nc33/MultiSpan_SQUAD huggingface dataset:
Group_(mathematics)

Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.

Question: What concept is of basic importance in modern physics?
Answer: Lie groups

Question: What connects continuous symmetries to conserved quantities?
Answer: Noether's theorem

Question: What term describes the basic symmetries of the laws of mechanics?
Answer: Rotation

Question: What concept relates measurements of time and velocity of two observers in motion relative to each other?
Answer: Lorentz transformations

Question: What describe the complete symmetry group of Minkowski space including translations?
Answer: Poincaré group
Group_(mathematics)

In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.

Question: What product is created if the requirement that every element has an inverse is eliminated?
Answer: monoid

Question: What type of numbers under addition form a monoid?
Answer: natural numbers N (including 0)

Question: What method formally adds inverses to elements to any monoid?
Answer: the Grothendieck group

Question: What can be replaced to simplify abstract algebra concepts?
Answer: the binary operation
Central_African_Republic

The Central African Republic (CAR; Sango: Ködörösêse tî Bêafrîka; French: République centrafricaine  pronounced: [ʁepyblik sɑ̃tʁafʁikɛn], or Centrafrique [sɑ̃tʀafʁik]) is a landlocked country in Central Africa. It is bordered by Chad to the north, Sudan to the northeast, South Sudan to the east, the Democratic Republic of the Congo and the Republic of the Congo to the south and Cameroon to the west. The CAR covers a land area of about 620,000 square kilometres (240,000 sq mi) and had an estimated population of around 4.7 million as of 2014[update].

Question: Where is the Central African Republic located?
Answer: Central Africa

Question: What country borders CAR in the North?
Answer: Chad

Question: What Country borders CAR in the South?
Answer: the Republic of the Congo

Question: What Country borders CAR in the West?
Answer: Cameroon

Question: What is the population of CAR approximately?
Answer: 4.7 million
Central_African_Republic

What is today the Central African Republic has been inhabited for millennia; however, the country's current borders were established by France, which ruled the country as a colony starting in the late 19th century. After gaining independence from France in 1960, the Central African Republic was ruled by a series of autocratic leaders; by the 1990s, calls for democracy led to the first multi-party democratic elections in 1993. Ange-Félix Patassé became president, but was later removed by General François Bozizé in the 2003 coup. The Central African Republic Bush War began in 2004 and, despite a peace treaty in 2007 and another in 2011, fighting broke out between various factions in December 2012, leading to ethnic and religious cleansing of the Muslim minority and massive population displacement in 2013 and 2014.

Question: Who established CAR's borders?
Answer: France

Question: What country ruled CAR as a colony?
Answer: France

Question: When did CAR become independent?
Answer: in 1960

Question: Who was the first democratically elected President?
Answer: Ange-Félix Patassé

Question: What religion is a minority in CAR?
Answer: Muslim minority
Central_African_Republic

Approximately 10,000 years ago, desertification forced hunter-gatherer societies south into the Sahel regions of northern Central Africa, where some groups settled and began farming as part of the Neolithic Revolution. Initial farming of white yam progressed into millet and sorghum, and before 3000 BC the domestication of African oil palm improved the groups' nutrition and allowed for expansion of the local populations. Bananas arrived in the region and added an important source of carbohydrates to the diet; they were also used in the production of alcoholic beverages.[when?] This Agricultural Revolution, combined with a "Fish-stew Revolution", in which fishing began to take place, and the use of boats, allowed for the transportation of goods. Products were often moved in ceramic pots, which are the first known examples of artistic expression from the region's inhabitants.

Question: How long ago did people start living in the area?
Answer: Approximately 10,000 years ago

Question: What agricultural job did people settling in the area perform?
Answer: farming

Question: What vegetation helped populations expand?
Answer: African oil palm

Question: What was an imported food that provided most of the carbohydrates?
Answer: Bananas

Question: What important protein helped with expansion of the inhabitants?
Answer: Fish
Central_African_Republic

During the 16th and 17th centuries slave traders began to raid the region as part of the expansion of the Saharan and Nile River slave routes. Their captives were slaved and shipped to the Mediterranean coast, Europe, Arabia, the Western Hemisphere, or to the slave ports and factories along the West and North Africa or South the Ubanqui and Congo rivers. In the mid 19th century, the Bobangi people became major slave traders and sold their captives to the Americas using the Ubangi river to reach the coast. During the 18th century Bandia-Nzakara peoples established the Bangassou Kingdom along the Ubangi River.

Question: When did the slave trade hit the CAR region?
Answer: 16th and 17th centuries

Question: What is one area where captive slaves were sent?
Answer: Europe

Question: Which people were major slave traders in the 19th century?
Answer: Bobangi people

Question: Who did the Bobangi sell slave to?
Answer: the Americas

Question: What river saw the establishment of a new Kingdom?
Answer: Ubangi River
Central_African_Republic

In 1920 French Equatorial Africa was established and Ubangi-Shari was administered from Brazzaville. During the 1920s and 1930s the French introduced a policy of mandatory cotton cultivation, a network of roads was built, attempts were made to combat sleeping sickness and Protestant missions were established to spread Christianity. New forms of forced labor were also introduced and a large number of Ubangians were sent to work on the Congo-Ocean Railway. Many of these forced laborers died of exhaustion, illness, or the poor conditions which claimed between 20% and 25% of the 127,000 workers.

Question: When was Equatorial Africa established?
Answer: 1920

Question: Where was Equatorial African ran from?
Answer: Brazzaville

Question: What plant was mandated to be grown by the French?
Answer: cotton

Question: What important infrastructure was built in the 1920s.
Answer: a network of roads

Question: What religion was spread through CAR?
Answer: Christianity
Central_African_Republic

In September 1940, during the Second World War, pro-Gaullist French officers took control of Ubangi-Shari and General Leclerc established his headquarters for the Free French Forces in Bangui. In 1946 Barthélémy Boganda was elected with 9,000 votes to the French National Assembly, becoming the first representative for CAR in the French government. Boganda maintained a political stance against racism and the colonial regime but gradually became disheartened with the French political system and returned to CAR to establish the Movement for the Social Evolution of Black Africa (MESAN) in 1950.

Question: During what war did French officers setup headquarters in CAR?
Answer: Second World War

Question: Who was elected in 1946 as the first representative?
Answer: Barthélémy Boganda

Question: How many votes did Boganda get?
Answer: 9,000 votes

Question: What was Bogandas platform that he ran for?
Answer: political stance against racism

Question: What caused Boganda to leave his elected post?
Answer: disheartened with the French political system
Central_African_Republic

In the Ubangi-Shari Territorial Assembly election in 1957, MESAN captured 347,000 out of the total 356,000 votes, and won every legislative seat, which led to Boganda being elected president of the Grand Council of French Equatorial Africa and vice-president of the Ubangi-Shari Government Council. Within a year, he declared the establishment of the Central African Republic and served as the country's first prime minister. MESAN continued to exist, but its role was limited. After Boganda's death in a plane crash on 29 March 1959, his cousin, David Dacko, took control of MESAN and became the country's first president after the CAR had formally received independence from France. Dacko threw out his political rivals, including former Prime Minister and Mouvement d'évolution démocratique de l'Afrique centrale (MEDAC), leader Abel Goumba, whom he forced into exile in France. With all opposition parties suppressed by November 1962, Dacko declared MESAN as the official party of the state.

Question: What was the overwhelming amount of votes MESAN captured?
Answer: 347,000 out of the total 356,000 votes

Question: How many seats did MESAN win?
Answer: every legislative seat

Question: Who was elected president of the Grand Council?
Answer: Boganda

Question: How did Boganda die?
Answer: a plane crash

Question: Who took over after Boganda died?
Answer: his cousin, David Dacko
Central_African_Republic

In April 1979, young students protested against Bokassa's decree that all school attendees would need to buy uniforms from a company owned by one of his wives. The government violently suppressed the protests, killing 100 children and teenagers. Bokassa himself may have been personally involved in some of the killings. In September 1979, France overthrew Bokassa and "restored" Dacko to power (subsequently restoring the name of the country to the Central African Republic). Dacko, in turn, was again overthrown in a coup by General André Kolingba on 1 September 1981.

Question: What caused a violent uprising?
Answer: young students protested against Bokassa's decree

Question: How many were killed in the April 1979 protests?
Answer: 100 children and teenagers

Question: Who overthrew Bokassa after this incident?
Answer: France

Question: Who did France restore into power?
Answer: Dacko

Question: Who eventually overthrew Dacko?
Answer: General André Kolingba
Central_African_Republic

By 1990, inspired by the fall of the Berlin Wall, a pro-democracy movement arose. Pressure from the United States, France, and from a group of locally represented countries and agencies called GIBAFOR (France, the USA, Germany, Japan, the EU, the World Bank, and the UN) finally led Kolingba to agree, in principle, to hold free elections in October 1992 with help from the UN Office of Electoral Affairs. After using the excuse of alleged irregularities to suspend the results of the elections as a pretext for holding on to power, President Kolingba came under intense pressure from GIBAFOR to establish a "Conseil National Politique Provisoire de la République" (Provisional National Political Council, CNPPR) and to set up a "Mixed Electoral Commission", which included representatives from all political parties.[citation needed]

Question: What was inspired by the fall of the Berlin wall?
Answer: a pro-democracy movement

Question: What large country pressured CAR to hold elections?
Answer: the United States

Question: When were free elections held?
Answer: October 1992

Question: Who helped with the Free Elections?
Answer: UN Office of Electoral Affairs

Question: What excuse did Kolingba use to deny the election results?
Answer: alleged irregularities
Central_African_Republic

When a second round of elections were finally held in 1993, again with the help of the international community coordinated by GIBAFOR, Ange-Félix Patassé won in the second round of voting with 53% of the vote while Goumba won 45.6%. Patassé's party, the Mouvement pour la Libération du Peuple Centrafricain (MLPC) or Movement for the Liberation of the Central African People, gained a simple but not an absolute majority of seats in parliament, which meant Patassé's party required coalition partners.[citation needed]

Question: When was a second democratic election held?
Answer: in 1993

Question: Who became the first democratically elected president?
Answer: Ange-Félix Patassé

Question: What percentage did Patasse win with?
Answer: 53% of the vote

Question: What was the winning party?
Answer: Mouvement pour la Libération du Peuple Centrafricain

Question: Did Patasse get a majority of the votes?
Answer: gained a simple but not an absolute majority
Central_African_Republic

Patassé purged many of the Kolingba elements from the government and Kolingba supporters accused Patassé's government of conducting a "witch hunt" against the Yakoma. A new constitution was approved on 28 December 1994 but had little impact on the country's politics. In 1996–1997, reflecting steadily decreasing public confidence in the government's erratic behaviour, three mutinies against Patassé's administration were accompanied by widespread destruction of property and heightened ethnic tension. During this time (1996) the Peace Corps evacuated all its volunteers to neighboring Cameroon. To date, the Peace Corps has not returned to the Central African Republic. The Bangui Agreements, signed in January 1997, provided for the deployment of an inter-African military mission, to Central African Republic and re-entry of ex-mutineers into the government on 7 April 1997. The inter-African military mission was later replaced by a U.N. peacekeeping force (MINURCA).

Question: When was the new constitution for CAR approved?
Answer: 28 December 1994

Question: When did a mutiny form against Patasse?
Answer: In 1996–1997

Question: The mutinies caused what effects on the country?
Answer: widespread destruction of property

Question: What agreement gave the authority for deployment of military intervention?
Answer: The Bangui Agreements

Question: Where did the peace corps evacuate to?
Answer: Cameroon
Central_African_Republic

In the aftermath of the failed coup, militias loyal to Patassé sought revenge against rebels in many neighborhoods of Bangui and incited unrest including the murder of many political opponents. Eventually, Patassé came to suspect that General François Bozizé was involved in another coup attempt against him, which led Bozizé to flee with loyal troops to Chad. In March 2003, Bozizé launched a surprise attack against Patassé, who was out of the country. Libyan troops and some 1,000 soldiers of Bemba's Congolese rebel organization failed to stop the rebels and Bozizé's forces succeeded in overthrowing Patassé.[citation needed]

Question: The failed coup caused what effects?
Answer: murder of many political opponents

Question: Which General was involved in another coup?
Answer: General François Bozizé

Question: Where did General Bozize flee to escape?
Answer: Chad

Question: When did Bozize finally attempt his coup?
Answer: March 2003

Question: Who succeeded in finally overthrowing Patasse?
Answer: Bozizé's forces
Central_African_Republic

In 2004 the Central African Republic Bush War began as forces opposed to Bozizé took up arms against his government. In May 2005 Bozizé won a presidential election that excluded Patassé and in 2006 fighting continued between the government and the rebels. In November 2006, Bozizé's government requested French military support to help them repel rebels who had taken control of towns in the country's northern regions. Though the initially public details of the agreement pertained to logistics and intelligence, the French assistance eventually included strikes by Mirage jets against rebel positions.

Question: What war started in 2004?
Answer: Bush War

Question: In what way did Bozize made his rule legitimate?
Answer: Bozizé won a presidential election

Question: When did CAR ask for assistance from the French against rebels?
Answer: November 2006

Question: How did the French assist against the rebels?
Answer: strikes by Mirage jets

Question: What did the rebels take over?
Answer: towns in the country's northern regions
Central_African_Republic

The Syrte Agreement in February and the Birao Peace Agreement in April 2007 called for a cessation of hostilities, the billeting of FDPC fighters and their integration with FACA, the liberation of political prisoners, integration of FDPC into government, an amnesty for the UFDR, its recognition as a political party, and the integration of its fighters into the national army. Several groups continued to fight but other groups signed on to the agreement, or similar agreements with the government (e.g. UFR on 15 December 2008). The only major group not to sign an agreement at the time was the CPJP, which continued its activities and signed a peace agreement with the government on 25 August 2012.

Question: What agreement called for the stop of Hostilities?
Answer: Syrte Agreement

Question: What did the Birao Peace Agreement call for?
Answer: the liberation of political prisoners

Question: What major group did not sign the peace agreement immediately?
Answer: CPJP

Question: When did the CPJP finally sign the peace agreement?
Answer: 25 August 2012

Question: When was the Birao Peace Agreement signed?
Answer: April 2007
Central_African_Republic

Michel Djotodia took over as president and in May 2013 Central African Republic's Prime Minister Nicolas Tiangaye requested a UN peacekeeping force from the UN Security Council and on 31 May former President Bozizé was indicted for crimes against humanity and incitement of genocide. The security situation did not improve during June–August 2013 and there were reports of over 200,000 internally displaced persons (IDPs) as well as human rights abuses and renewed fighting between Séléka and Bozizé supporters.

Question: Who became president in 2013?
Answer: Michel Djotodia

Question: What was Bozize indicted for?
Answer: crimes against humanity

Question: What mass murder did Bozize commit?
Answer: genocide

Question: How many people were displaced in the unrests?
Answer: 200,000

Question: What faction was fighting against the remaining Bozize loyalists?
Answer: Séléka
Central_African_Republic

In the southwest, the Dzanga-Sangha National Park is located in a rain forest area. The country is noted for its population of forest elephants and western lowland gorillas. In the north, the Manovo-Gounda St Floris National Park is well-populated with wildlife, including leopards, lions, cheetahs and rhinos, and the Bamingui-Bangoran National Park is located in the northeast of CAR. The parks have been seriously affected by the activities of poachers, particularly those from Sudan, over the past two decades.[citation needed]

Question: What national part is located in the South West?
Answer: Dzanga-Sangha National Park

Question: What large animals reside in the national park?
Answer: forest elephants

Question: Which Primate can be found in the national park?
Answer: lowland gorillas

Question: What National Park can be found in the North?
Answer: Manovo-Gounda St Floris

Question: What has threatened the wildlife in this park?
Answer: the activities of poachers
Central_African_Republic

In 2006, due to ongoing violence, over 50,000 people in the country's northwest were at risk of starvation but this was averted due to assistance from the United Nations.[citation needed] On 8 January 2008, the UN Secretary-General Ban Ki-Moon declared that the Central African Republic was eligible to receive assistance from the Peacebuilding Fund. Three priority areas were identified: first, the reform of the security sector; second, the promotion of good governance and the rule of law; and third, the revitalization of communities affected by conflicts. On 12 June 2008, the Central African Republic requested assistance from the UN Peacebuilding Commission, which was set up in 2005 to help countries emerging from conflict avoid devolving back into war or chaos.

Question: Due to fighting, what threatened people in the NorthWest?
Answer: risk of starvation

Question: Who assisted in saving the people from starvation?
Answer: United Nations

Question: Who headed the UN effort to rebuild CAR?
Answer: Secretary-General Ban Ki-Moon

Question: When did CAR request assistance directly to prevent war?
Answer: 12 June 2008

Question: Who assisted CAR in avoiding war?
Answer: UN Peacebuilding Commission
Central_African_Republic

A new government was appointed on 31 March 2013, which consisted of members of Séléka and representatives of the opposition to Bozizé, one pro-Bozizé individual, and a number representatives of civil society. On 1 April, the former opposition parties declared that they would boycott the government. After African leaders in Chad refused to recognize Djotodia as President, proposing to form a transitional council and the holding of new elections, Djotodia signed a decree on 6 April for the formation of a council that would act as a transitional parliament. The council was tasked with electing a president to serve prior to elections in 18 months.

Question: When was the new Government seated in CAR?
Answer: 31 March 2013

Question: What did the former opposition parties declare?
Answer: boycott the government

Question: Who was refused as new president?
Answer: Djotodia

Question: Who would rule the country temporarily?
Answer: a transitional parliament

Question: How long did the parliament have until the next election?
Answer: 18 months