Aarushhh/wikipedia-simple-splitted huggingface dataset:
Interval arithmetic is a specific type of computer arithmetic for (mathematical) intervals. It is mainly used for the automated detection of errors. There is a value, which isn't known exactly, but which can be given by an interval: the value is known to be inside the interval. There's a function to calculate the error. This function should be given the unknown value, but instead can only be given the interval. The result is a function which will map intervals.

Interval arithmetic can be used to treat rounding errors, or to treat insecurities with measurements: Each measurement has a certain error, which cannot be determined exactly.

Definition
For real intervals (interval of real numbers), interval arithmetic is defined as follows:

 Addition: 
 Subtraction: 
 Multiplication: 
 Division:

where

Applications
Interval arithmetic is mainly used in the field of validated numerics. It is also used in other technical areas.

Implementations
Implementations

Since the birth of interval arithmetic, many experts have made interval arithmetic programs. The most famous works are INTLAB (made with MATLAB), arb, JuliaIntervals, and kv.

Community
There are several international conferences about interval arithmetic. One of the most largest meeting is the International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (usually abbreviated as SCAN). There are also SWIM (Small Workshop on Interval Methods), PPAM (International Conference on Parallel Processing and Applied Mathematics), and REC (International Workshop on Reliable Engineering Computing).

References

Other websites
 Interval arithmetic (Wolfram Mathworld)
 Interval Methods from Arnold Neumaier , University of Vienna

Workshops
SWIM (Summer Workshop on Interval Methods)
International Conference on Parallel Processing and Applied Mathematics
Libraries
 INTLAB, Institute for Reliable Computing 
 Ball arithmetic by  Joris van der Hoeven
 kv - a C++ Library for Verified Numerical Computation
 Arb - a C library for arbitrary-precision ball arithmetic
 Interval and related software 

Numerical analysis
Computer science
Arithmetics
Strawberry and Chocolate () is a 1993 Cuban Mexican comedy drama movie directed by Tomás Gutiérrez Alea and Juan Carlos Tabío and is based on the 1990 short story The Wolf, The Forest and the New Man by Senel Paz. It stars Jorge Perugorría, Vladimir Cruz, Mirta Ibarra, Francisco Gattorno and was distributed by Miramax Films. It was nominated for an Academy Award in 1995.

Other websites

1993 comedy-drama movies
1990s LGBT movies
Movies based on short stories
Cuban movies
Mexican comedy movies
Mexican drama movies
Mexican LGBT movies
Movies directed by Juan Carlos Tabío
Movies directed by Tomás Gutiérrez Alea
Movies set in the 1970s
Movies set in Cuba
Remote Control is a 1992 Icelandic comedy movie directed by Óskar Jónasson and stars Björn Jörundur Friðbjörnsson, Icelandic metal band HAM, Helga Braga Jónsdóttir, Björn Karlsson.

Other websites

1992 comedy movies
Icelandic movies
Z for Zachariah is a 2015 Icelandic New Zealand Swiss science fiction movie directed by Craig Zobel and based on the novel of the same name by Robert C. O'Brien. It stars Chris Pine, Margot Robbie, Chiwetel Ejiofor and was distributed by Lionsgate Films.

Other websites
 

2015 science fiction movies
Icelandic movies
New Zealand science fiction movies
Swiss movies
Movies directed by Craig Zobel
Post-apocalyptic movies
Dystopian movies
Faysal Ahmed is a Somali-American actor from Minneapolis, Minnesota. He was born in Mogadishu, Somalia in 1985. He was raised in Yemen in his childhood and at the age of 14 his family settled in USA.

He is most known for his role in the 2013 movie "Captain Phillips", where he played Najee.

References

1985 births
Living people
Actors from Minnesota
People from Mogadishu‎
African actors
Ashes and Diamonds is a 1958 Polish World War II drama movie directed by Andrzej Wajda and based on the 1948 novel of the same name by Jerzy Andrzejewski. It stars Zbigniew Cybulski, Ewa Krzyżewska, Adam Pawlikowski, Ignacy Machowski and was distributed by KADR.

Other websites

 

1958 drama movies
1958 war movies
Polish drama movies
World War II movies
Movies based on books
Movies directed by Andrzej Wajda
Space Master X-7 is a 1958 American science fiction movie directed by Edward Bernds and starring Bill Williams, Lyn Thomas, Robert Ellis, Paul Frees, Rhoda Williams, Moe Howard, Thomas Browne Henry. It was distributed by 20th Century Fox.

Other websites
 
 
 

1958 science fiction movies
American science fiction movies
Movies directed by Edward Bernds
Blood Arrow is a 1958 American western movie directed by Charles Marquis Warren and starring Scott Brady, Paul Richards, Phyllis Coates, Don Haggerty, Diana Darrin, Jeanne Bates. It was distributed by 20th Century Fox.

Other websites
 

1958 movies
1950s Western (genre) movies
American Western (genre) movies
Movies directed by Charles Marquis Warren
20th Century Fox movies
Moulin Rouge is a 1952 British drama movie directed by John Huston and based on the 1950 novel of the same name by Pierre La Mure. It stars Zsa Zsa Gabor, José Ferrer, Suzanne Flon, Katherine Kath, Peter Cushing, Christopher Lee, Michael Balfour and was distributed by United Artists. It was nominated for 7 Oscars and won 2 Academy Awards in 1953.

Other websites

1952 drama movies
British drama movies
Movies set in the 1890s
Movies based on books
Movies directed by John Huston
Rabie Ablak, or Rabie Al-Ablak (born 1987), is a Moroccan journalist. He is a part of the Hirak Rif Movement. He has been on hunger strike to protest his detention and inhumane treatment.
Some of his hunger strikes lasted more than 40 days;  he was taken to hospital several times for treatment. The total of his hunger strikes are more than 284 days.

Career 
He was a writer for the electronic newspaper Badil, founded by Hamid El Mahdaoui, in the town of Al Hoceima, where he had a part in the Popular Rif movement along with Nasser Zafzafi.

Rabie was arrested on 28 May 2017, in the town of Al Hoceïma. 
According to Amnesty International, he was tortured. 
He was sentenced to five years' of prison in Tangier II prison. On 6 September 2019, he began a new hunger strike.

References 

Moroccan writers
Journalists
1987 births
High Noon is a 1952 American western movie directed by Fred Zinnemann and starring Gary Cooper, Thomas Mitchell, Grace Kelly, Lloyd Bridges, Otto Kruger, Lon Chaney Jr., Harry Morgan, Katy Jurado, Lee Van Cleef. It was distributed by United Artists and was nominated for 7 Oscars and won 4 Academy Awards in 1953.

Other websites
 
 
 

1952 movies
1950s Western (genre) movies
American Western (genre) movies
Movies directed by Fred Zinnemann
Antifeminism is opposition to some or all forms of feminism. It has changed over the years and in different cultures. In the late 19th century and early 20th century antifeminists were opposed to women's suffrage, that is allowing women to vote in elections. In the United States in they also opposed the Equal Rights Amendment, which would give change the Constitution to give both men and women equal rights. In the 21st century, antifeminists believe that feminism is not about rights for women, but is about taking away the rights of men.

References

Antifeminism
A Talking Cat!?! is a 2013 independent children's film directed by David DeCoteau. The film was released by Phase 4 Films direct to DVD on February 18, 2013. Eric Roberts is featured as the voice of the talking cat.

Synopsis
Two families with one parent are brought together by Duffy (Eric Roberts), a cat who can talk. Phil Barber, (Johnny Whitaker), a wealthy man, recently sold his computer company to spend more time with his son Chris (Justin Cone), a model, who does not care about this decision. At the same time, Susan (Kristine DeBell) is finding it hard to make enough money as a caterer with her two children Tina (Janis Peebles) and Trent (Daniel Dannas). Duffy then enters the families' lives, talking to them to give them advice, but can only talk to each person once.

Cast
 Johnny Whitaker as Phil Barber
 Kristine DeBell as Susan
 Justin Cone as Chris Barber
 Janis Peebles as Tina
 Alison Sieke as Frannie
 Daniel Dannas as Trent
 Eric Roberts as Duffy (voice)
Production
The film is one of several direct-to-video family films directed by David DeCoteau using the false name Mary Crawford. It was shot in three days in the same mansion as his 1313 series. Eric Roberts' dialogue was recorded in 15 minutes.

Reception
The film is mostly hated. Film.com hated Duffy. The A.V. Club gave a mostly negative review for the film, but said "for lovers of utter, unredeemable trash, it is highly recommended." CraveOnline also gave a negative review, but said the film should be for "Bad Movie Night".

In an interview, DeCoteau, talking about the film, said "people have called me who I haven't seen since high school who said, 'David, after 100 movies you've finally made a movie we like.'" He added, "I watched it again, because I hadn't seen it since we made it, and it is so ridiculous and hilarious and over-the-top."

References

Other websites
 
 

2013 comedy movies
Movies about cats
American movies
American children's comedy movies
Ulrich Müther (21 July 1934 - 21 August 2007) was an East German builder.

Life 
He was born in Binz. In 1953, his family's construction firm was taken. In 1958, he became manager of the company. In 1993, his firm went bankrupt, during German reunification.

He was influenced by Felix Candela and Oscar Niemeyer. He designed and built about 74 concrete shell buildings.

Buildings 

 Rostock-Schutow (1966).
 Ostseeperle beach restaurant in Glowe (1968)
 "Tea pot" in Warnemünde
 Lifeguard station in Binz.
 The Hyparschale (1969)

Further reading 
 Ulrich Müther. Shell Structures in Mecklenburg-Western Pomerania, 2010. ISBN 97837212-07477
 Beckh, Matthias, Juan Ignacio del Cueto Ruiz-Funes, Matthias Ludwig, Andreas Schätzke and Rainer Schützeichel (2020). Candela Isler Müther: Positions on Shell Construction. Positionen zum Schalenbau. Posturas sobre la construcción de cascarones. Basel: Birkhäuser Publishers. ISBN 978-3-0356-2096-2.

References 

1934 births
2007 deaths
East German people
Groesbeek is a town and former municipality in the province of Gelderland, the Netherlands. On 1 January 2015, the former municipality merged with Millingen aan de Rijn and Ubbergen. The larger area was known as Groesbeek until 1 January 2016, when its name was changed to Berg en Dal.

References 

21st-century disestablishments in the Netherlands
Former municipalities of Gelderland
Settlements in Gelderland
Berg en Dal
Millingen aan de Rijn is a town and former municipality in the province of Gelderland, the Netherlands. Since 2015, it has been part of the new municipality of Berg en Dal (formerly known as Groesbeek).

21st-century disestablishments in the Netherlands
Former municipalities of Gelderland
Settlements in Gelderland
Berg en Dal
Slochteren is a village and former municipality in the province of Groningen, the Netherlands. Since 2018, it has been part of the new municipality of Midden-Groningen.

21st-century disestablishments in the Netherlands
Former municipalities of Groningen (province)
Settlements in Groningen (province)
Midden-Groningen
Borger-Odoorn is a municipality in the province of Drenthe, the Netherlands. In 2019, 25,372 people lived there.

Municipalities of Drenthe
De Wolden is a municipality in the province of Drenthe, the Netherlands. In 2019, 24,110 people lived there.

Municipalities of Drenthe
Hoogeveen (Dutch Low Saxon:  't Ogeveine or  't Oveine) is a town and municipality in the province of Drenthe, the Netherlands. In 2019, 55,662 people lived there.
Midden-Drenthe is a municipality in the province of Drenthe, the Netherlands. In 2019, 33,178 people lived there.

The municipality was created on 1 January 1998, in a merger of the former municipalities of Beilen, Smilde, and Westerbork. Between 1998 and 2000, the name of the municipality was Middenveld.

Municipalities of Drenthe
Noordenveld is a municipality in the province of Drenthe, the Netherlands. In 2019, 31,290 people lived there.

Municipalities of Drenthe
Tynaarlo is a municipality in the province of Drenthe, the Netherlands. In 2019, 33,698 people lived there.

Settlements in Drenthe
Municipalities of Drenthe
Westerveld is a municipality in the province of Drenthe, the Netherlands. In 2019, 19,348 people lived there.

Municipalities of Drenthe
Marcelo Spina (born July 23, 1970) is an Argentinean-American architect (AIA) and educator. He is a partner in Los Angeles-based architecture firm PATTERNS, which he founded in 2002. Since 2001, he has been a Design and Applied Studies Faculty at SCI-Arc.

Education
He holds a B.Arch. from the National University of Rosario, Argentina (1994) and a Master in Advanced Architectural Design from the Graduate School of Architecture, Planning and Preservation of Columbia University in New York (1997).

Career
Spina has worked for RUR Architects and Keller Easterling in New York and Gerardo Caballero Architects. He opened his own office Banchini + Spina Arquitectos in Rosario, Argentina (1998-2002). At SCI-Arc, he was the coordinator of the Applied Studies Program from 2005 to 2009 and the Architectural Technologies Postgraduate Program from 2011 to 2019. He has been a member of the Board of Trustees since 2016.
Juries and advisory
He has served on national juries and advisory boards such as The Architectural League of New York, Progressive Architecture Awards and the Mies Crown Hall Americas Prize. He has been a visiting professor at the Universities of Pennsylvania, Syracuse, Harvard, Berkeley, Vienna, Innsbruck, and Di Tella among others. In 2013, he was the Louis I. Kahn visiting assistant professor of Architectural Design at Yale University School of Architecture.

As co-author
Spina is the co-author of PATTERNS Embedded (ACDCU, 2010), Material Beyond Materials (SCI-Arc Press 2012)  and Mute Icons and other Dichotomies of the Real in Architecture (Princeton 2016). He co-curated Matters of Sensation at Artists Space with Georgina Huljich.
Projects
 Jujuy Redux Apartment in Rosario, Argentina (2012)
 Prism Gallery in Los Angeles, California (2009)
 Zhixin Hybrid office building in Chengdu, China (2010)
 FYF Residence in Rosario, Argentina (2009)
 League of Shadows even structure in Los Angeles, California (2013)
 MOCA Textile Room Pavilion, Los Angeles, CA (2012)
 The White Album Performance, New York, NY & Los Angeles, CA (2019)
 Land Tiles Temporary Installation, Los Angeles, CA (2003)
 Snake-Rice Sculpture, Icheon, South Korea (2003)
 Jujuy 2056 Apartment in Rosario, Argentina (2003)

Awards and Recognition
2019: AIA LA Merit Award, Casa del Sol, Mykonos

2017: AIA LA Merit Award, Janoian Medical Building, Glendale, CA

2016: AIA LA Merit Award, Victory Healthcare, North Hollywood, CA

2015: ACSA Faculty Award, Toronto, Canada

2014: American Architecture Award, The Chicago Athenaeum, Jujuy Redux, with MSA

2013: United States Artists Grigor Fellow, Los Angeles
2012: Honorable Mention, Jujuy Redux, AIA Annual Design Review AIA LA Merit Award, Jujuy Redux, Rosario, Argentina AIA LA Honor Award, Collective Void Dormitory, Puerto Rico First Prize, SCI-Arc Graduation Pavilion Competition, Los Angeles, CA

2011: Emerging Voices, Architectural League of New York, NY

2008: Graham Foundation Grant, "Matters of Sensation" Artists Space, New York, NY

2007: Honorific Mention, International Competition, Skopje Concert Hall, Skopje, Macedonia

2006: First Prize, Vertical Garden Invited Competition, MAK Center at the Schindler House, Los Angeles, CA

2004: Design Vanguard Selection, Architectural Record, New York, NY

2003: First Prize, SCI_Arc CafÈ, SCI-Arc Faculty Competition, Los Angeles, CA Third Prize, Young Architect of the Year Award, International Award Competition, Building Design, London, UK

1997: Honor Award for Excellence in Design, Columbia University, GSAPP, New York, NY William Kinne Prize
Among other places, his designs have most notably been exhibited at the Venice Biennale in Italy, MOCA,  The Chicago Biennial,  The MAK Museum, The Art Institute of Chicago,  and the San Francisco MOMA.

References

Other website
 Patterns

1970 births
Living people
Argentine architects
American architects
People from Rosario, Argentina
Amstelveen is a municipality in the Dutch province of North Holland. In 2019, 90,838 people lived there.

Settlements in North Holland
Municipalities of North Holland
Beemster is a former municipality in the Dutch province of North Holland. In 2021, about 10,100 people lived there. 

Since 2022, it has been part of the municipality of Purmerend.

World Heritage Sites in the Netherlands
21st-century disestablishments in the Netherlands
Former municipalities of North Holland
Purmerend
Valmigère is a commune of 17 people (2017). It is in the region Occitanie in the Aude department in the south of France.

References 

Communes in Aude
Pakistan International Airlines Flight 8303 was a flight in Pakistan. It was between Allama Iqbal International Airport in Lahore, Punjab and Jinnah International Airport in Karachi, Sindh. The plane crashed on its final approach into Karachi in the Model Colony area of the city on 22 May 2020. The crash killed 97 people of the 99 people on board and one on the ground. It injured 9 others: 2 on the plane and 7 on the ground.

References

2020 disasters in Asia
International Airlines Flight 8303
Aviation accidents and incidents in Asia
2020s in Sindh
Karachi
May 2020 events
2020 in Pakistan
Aviation accidents and incidents in 2020
Live Forever or Liveforever may refer to:

Plants
Dudleya, a genus of succulent plants
Hylotelephium, a genus of succulent perennial plants
Sempervivum, a genus of succulent plants

Music

Albums
Live Forever (The Screaming Jets album), 2002
Live Forever (Matthew West album), 2015 
Live Forever – The Album, a 2007 album by Magnus Carlsson
Live Forever: The Stanley Theatre, Pittsburgh, PA, September 23, 1980, a 2011 live album by Bob Marley
Live Forever (Lil Peep mixtape), 2015

Songs
"Live Forever" (The Band Perry song), 2015
"Live Forever" (Magnus Carlsson song), 2007
"Live Forever" (Oasis song), 1994
"Live Forever", a song by Black Sabbath from the album 13
"Live Forever", a song by Hollywood Undead from Day of the Dead
"Live Forever", a song by Drew Holcomb and the Neighbors
"Live Forever", a 2010 single by Lange featuring Emma Hewitt

Other
Immortality, living for an infinite length of time
Live Forever: The Rise and Fall of Brit Pop, a 2003 documentary film
Related pages
Aizoon (Greek: "live forever"), a plant species named by Max Koch
Wilson Roosevelt Jerman (January 21, 1929 – May 16, 2020) was a butler. He worked for 11 different American presidents in the White House. He was born in Seaboard, North Carolina. 

Jerman was promoted to butler under John F. Kennedy, and continued in that role until his retirement in 1993 during the Bill Clinton administration. He returned to the White House in 2003 in the George W. Bush administration. He worked as a maitre d' and elevator operator for Barack Obama before his final retirement in 2012.

Jerman died at the age of 91 on May 16, 2020 from COVID-19 in Woodbridge, Virginia at the age of 91.

References

1929 births
2020 deaths
Deaths from the COVID-19 pandemic in the United States
People from North Carolina
Seaboard is a town in Northampton County, North Carolina, United States.

The population was 632 at the 2010 census. It is part of the Roanoke Rapids, North Carolina Micropolitan Statistical Area.

References

Towns in North Carolina
Northampton County is a county located in the U.S. state of North Carolina. As of the 2020 census, the population was 17,471. Its county seat is Jackson.

References

18th-century establishments in North Carolina
1741 establishments in the Thirteen Colonies
North Carolina counties
Jackson is a town in Northampton County, North Carolina, United States. The population was 513 at the 2010 census. It is the county seat of Northampton County.

Jackson is part of the Roanoke Rapids, North Carolina Micropolitan Statistical Area.

References

Towns in North Carolina
County seats in North Carolina
Roanoke Rapids () is a city in Halifax County, North Carolina, United States. The population was 15,754 at the 2010 census.

References

Cities in North Carolina
Halifax County is a county located in the U.S. state of North Carolina. As of the 2010 census, the population was 54,691. Its county seat is Halifax.

References

1750s establishments in North Carolina
1758 establishments
North Carolina counties
Halifax is a town in Halifax County, North Carolina, United States. The population was 234 at the 2010 census. It is the county seat of Halifax County.

References

Towns in North Carolina
County seats in North Carolina
Weldon is a town in Halifax County, North Carolina, United States. The population was 1,655 at the 2010 census.

References

Towns in North Carolina
Woodbridge is a census-designated place (CDP) in Prince William County, Virginia, United States, located  south of Washington, D.C. It had 54,275 residents at the 2010 census. As of 2020, Woodbridge has 71,553 residents.

References

Census-designated places in Virginia
Berith Maria Kristina Bohm (23 August 1932 – 14 May 2020) was a Swedish opera singer and actress. She performed in a talent show during her teens in Bromma and performed the song Fjorton år tror jag visst att jag var. 

She began her stage career in Stockholm and then went to Stora Teatern in Gothenburg. Her best known theatre role was as Csardasfurstinnan in "Sköna Helena". She also performed at Volksoper in Vienna, Austria.

Bohm died on 14 May 2020 at the age of 87.

References

1932 births
2020 deaths
Swedish stage actors
Singers from Stockholm
Actors from Stockholm
Neil Howlett (24 July 1934 – 21 May 2020) was an English operatic baritone. He sang leading roles in major opera houses and festivals. He performed at the Royal Opera House, Teatro Colón, and the English National Opera, where he was the Principal Baritone for seventeen years. He was born in Mitcham, Greater London. 

Howlett was a professor at the Guildhall School of Music, and later, after retiring from full-time performance, Head of Vocal Studies at the Royal Northern College of Music. He taught privately in London and Lincolnshire.

Howlett died on 21 May 2020, aged 85.

References

1934 births
2020 deaths
British academics
Singers from London
Arnulf Kolstad (23 April 1942 – 21 May 2020) was a Norwegian social psychologist. He was born in Oslo. He was a  professor emeritus of Social Psychology at the Norwegian University of Science and Technology (NTNU). 

He was appointed by the King-in-Council at the then-University of Trondheim in 1986 and was head of department for the Department of Psychology from 1990 to 1992. He became professor emeritus in 2012.

He was critical of the 2010 Nobel Peace Prize going to Liu Xiaobo as "western arrogance".

Kolstad died on 21 May 2020 in Oslo, aged 78.

References

1942 births
2020 deaths
Norwegian academics
Norwegian scientists
Norwegian psychologists
Writers from Oslo
Sergei Makarovich Kramarenko (; 10 April 1923 – 21 May 2020) was a Soviet Air Force officer. He fought in World War II and the Korean War. He was honored withHero of the Soviet Union. He retired in 1977 with the rank of major-general. He was the last living Soviet flying ace of Korean War.

Kramarenko died on 21 May 2020, aged 97.

References

Other websites

1923 births
2020 deaths
Soviet military personnel of World War II
Alan Gilbert Merten (December 27, 1941 – May 21, 2020) was an American educator. He was the fifth President of George Mason University from 1996 until his retirement in 2012. He was born in Milwaukee, Wisconsin.

Merten died on May 21, 2020 in Florida from Parkinson's disease-related problems, aged 78.

References

1942 births
2020 deaths
Deaths from Parkinson's disease
Educators from Milwaukee
Writers from Milwaukee
John David Pawson (25 February 1930 – 21 May 2020) was an English evangelical minister, writer, theologian and Bible. He was born in Newcastle upon Tyne, England. He was the pastor of Guildford Baptist Church. 

In The Normal Christian Birth, Pawson argued that for a person to enter into Christianity, it should involve more than the simple "Sinner's Prayer". He also believed that a person who goes to hell, should stay there for eternity.

Pawson died on 21 May 2020, aged 90.

References

Other websites
 
 David Pawson Teaching Trust, UK – a non-profit making trust designed to protect and promote the teaching for future years.

1930 births
2020 deaths
British teachers
English Protestants
English theologians
Writers from Tyne and Wear
Evangelicals
People from Newcastle upon Tyne
Ashley John Cooper AO (15 September 1936 – 22 May 2020) was an Australian tennis player. He was born in Melbourne. He  played from 1953 until 1968. He was seen as the world's best amateur player during the years of 1957 and 1958. Cooper won four singles and four doubles titles at Grand Slam tournaments. He won three of the four Grand Slam events in 1958. 

Cooper died on 22 May 2020 at the age of 83 after a long illness in Melbourne.

References

1936 births
2020 deaths
Australian tennis players
Sportspeople from Melbourne
Green Island is a coterminous town-village in Albany County, New York, United States. The population was 2,620 at the 2010 census. The postal code is 12183.

References

Towns in New York (state)
Villages in New York (state)
Herkimer is a village on the north side of the Mohawk River and the county seat of Herkimer County, New York, United States. As of the 2010 census, it had a population of 7,743.

References

Villages in New York (state)
County seats in New York (state)
German Flatts is a town in Herkimer County, New York, United States. The population was 13,258 at the 2010 census.

References

Towns in New York (state)
Webb is the northernmost town in Herkimer County, New York, United States. As of the 2010 census it had a population of 1,807.

References

Towns in New York (state)
Mory Kanté (29 March 1950 – 22 May 2020) was a Guinean singer. He was born in Albadaria, French Guinea.

He was best known for his 1987 hit song "Yé ké yé ké", which reached number-one in Belgium, Finland, the Netherlands, and Spain. His album, Akwaba Beach, was the best-selling African record of its time. On 16 October 2001, Kanté was nominated Goodwill Ambassador of the Food and Agriculture Organization of the United Nations (FAO).

On 22 May 2020, Kanté died at a hospital in Conakry from a chronic disease, at the age of 70.

References

Other websites
 Official website
 Mory Kanté at Mondomix
 Mory Kanté at Leopardmannen

1950 births
2020 deaths
Guinean people
Singers
Anatoliy Matviyenko (22 March 1953 – 22 May 2020) was a Ukrainian politician. He was born in Bershad, Vinnytsia Oblast. He was Governor of the Vinnytsia Oblast from 1996 to 1998. He was a member of the Verkhovna Rada from 1990 to 1994, 1998 to 2005, 2006 to 2007 and again from 2014 until his death.

He was an activist of Komsomol (LKSMU) and by 1985 became a secretary of the Central Committee of LKSMU. In 1989-91 Matviyenko became the first secretary of the Ukrainian Komsomol and became a member of the Communist Party of Ukraine.

Matviyenko died on 22 May 2020 in Kiev, at the age of 67.

References

Other websites
 Who is who at the Ukraine Official.
 Biography

1953 births
2020 deaths
Members of the Verkhovna Rada
Luigi "Gigi" Simoni (22 January 1939 – 22 May 2020) was an Italian football player and manager. He was born near Bologna, Italy.

He played for A.S.D. Mantova F.C., S.S.C. Napoli, Torino F.C., Juventus F.C., Brescia Calcio and Genoa C.F.C.. His playing career lasted from 1959 to 1974. He was known for managing Napoli and Inter Milano. His managing career lasted from 1974 to 2012.

Simoni died at his home on 22 May 2020 in Pisa, Italy from stroke-related problems, aged 81.

References

1939 births
2020 deaths
Deaths from stroke
Footballers from Bologna
Italian football managers
Giulio Savelli (27 September 1941 – 12 May 2020) was an Italian politician and publisher. He was born in Rome. Savelli was elected to the Chamber of Deputies as a member of Forza Italia. He was a deputy from 1996 and 2001.  

Savelli died on 12 May 2020 in Rome at the age of 78.

References

1941 births
2020 deaths
Publishers
Politicians from Rome
The 2014 United States Senate election in Iowa took place in Iowa on November 4, 2014. In it, Republican State Senator Joni Ernst faced off Democrat Bruce Baley. Ernst won the election with 52.1% of the vote to Baley's 43.8%.

Fundraising 
Baley's campaign raised slightly more money than Ernst's. His campaign also spent a lot more of that money, spending $10 million, while Ernst's spent $6.6 million.

Three Debates 
Three televised debates were set to occur, one in Des Moines, one in Davenport and one in Sioux City.

Republican Primaries

Joni Ernst 
State Senator Joni Ernst ran in the primaries. She won all but eight of the counties in Iowa in the primaries, and 56.1% of the vote.

Mark Jacobs 
C.E.O. Mark Jacobs ran in the primaries. He won just one county in North Iowa, and 16.8% of the vote.

Sam Clovis 
Radio host Sam Clovis ran in the primaries. He won seven counties in Northwest Iowa, and 18.0% of the vote.

Steve King 
Congressman Steve King decided against running.
Matthew Whitaker 
Matthew Whitaker, an attorney, ran, but did not win any counties, and carried just 7.5% of the vote.

United States Senate election in Iowa
2010s elections in the United States
United States Senate
21st century in Iowa
Ventenac-Cabardès is a commune. It is in the region Occitanie in the Aude department in the south of France.

References 

Communes in Aude
Lowndes County is a county in the U.S. state of Georgia. As of the 2020 census, 118,251 people lived there. The county seat is Valdosta.

References

1825 establishments in Georgia (U.S. state)
Georgia (U.S. state) counties
Coronado is a city in San Diego County, California.

Cities in California
Settlements in San Diego County, California
Cook County is a county in the U.S. state of Georgia. As of the 2020 census, 17,229 people lived there. The county seat is Adel.

References

1910s establishments in Georgia (U.S. state)
1918 establishments in the United States
Georgia (U.S. state) counties
Adel is a city in the U.S. state of Georgia. It is the county seat of Cook County.

Cities in Georgia (U.S. state)
County seats in Georgia
Argyle is a town in the U.S. state of Georgia. It is in Clinch County.

Towns in Georgia (U.S. state)
Dawson County is a county in the U.S. state of Georgia. As of the 2020 census, 26,798 people lived there. The county seat is Dawsonville.

References

1857 establishments in Georgia (U.S. state)
Georgia (U.S. state) counties
Dawsonville is a city in the U.S. state of Georgia. It is the county seat of Dawson County. The population was 3,720 at the 2020 census.

References 

Cities in Georgia (U.S. state)
County seats in Georgia
Woodsfield is a village in Ohio in the United States. It is the county seat of Monroe County.

Villages in Ohio
County seats in Ohio
Evans County is a county in the U.S. state of Georgia. As of the 2020 census, 10,774 people lived there. The county seat is Claxton.

References

1914 establishments in Georgia (U.S. state)
Georgia (U.S. state) counties
"Rain on Me" is a song by American singers Lady Gaga and Ariana Grande.  It was released on May 22, 2020, as the second single from Gaga’s sixth studio album, Chromatica. It was written by the singers with Rami Yacoub, Nija Charles, Alexander Ridha, and its producers, BloodPop, Tchami, and BURNS.

On June 1, 2020, it was announced that the song entered at number one on the Billboard Hot 100.  The song became Gaga’s fifth number-one single in the US and Grande’s fourth. Grande became the first artist with four songs on the Hot 100 to enter at the top, passing Justin Bieber, Drake, and Mariah Carey, who had three each at the time. It became Gaga's second number-one entrance after "Born This Way" in 2011. The song is also the only female collaboration to enter at number one in the US.

Charts

Weekly charts

Monthly charts

Year-end charts

References 

2020 songs
Lady Gaga songs
Ariana Grande songs
Dance-pop songs
Grammy Award winning songs
House songs
Disco songs
Super Cyclonic Storm Amphan was a very powerful tropical cyclone that caused a lot of damage in East India and Bangladesh in May 2020. It caused over US$13 billion dollars of damage and killed a total of 118 people. It was the strongest cyclone to hit the Ganges Delta since Cyclone Sidr in 2007.

It formed on the 16 May in the Bay of Bengal and tracked into the Ganges Delta before dissipating on the 21 May.

References

May 2020 events
Tropical cyclones in Asia
2020 in weather
Simone Budde (born 2 January 1979) is a German water polo player. She was part of the Germany women's national water polo team at the 2003 World Aquatics Championships, 2007 World Aquatics Championships, and 2009 World Aquatics Championships.

References

Other websites 
 Simone Budde - Simone Budde Photos - Zimbio

1979 births
Living people
German water polo players
Super Cyclonic Storm Kyarr was a powerful tropical cyclone that was the first super cyclonic storm since 2007. The storm moved across the Arabian Sea and affected Western India, Arabia, and Somalia. Nobody was killed from the storm, as it never tracked over land.

References

October 2019 events
November 2019 events
Tropical cyclones in Asia
2019 in weather
The 2020 North Indian Ocean cyclone season is an ongoing event in the annual cycle of tropical cyclone formation. The North Indian Ocean cyclone season has no real bounds, but cyclones usually form between April and November, with the highest amount of storms in May and October.

There has been one tropical cyclone so far in the season, Cyclone Amphan. It was the strongest cyclone since 2007.

2020 in weather
North Indian Ocean cyclones
Tetraoxygen (O4), or oxozone, is a molecule made up of four oxygen atoms. It does not exist in nature anywhere and can only be made under extreme conditions in a lab. The molecule was first created in a lab in 2001.

References

Oxygen
June Dalziel Almedia (5 October 1930 – 1 December 2007) was a Scottish virologist. She had very good skills in electron microscopy. During the 2019–20 coronavirus outbreak, her research was used to help beat the virus.

References

1930 births
2007 deaths
British virologists
William Lyon (March 9, 1923 – May 22, 2020) was a major general of the United States Air Force. He was Commander of the United States Air Force Reserve Command. As chief of Air Force Reserve, Lyon was the principal adviser on Reserve matters to the Air Force Chief of Staff. He was born in Los Angeles, California.

Lyon died on May 22, 2020 in Coto de Caza, California at the age of 97.

References

1923 births
2020 deaths
American generals
People from Los Angeles
Military people from California
Coto de Caza (meaning hunting preserve in Spanish) is a census-designated place (CDP) and guard-gated private community in Orange County, California. The population was 14,710 at the 2020 census.

References

Other websites
CZ Master Association, official community website.
Los Ranchos Estates Homeowner's Association, official community website.

Census-designated places in California
Settlements in Orange County, California
was a Japanese female professional wrestler. She wrestled for  Stardom. Her mother is former wrestler Kyoko Kimura. Kimura was born in Yokohama, Japan.

Kimura was trained at  Wrestle-1's Professional Wrestling University.

She debuted on March 30, 2016 against Reika Saiki in a losing effort for Wrestle-1. The pair wrestled against each many times throughout 2016 for Wrestle-1.

Kimura killed herself by swallowing hydrogen sulfide on May 23, 2020, at the age of 22.

References

1997 births
2020 deaths
Drug-related suicides
Japanese professional wrestlers
Sportspeople from Yokohama
Syed Muhammad Fazal Agha (; (1946 – 20 May 2020) was a Pakistani politician. He was Governor of Balochistan from August 18 to October 12 1999. He also was Deputy Chairman of the Senate of Pakistan from 1988 to 1991. from Balochistan. He was a member of the Provincial Assembly of Balochistan from 13 August 2018 till his death.

Agha was born in Killi Huramzai, Pishin District. He died on 20 May 2020 from COVID-19 in Karachi, aged 78.

References

1946 births
2020 deaths
Deaths from the COVID-19 pandemic in Pakistan
Politicians from Balochistan (Pakistan)
Pishin District
In complex analysis, Euler's formula, also sometimes called Euler's relation, is an equation involving complex numbers and trigonometric functions. More specifically, it states that

where x is a real number, e is Euler's number and i is the imaginary unit.

It makes a relation between trigonometric functions and exponential functions of complex numbers. It is named after Leonhard Euler, who published it in 1748. When he published it, Euler said that the angle must be a real number. Later, it turned out that the formula also works if the angle is not a real number, but a complex one.

When the angle is  and , Euler's formula becomes   and , respectively.

Related pages 

 Euler's identity

References 

Complex analysis
Trigonometry
Atropatene was an ancient kingdom that existed in part of what is now Iran. It existed with Darius III of Persia and Alexander the Great. It started in the 4th century BCE, in what is now northern Iran. Its capital was Ganzak. It ended as a vassal kingdom of the Parthian empire. In 226, the Sasanian empire conquered it. At that time it was probably more of a province of the Parthian empire than a kingdom, even though its rulers were kings. 

Today, many people see it as a predecessor of the modern state of Azerbaijan.

History of Iran
Former countries in the Middle East
Former monarchies of Asia
The Virgin Komi Forests is a large woodland in the northern part of the Ural mountain range, in Russia. The forests are part of the Komi Republic of Russia. The forests cover an area of  and are the largest virgin forests in Europe.

They were made a UNESCO World Heritage site in 1995. Most of the area is flat Taiga plain, about  above sea level. They rise towards the Ural mountains.

They are threatened because parts of the area contain a lot of gold. Illegal logging is also a threat.

World Heritage Sites in Russia
Leo the Last is a 1970 British drama movie directed by John Boorman and based on the play The Prince by George Tabori. It stars Marcello Mastroianni, Billie Whitelaw, Calvin Lockhart, Brinsley Forde, Graham Crowden and was distributed by United Artists.

Other websites
 
 

1970 drama movies
British drama movies
British plays adapted into movies
Movies directed by John Boorman
Knife in the Water () is a 1962 Polish drama movie directed by Roman Polanski in his directorial debut and stars Leon Niemczyk, Jolanta Umecka, Zygmunt Malanowi. It was nominated for an Academy Award in 1964.

Other websites
 
 
 

1962 drama movies
Polish drama movies
Movies directed by Roman Polanski
Numerical methods for partial differential equations are computational schemes to obtain approximate solutions of partial differential equations (PDEs).

Scientific Background

Motivation of this area
Many PDEs appeared for the study of physics and other areas in science. Therefore, many mathematicians have challenged to make methods to solve them, but there is no method to mathematically solve PDEs except the Hirota direct method and the inverse scattering method. This is why numerical methods for PDEs are needed.

The Finite Difference Method (FDM) and its problems
One of the most basic PDE solver is the finite difference method (FDM). This method approximates derivatives as differences:
This method works for easy problems. But it is powerless to some equations (such as the Navier–Stokes equations) because they are non-linear. Since this difficulty appeared, numerical analysts started to study other methods (just like the finite element method, FEM). On the other hand, some experts started to consider improvements for FDM.

Evolution of the FDM
Experts have discovered difference methods which preserves the property of the given PDE.

Integrable Difference Schemes
Ryogo Hirota, Mark Ablowitz and others have made methods that preserves the integrability (important mathematical property in the theory of dynamical systems) of PDEs. These methods are known to have better accuaracy than the original FDM.
Structure Preserving Numerical Methods
Many PDEs have appeared from physics. So we can think about difference methods preserving physical properties. These difference methods are known as structure preserving numerical methods. The following list is the examples of them:
 Symplectic integrators
 Discrete gradient method
 Discrete variational derivative method (DVDM)
Some experts are studying their relation between numerical linear algebra.

Others
The difference mthods in above have high accuracy, but their usage is limited because they depend on the behaviour of the given PDEs. This is why new types of FDM are still studied. For example, the following methods are studied:
 Shortley-Weller approximation
 Swarztrauber-Sweet approximation
 Ascher-Mattheij-Russell difference formula

Validated Numerics for PDEs
Not only approximate solvers, but the study to "verify the existence of solution by computers" is also active. This study is needed because numerically obtained solutions could be phantom solutions (fake solutions). This kind of incident is already reported.

PDEs that have been Studied in the Context of Validated Numerics

Journal
The scientific journal "Numerical Methods for Partial Differential Equations" is published to promote the studies of this area.

Related Software
Chebfun is one of the most famous software in this field. They are also many libraries based on the finite element method such as:
 FreeFem++
 FEniCS Project

Experts in this Field

 Israel Gelfand
 John von Neumann
 Masatake Mori
 Peter Deuflhard
 Peter Lax
 Shinichi Oishi

References
References

Further Reading
 Iserles, A. (2009). A first course in the numerical analysis of differential equations. Cambridge University Press.
 Computational Partial Differential Equations Using MATLAB, Jichun Li and Yi-Tung Chen, Chapman & Hall.
 Ames, W. F. (2014). Numerical methods for partial differential equations. Academic Press.
 Ganzha, V. G. E., & Vorozhtsov, E. V. (1996). Numerical solutions for partial differential equations: problem solving using Mathematica. CRC Press.
Literatures for specific solvers are described as follows.

Finite Element Method
Brenner, S., & Scott, R. (2007). The mathematical theory of finite element methods. Springer Science & Business Media.
 Johnson, C. (2012). Numerical solution of partial differential equations by the finite element method. Courier Corporation.
 Strang, G., & Fix, G. J. (1973). An analysis of the finite element method. Englewood Cliffs, NJ: Prentice-hall.
 Boffi, D., Brezzi, F., & Fortin, M. (2013). Mixed finite element methods and applications. Heidelberg: Springer.
 Braess, D. (2007). Finite elements: Theory, fast solvers, and applications in solid mechanics. Cambridge University Press.

Finite Difference Method
 Smith, G. D. (1985). Numerical solution of partial differential equations: finite difference methods. Oxford University Press.
 Strikwerda, J. C. (2004). Finite difference schemes and partial differential equations. SIAM.
Finite Volume Method
 Eymard, R. Gallouët, T. R. Herbin, R. (2000) The finite volume method, in Handbook of Numerical Analysis, Vol. VII, 2000, p. 713–1020. Editors: P.G. Ciarlet and J.L. Lions.
 LeVeque, Randall (2002), Finite Volume Methods for Hyperbolic Problems, Cambridge University Press.

Boundary Element Method
Banerjee, Prasanta Kumar (1994), The Boundary Element Methods in Engineering (2nd ed.), London, etc.: McGraw-Hill.
 Beer, Gernot; Smith, Ian; Duenser, Christian, The Boundary Element Method with Programming: For Engineers and Scientists, Berlin – Heidelberg – New York: Springer-Verlag, pp. XIV+494.
 Cheng, Alexander H.-D.; Cheng, Daisy T. (2005), "Heritage and early history of the boundary element method", Engineering Analysis with Boundary Elements, 29 (3): 268–302.
 Katsikadelis, John T. (2002), Boundary Elements Theory and Applications, Amsterdam: Elsevier, pp. XIV+336.
 Wrobel, L. C.; Aliabadi, M. H. (2002), The Boundary Element Method, New York: John Wiley & Sons, p. 1066, (in two volumes).

Spectral Method
Spectral Method

 Lloyd N. Trefethen (2000) Spectral Methods in MATLAB. SIAM, Philadelphia, PA.
 D. Gottlieb and S. Orzag (1977) "Numerical Analysis of Spectral Methods : Theory and Applications", SIAM, Philadelphia, PA.
 J. Hesthaven, S. Gottlieb and D. Gottlieb (2007) "Spectral methods for time-dependent problems", Cambridge UP, Cambridge, UK.
 Canuto C., Hussaini M. Y., Quarteroni A., and Zang T.A. (2006) Spectral Methods. Fundamentals in Single Domains. Springer-Verlag, Berlin Heidelberg

Structure Preserving Numerical Methods
Leimkuhler, B. and Reich, S., Simulating Hamiltonian Dynamics, Cambridge University Press, Cambridge, 2004.
 Sanz‐Serna, J. M. and Calvo, M. P., Numerical Hamiltonian Problems, Applied Mathematics and Mathematical Computation 7, Chapman & Hall, London, 1994.
 Arnold, D. N., Bochev, P. B., Lehoucq, R. B., Nicolaides, R. A. and Shashkov, M. (eds.), Compatible Spatial Discretizations, in The IMA Volumes in Mathematics and Its Applications, Springer, New York, 2006.
 Budd, C. and Piggott, M. D., Geometric integration and its applications, in Handbook of Numerical Analysis, XI, North‐Holland, Amsterdam, 2003, 35‐139.
 Christiansen, S. H., Munthe‐Kaas, H. Z. and Owren, B., Topics in structure‐preserving discretization, Acta Numerica, 20 (2011), 1‐119.
 Shashkov, M., Conservative Finite‐Difference Methods on General Grids, CRC Press, Boca Raton, 1996.

Partial differential equations
Numerical analysis
Ivan's Childhood (), sometimes released as My Name Is Ivan is a 1962 Russian World War II drama movie directed by Andrei Tarkovsky and is based on the 1957 short story Ivan by Vladimir Bogomolov. It stars Nikolai Burlyaev, Valentin Zubkov, Evgeny Zharikov, Nikolai Grinko and was distributed by Mosfilm.

Other websites

1962 drama movies
1962 war movies
World War II movies
Russian drama movies
Movies directed by Andrei Tarkovsky
Strike (, translit. Stachka) is a 1925 Russian drama movie directed by Sergei Eisenstein and stars Maskim Shtraukh, Grigori Aleksandrov, Aleksandr Antonov. It was distributed by Goskino Proletkult.

Other websites
 
 

1925 drama movies
Russian drama movies
Russian silent movies
Movies directed by Sergei Eisenstein
Ariel is a 1988 Finnish drama movie directed and written by Aki Kaurismäki and starring Turo Pajala, Susanna Haavisto, Matti Pellonpää. It was distributed by Finnkino.

Other websites
 
 

1988 drama movies
1980s road movies
Finnish movies
Movies directed by Aki Kaurismäki
Drifting Clouds () is a 1996 Finnish comedy drama movie directed by Aki Kaurismäki and starring Kati Outinen, Kari Väänänen, Markku Peltola, Elina Salo. It was distributed by Sputnik.

Other websites
 
 

1996 comedy-drama movies
Finnish movies
German drama movies
French drama movies
Movies directed by Aki Kaurismäki
Kiss of the Spider Woman () is a 1985 Brazilian American drama movie directed by Héctor Babenco and based on the 1976 novel of the same name by Manuel Puig. It stars William Hurt, Raul Julia, Sônia Braga, José Lewgoy, Milton Gonçalves, Míriam Pires and was distributed by Island Pictures. It was nominated for 4 Oscars, including Best Picture and won Best Actor for Hurt in 1986.

Other websites
 

1985 drama movies
1980s LGBT movies
American drama movies
Brazilian movies
Movies directed by Héctor Babenco
American independent movies
The UK Championship is a snooker tournament. It is one of the Triple Crown events, along with the World Championship and the Masters. It is the second-biggest ranking tournament, after the World Championship. Ronnie O'Sullivan has won the most times. Ding Junhui is the current champion.

Winners 
''

Statsistics

References