compounded the issue of a reduced market with its intermittent commitment to the project. Repeated attempts to start production have had limited success. Western European countries, including Germany, at one stage assessed the aircraft for procurement, but many later decided against it.


title: Antonov An-70

text: The origins of the An-70 can be traced back to the mid-1970s, when Antonov Design Bureau began preliminary design work on a successor for the An-12 four-engine turboprop aircraft. The Soviet Armed Forces, by the 1980s, were looking for a replacement for the An-12 and a complement to the Ilyushin Il-76 four-engine jet transporter; in 1987, the Ministry of Defence, with a new emphasis on air mobility, specified an aircraft with a quick loading time, the ability to operate from short unprepared airfields, could carry up to 300 troops, and have good operating economy. The initial contract for work on the An-70 was concluded in May 1989; Antonov began advanced design work on the new aircraft during the same year. After the collapse of the Soviet Union, in June 1993, the Russian and Ukrainian governments agreed to jointly develop the An-70, with 80 percent of the funding expected to come from Russia. The following year, twenty companies and organisations from the former Soviet Union agreed to jointly develop, market and support the aircraft.


title: Antonov An-70

text: There were plans to establish mass ("serial") production of the model at the Kyiv Aircraft Production Plant (later renamed as Antonov Serial Production Plant), which was associated with but separate from the Antonov Design Bureau, and at the Samara Aircraft Production Plant (later reorganised as Aviakor) in Samara, Russia. At one stage during early development, Russia was showing reluctance at supporting the development of the An-70, and so Uzbekistan sought, unsuccessfully, to establish a final assembly plant in the capital at the Tashkent Aircraft Production Plant, where the production of the An-70's wings and the Il-76 were taking place. Construction of the first prototype had started in Kyiv in 1991. The maiden flight of the aircraft had originally been scheduled for late 1992. However, due to financing and design issues, this was pushed back until 1994. In particular, the weakened national currency diminished the firm's ability to pay for the aircraft's components, especially those sourced from Russia, and workers' salaries. In addition, engineers discovered numerous design and manufacturing deficiencies during the final ground checks, the majority of which were non-critical yet necessitated lengthy corrections. In the end, the aircraft made its maiden flight on 16 December 1994.


title: Antonov An-70

text: Crewed by a seven-man team, the first aircraft performed a short take off from Svyatoshino Airfield, Kyiv. This was the first flight of an aircraft that was powered only by propfans. Due to worsening weather conditions over Antonov's headquarters and the flight test area in Kyiv, the flight was cut short, and the flight ceiling was capped at 2,000 m (6,500 ft). The crew took the aircraft to a height of 450 m (1,475 ft), while performing basic checkouts of the prototype's systems. After having been airborne for less than half an hour, the aircraft landed at Antonov's flight test facility at Hostomel. During the flight, engineers identified problems with the engine gearboxes, and so the aircraft was grounded for eight weeks while the issues were fixed.


title: Antonov An-70

text: Originally, the aircraft was to conduct flight tests at Hostomel for three months before transferring to the Gromov Flight Research Institute in Zhukovsky, near Moscow. However, the first prototype was lost when it was making its fourth flight on 10 February 1995. During the flight, the aircraft suffered a sudden deviation from its intended flightpath and collided with the An-72 chase plane before spiralling into the ground, erupting into flames; the test crew of seven were killed. Although there were initial allegations of technical issues with the aircraft, it was later determined that the crash had been caused by human error.


title: Antonov An-70

text: Antonov subsequently converted the static-test prototype into a flying prototype equipped with a modified flight-control system. The second airframe was rolled out in December 1996 in Kyiv, before making its first flight on 24 April 1997 from Svyatoshino Airfield, during which the aircraft was airborne for 31 minutes; according to Jane's, however, the aircraft had taken off from Hostomel for a 26-minute flight. The second prototype's initial flight nearly ended in disaster, as the flight-control system repeatedly malfunctioned. Test pilot Oleksandr Halunenko was forced to manually land the prototype, for which he was honored with the Hero of Ukraine title. By this time, more than US$2.5 billion had been spent on the programme, with a further $200 million to be spent to prepare the aircraft for production, which was expected to have started in 1999 with 20–25 aircraft produced annually. The Russian and Ukrainian Air Forces reportedly had long-term plans to procure 500 and 100 aircraft, respectively. The second airframe was severely damaged during cold weather testing on 27 January 2001 in a crash landing after take-off.


title: Antonov An-70

text: In the early 1990s, the An-70 was unsuccessfully considered as a platform to meet the European Staff Requirement (ESR) for the Future Large Aircraft (FLA) programme; the programme envisaged the development of a transport aircraft that is midway in size and capability between the Lockheed Martin C-130J and the McDonnell Douglas C-17 to replace the C-130 Hercules. In October 1997, however, the German Defence Minister Volker Rühe announced his intention to study whether the An-70 could be the basis for the FLA. The decision arose out of the German government's objective of providing industrial aid to and thus enhancing political ties with Eastern Europe. In December 1997, France, Germany, Russia and Ukraine agreed to evaluate the An-70 as a candidate for the FLA programme.


title: Antonov An-70

text: Antonov proposed a "westernised" version of the An-70, the An-7X. The German government tasked DaimlerChrysler Aerospace (DASA) with the responsibility of evaluating the An-70 and assessing whether it would fulfill the ESR for a common tactical airlifter. Airbus provided data of the aircraft to DASA, who confirmed the data with its own wind-tunnel tests. According to the DASA study from 1999, the An-70 fulfilled the ESR, and that westernisation is possible, but work in key areas would have been necessary and risks existed. Areas identified include the introduction of full authority digital engine control, a completely new cockpit, a new flight-control system computer, the addition of in-flight refuelling capability, as well as modifications to allow paratroopers to be dropped from the rear cargo door. DASA recommended a change in the manufacturing method of the carbon-fiber-reinforced polymer components. Also the fuselage manufacturing-method was considered uneconomical. German, Ukrainian and Russian companies had formed the joint-venture "AirTruck" to plan and manage the modifications needed to westernise the An-70.


title: Antonov An-70

text: The German government, for political reasons, preferred the An-70. During a separate German Ministry of Defence evaluation of the An-7X, the aircraft was apparently considered to be superior to the A400M designed by the military branch of Airbus. According to AirTruck, the Defence Ministry estimated the An-7X to be 30 percent cheaper than its rival, would provide industrial benefits as Germany would receive substantial workshare, and was deemed to be technically superior, due mainly to its new propfan technology; however, a Defence Ministry spokesperson denied that a conclusion had been reached. On the other hand, DASA preferred the A400M, and refused to be the prime contractor for the An-70 if it was to be chosen. In the meantime, Belgium, France, Italy, Portugal, Spain, Turkey and the UK, were tentative members of the FLA programme and were estimated to have a requirement for up to 288 aircraft; Russia and Ukraine themselves were looking to acquire 210 An-70s. Other contenders for the FLA were the C-17 and C-130J. In April 2000, the German government, the strongest supporter of the An-70, stated that it was committed to buying the same aircraft as the other countries. In the end, the A400M was chosen for the FLA project; had the An-70 been chosen, fifty percent of the aircraft would have been manufactured by Airbus.


title: Antonov An-70

text: In December 1999, the Russian government outlined that it planned to purchase 164 aircraft by 2018. The Ukrainian government in October 2000 estimated that the country had a requirement for 65 aircraft. By then, the Russian government had awarded the Polyot plant, which was based in Omsk, the right to produce the aircraft, ahead of Aviakor and Aviastar of Samara and Ulyanovsk, respectively. The Kyiv Aircraft Production Plant was expected to produce the first aircraft in 2003, and Polyot, in 2004. As the An-70 flight test programme had reached its final stages by the end of 2000, it was expected that the Russian and Ukraine Defence Ministries would approve of mass production at the start of 2001. On 27 January 2001, however, the second An-70 prototype made a crash landing on its belly after losing power in two engines on take-off during cold weather testing in Omsk, and was severely damaged. Four of the 33 people on board were injured. Antonov recovered the crashed aircraft and repaired it, but the project still lacked funding.


title: Antonov An-70

text: In January 2002, preparations started on mass production as the Russian government affirmed that the aircraft was in the country's nine-year military budget; by now, Ukraine had already placed an order for five aircraft. Despite the affirmation that the country was committed to the project, there were other indications that Russia had lost considerable interest in the An-70. In February 2002, for example, the Defence Ministry did not contribute towards the An-70's development costs for the period, and at the same time military experts were withdrawn from the test programme. The following year, senior Russian Air Force officials publicly discredited the project; Commander-in-chief of the Russian Air Force, General Vladimir Mikhaylov, labelled it as undeveloped, and the aircraft as "dangerous," too heavy and too expensive. Indeed, there were rumours that Russia would soon abandon the project; however, in May 2003, Russian President Vladimir Putin reassured his Ukrainian counterpart that Russia was committed to the project.


title: Antonov An-70

text: Nevertheless, Antonov looked elsewhere for an industrial partner. In September that year, the company signed a memorandum of understanding (MoU) with China Aviation Industry Corporation II that covered the possible joint development of transport aircraft. Russian ambivalence towards the An-70 was made evident when the Russian Defence Ministry did not allocate any funds in the near future towards the procurement of the aircraft for its air force. Instead, resources were dedicated towards the upgraded Il-76MF. After the Orange Revolution in late 2004, and with Ukraine openly aiming for NATO membership, political will for the project evaporated. In April 2006, General Mikhaylov announced that Russia was withdrawing from the project, although at the time there was no official confirmation from the Russian government itself. Mikhaylov had reportedly been a staunch opponent of the An-70, claiming that the D-27 engine was "unreliable", and had advocated for the adoption of the Il-76MF, which was estimated to cost half that of the An-70. Up until then, Russia had provided around 60 percent of the estimated $5 billion invested in the project.


title: Antonov An-70

text: Intermittent commitment from the Russian side plagued the project, as Russia owed the programme an outstanding debt for the three years through 2009. According to various reports, Russia's conflict with Georgia in August 2008 highlighted the need for an airlifter in the class of the An-70, one that had a spacious cargo bay and the ability to operate from unpaved airstrips. Consequently, in August 2009, both countries agreed to resume development of the An-70. Ukraine continued to pursue flight testing of the sole prototype while making upgrades to the aircraft's avionics, sensors and propulsion system. It was reported that the Ukrainian Air Force would take delivery of its first two An-70s in 2011 and 2012; Volga-Dnepr Airlines had also signed an MoU with Antonov for five commercial-standard An-70Ts. A requirement for 60 An-70s was included in Russia's 2011–2020 national armament programme when it was issued in December 2010.


title: Antonov An-70

text: In late July 2010, Antonov suspended the flight test programme to update the aircraft. After an extensive series of modifications, including revised avionics (which reduced the flight crew from five to four) and changes to the aircraft's propellers to improve reliability and decrease noise, the second prototype An-70 flew again on 27 September 2012 and took part in the Aviasvit XXI airshow in Kyiv. During the same year, Russian and Ukrainian authorities agreed on the basic workshare of the production programme. Antonov in Kyiv would now produce the wings, tail surfaces and engine nacelles. The KAPO factory in Kazan, Russia, would be responsible for the manufacture of the fuselage, the final assembly of the aircraft, and flight testing. Other major components would come from Novosibirsk, Ulyanovsk and Voronezh; construction of the fuselage of the first production aircraft was reportedly complete in December 2012.


title: Antonov An-70

text: The test programme would last from September 2012 until April 2014, when the aircraft passed state acceptance trials. During that time, the An-70 conducted approximately 120 flights totalling 220 hours, with much of the certification effort carried out by Ukrainian specialists and officials. This is because, despite the aircraft's inclusion in Russia's state rearmament programme, Russia had withdrawn from the project in November 2012 reportedly due to slow progress, a fact that was disclosed only in April 2013. According to a report, the withdrawal of Russia from the project was, apart from a response to the Ukrainian government's EU choices, the result of political manoeuvring by Russian government officials with links to Ilyushin to pressure the government to purchase the Il-476, a re-winged variant of the Il-76. In total, the An-70 had conducted some 735 flights and had accumulated 930 hours during state tests.


title: Antonov An-70

text: As a result of the Crimean crisis, the Ukrainian government, in April 2014, announced that it would halt all military-technical cooperation with Russia. In August 2014, a Ukrainian court ordered the Russian Defence Ministry to make outstanding payments to Antonov. In March 2015, Russia Defence Ministry declared that it is ruling out the An-70 for state procurement. It also declared that, as in their opinion, Ukraine has withdrawn from the military and defence agreements signed before the crisis between them by completing the aircraft without Russian involvement, it would request return of 2.95 billion rubles that Russian government had spent on An-70 project.


title: Antonov An-70

text: The An-70 is a monoplane with a high-mounted wing design that features four distinctive propfan engines. Designed by the Progress Design Bureau, each of the D-27 engines is rated at 13,800 shp (which can be uprated to 16,000 shp), which is used to drive the SV-27 contra-rotating scimitar propellers designed by Aerosila; eight on the front propeller and six on the aft propeller. The propfan engines deliver slipstream to the supercritical wings that feature double-slotted trailing edges to provide high lift coefficients at low speeds. The modernisation of the aircraft during 2010–12 saw upgrades to the engines, including the incorporation of FADEC, and the further separation of the two propellers. The aircraft's cruise speed is 750 km/h (405 kt) at an operational altitude of ; Antonov claimed in 1997 that the aircraft had a design maximum speed of 850 km/h (460 kt, or Mach 0.8), which would have compared favourably with Mach 0.77 of the larger turbofan-powered C-17. According to DASA's evaluation, the propfan engines were 10 percent more efficient than conventional turboprops.


title: Antonov An-70

text: Similar to many aircraft designs of the Soviet Union, the An-70 was designed as an airlifter that could operate from unprepared fields. In short take-off and landing (STOL) configuration, the aircraft could lift off from a dirt strip with of cargo and fly for . Alternatively, it could fly the same distance with of cargo if it took off from a paved runway. For a payload-heavy mission, the An-70 can haul of cargo for a range of , but if range was essential, the aircraft can carry a load of over . In exceptional circumstances, the An-70 subjected to lower-"g" take-offs, can airlift a T-80U main battle tank and fly it for . The fully pressurised internal cabin measures wide and high, and has a length of from the front to the ramp; with the ramp included, the total cabin length is . In comparison, the turbofan-powered Il-76 has a lower cross-sectional cargo area, but exceeds the An-70 in payload capability and ramp length. The An-70's cargo hold is serviced by four electrical hoists that facilitate autonomous cargo loading. A central floor can be rapidly installed for the accommodation of 300 soldiers or 200 injured personnel over two decks.