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Galois theory , named after Évariste Galois , was introduced to give criteria deciding if an equation is solvable using radicals .	Galois theory , named after Évariste Galois , were introduced to give criteria deciding if an equation is solvable using radicals .
It follows that the study of algebraic equations is equivalent to the study of polynomials .	So the study of algebraic equations is equivalent to the study of polynomials .
Finally Niels Henrik Abel proved , in 1824 , that equations of degree 5 and equations of higher degree are not always solvable using radicals .	Finally Niels Henrik Abel proved in 1824 that the equation of degree 5 and the equations of higher degree can not always be solved by using radicals .
During the Renaissance , Gerolamo Cardano found the solution to equations of degree 3 and Lodovico Ferrari solved equations of degree 4 .	During the Renaissance , Gerolamo Cardano solved the equation of degree 3 and Lodovico Ferrari solved the equation of degree 4 .
In this case the equation is a diophantine equation .	Then , the equation is a diophantine equation .
The ancient Egyptians knew how to solve equations of degree 2 in this manner .	The ancient Egyptians knew how to solve equations of degree 2 ( that is equations in which the highest power of the variable is 2 ) in this manner .
Two equations are equivalent if they have the same set of solutions .	Two equations are called equivalent if they have the same set of solutions .
Ancient mathematicians wanted the solutions in the form of radical expressions , like for the positive solution of .	Ancient mathematicians wanted the solutions of univariate equations ( that is , equations with one variable ) in the form of radical expressions , like for the positive solution of .
In particular the equation is equivalent with .	The equation is equivalent with .
A polynomial equation over the rationals can always be converted to an equivalent one in which the coefficients are integers .	If an algebraic equation is over the rationals , it can always be converted to an equivalent one , where all the coefficients are integers .
In mathematics , an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field , often the field of the rational numbers .	In mathematics , an algebraic equation , also called polynomial equation over a given field is an equation of the form where P and Q are polynomials over that field , and have one ( univariate ) or more than one ( multivariate ) variables .
Transcendence theory is the study of the real numbers which are not solutions to an algebraic equation over the rationals .	For example is an algebraic equation over the rational numbers .
For example , for an equation over the rationals one may look for solutions in which all the variables are integers .	For example , for an equation over the rationals , one can find solutions in the integers .
However , it is a polynomial equation in the three variables x , y , and z over the field of the elementary functions in the variable T . As for any equation , the solutions of an equation are the values of the variables for which the equation is true .	The equation is converted to The solutions of an equation are the values of the variables for which the equation is true .
For univariate algebraic equations these are also called roots , even if , properly speaking , one should say the solutions of the algebraic equation P = 0 are the roots of the polynomial P . When solving an equation , it is important to specify in which set the solutions are allowed .	But for algebraic equations there are also called roots .
The derivative ( rate of change ) of the exponential function is the exponential function itself .	Two mathematical examples of exponential functions are shown below .
The importance of the exponential function in mathematics and the sciences stems mainly from properties of its derivative .	In mathematics , an exponential function is a function that quickly grows .
Prosperity has always returned and will again . ''	Prosperity ( wealth ) has always returned ( come back ) and will again . ''
Even after the Wall Street Crash of 1929 , optimism persisted for some time ; John D. Rockefeller said that `` These are days when many are discouraged .	John D. Rockefeller said that `` These are days when many are discouraged .
Tickets for the show sold out in five minutes .	The tickets sold out in five minutes .
The band played a `` secret show '' at the Manhattan Center Grand Ballroom in New York City on November 4 , 2009 , with label mates Civil Twilight .	The band played a sold-out `` secret show '' at the Manhattan Center Grand Ballroom in New York City on November 4 , 2009 , along with label-mates Civil Twilight .
Evanescence is an American rock band founded in Little Rock , Arkansas in 1995 by singer\/pianist Amy Lee and guitarist Ben Moody .	It was founded in 1995 in Little Rock , Arkansas by singer Amy Lee and former-guitarist Ben Moody .
On June 12 , 2011 , Amy Lee announced through her Twitter account that Troy McLawhorn was officially back with Evanescence and that the release date for the new album would be October 4 , 2011 .	On June 12 , Lee announced through her Twitter account that McLawhorn was officially back with Evanescence and that the new release date for the album was October 4 , 2011 .
This performance acted as a warm-up for their headline appearance at the Maquinária Festival in São Paulo , Brazil , which took place on November 8 .	Lee told the audience that the bands ' appearance was a warm-up for their headlining appearance at the Maquinária festival in São Paulo , Brazil , which took place on November 8 .
The second single , `` My Heart Is Broken '' , was sent to radio stations in October 31 , 2011 .	`` My Heart is Broken '' was chosen as the second single and sent to radio stations in October 31 , 2011 .
A spokesperson for the band 's label confirmed on July 14 , 2006 , that bassist Will Boyd had left the band for `` not wanting to do another big tour '' and wanting `` to be close to his family . ''	Will Boyd left the band in 2006 for `` not wanting to do another big tour '' and for wanting `` to be close to his family '' .
On May 4 , 2007 , John LeCompt announced that he had been fired from Evanescence , and also stated that drummer Rocky Gray had decided to quit .	On May 4 , 2007 , John LeCompt said that he was fired from Evanescence , and that Rocky Gray left the band .
Evanescence entered the studio on February 22 , 2010 , to begin recording .	Evanescence entered the studio on February 22 , 2010 to begin recording and chose Steve Lillywhite to produce the album .
Evanescence was founded by singer , pianist and songwriter Amy Lee and former lead guitarist and songwriter Ben Moody .	The people who founded Evanescence are singer , songwriter and pianist Amy Lee and guitarist and songwriter Ben Moody who is no longer a member in the band .
Announced in June 2009 , the newest line-up of the band eventually returned with Evanescence , their self-titled third studio album , released on October 11 , 2011 .	Evanescence , the bands ' self-titled third studio album , was eventually released on October 11 , 2011 .
In 2006 , the band released their second studio album , The Open Door , which sold more than five million copies .	In 2006 , the band released their second studio album , The Open Door , which was positively received .
After recording independent albums , the band released their first full-length album , Fallen , on Wind-up Records in 2003 .	The band released Fallen , their first full-length album , in 2003 .
Billboard ranked Evanescence No. 71 on the Best Artists of the Decade chart .	Evanescence was ranked at # 71 on the Best Artists of the Decade chart .
Moody was replaced by Terry Balsamo from Cold .	Moody was replaced by another guitarist , Terry Balsamo .
A year later , Evanescence released their first live album , Anywhere but Home , which sold more than one million copies worldwide .	In 2004 , Evanescence released Anywhere but Home , their first live album .
The two met in 1994 at a youth camp in Little Rock , where Moody heard Lee playing `` I 'd Do Anything for Love ( But I Wo n't Do That ) '' by Meat Loaf on the piano .	They met in a youth camp in 1994 , when Moody heard Lee playing a song on the piano .
Two of Lee and Moody 's songs were played on local radio stations , raising local awareness of the group and demand for a concert .	Two of their songs were played on the local radio station and the listeners wanted them to do a concert .
The album has sold more than a million copies worldwide .	The album was a critical and commercial success and sold more than 17 million copies worldwide ; spawning the hit singles `` Bring Me to Life '' and `` My Immortal '' .
The first single , `` What You Want '' , was released on August 9 , 2011 .	`` What You Want '' became the first single off the album , and was released in August 9 , 2011 to positive critical reception .
The band eventually appeared live , and became one of the most popular acts in the area .	They later appeared live and became a popular act in their area .
The album also debuted at No. 1 on four other different Billboard charts ; the Rock Albums , Digital Albums , Alternative Albums , and the Hard Rock Albums charts .	It debuted at # 1 in 5 Billboard charts , including the Hot 200 and Rock Albums charts .
Fallen spent 43 weeks on the Billboard Top 10 ; was certified 7x Platinum in the United States ; and sold more than 17 million copies worldwide .	It sold over 15 million copies and was certified 7x platinum in the United States .
Also on the CD are the live songs `` Breathe No More '' ( from the Elektra movie soundtrack ) , `` Farther Away '' , and the band 's cover of Korn 's `` Thoughtless '' .	The CD also had three live songs , Breathe No More , Farther Away , and the band 's cover of Korn 's Thoughtless .
Fallen sold more than 17 million copies worldwide and helped the band win two Grammy Awards and seven nominations , as well as scoring No. 6 in CBS 's `` Top Bestselling Albums of the Last 10 Years '' ( 2008 ) .	It also helped the band win two Grammy awards .
The album was listed for 104 weeks on the Billboard 200 , and it was one of eight albums in the history of the chart to spend at least a year on the Billboard Top 50 .	It is also one of the eight albums to stay for at least a year within the Billboard Top 50 charts .
However , on June 21 , 2010 , Lee announced on EvThreads.com that Evanescence had temporarily left the studio to work further on the album and `` get our heads into the right creative space '' .	In June 21 , Lee announced in Evthreads.com that the band have temporarily left the studio to work further on the songs and that their label company was going through `` uncertain times '' , which could delay the release of the album .
Kiddieland Amusement Park , was an amusement park located just west of Chicago at the corner of North Avenue and First Avenue in Melrose Park , Illinois .	Kiddieland Amusement Park was an amusement park located just west of Chicago at the corner of North Avenue and First Avenue in Melrose Park , Illinois .
The park closed on September 27 , 2009 , and demolished in 2010 to make way for a new Costco store .	The park closed on September 27 , 2009 at 8 PM , and demolished in 2010 to make way for a new Costco store .
It was home to several classic rides including the Little Dipper roller coaster , which opened in 1929 .	It was home to several classic rides including the Little Dipper roller coaster , which opened in 1950 .
The park saw its first major expansion in the 1950s with the addition of the Little Dipper and the Carousel , both of which lasted until the park 's closing .	The park saw its first major expansion in the 1950s with the addition of the Little Dipper and the Carousel , of which both still exist today .
A Costco store now occupies the land .	A Costco store will be built in its place .
Samuel Finley Breese Morse ( April 27 , 1791 - April 2 , 1872 ) was an American painter who turned inventor .	Samuel Finley Breese Morse ( April 27 , 1791 - April 2 , 1872 ) was an American inventor .
He was a co-developer of the Morse code , and helped to develop the commercial use of telegraphy .	He was the first person to make a telegraph with only one wire , and also helped come up with the idea of Morse code .
In Alcestis , the eponymous heroine agrees to give up her own life in order to spare the life of her husband , Admetus .	For example , in Euripides ' play Alcestis , the heroine agrees to give up her own life in order to spare the life of her husband , Admetus .
A frequently cited example is Euripides ' Medea , in which the deus ex machina , a dragon-drawn chariot sent by the sun god , is used to convey his granddaughter Medea , who has just committed murder and infanticide , away from her husband Jason to the safety and civilization of Athens .	A more frequently cited example is Euripides ' Medea in which the deus ex machina is used to convey Medea , who has just committed murder and infanticide , away from her husband Jason to the safety and civilization of Athens .
God remarks `` Deus ex machina '' then simply turns back time .	Deus ex machina is the Latin version of an ancient Greek phrase ἀπὸ μηχανῆς θεός .
Denim was traditionally colored blue with indigo dye to make blue jeans , although `` jean '' formerly denoted a different , lighter , cotton fabric .	Denim was usually colored blue with indigo dye to make blue `` jeans '' , though `` jean '' meant a different , lighter cotton textile .
These patterns have specific names : Between 1973 and 1975 Volkswagen produced the Jeans Beetle , which had all-denim trim .	Between 1973 and 1975 , Volkswagen made the Jeans Beetle , which had all-denim trim .
It was originally called serge de Nîmes but the name was soon shortened to `` denim . ''	First called serge de Nîmes , the name was soon shortened to denim .
The word `` denim '' comes from the name of a fabric that was first made in the city of Nîmes , France , by the André family .	Serge was first made in Nîmes , France , by the André family .
They had close ties with the Angevin kings of Sicily .	They had a close relationship with the Angevin kings of Sicily .
The Fieschi were a noble merchant family from Genoa , Italy , from whom descend the Fieschi Ravaschieri Princes of Belmonte .	The House of Fieschi were a noble merchant family from Genoa , Italy .
The Full Moon Party takes place every month throughout the year .	The Full Moon Party is a beach party held on every night where there is a full moon .
`` Rose '' ears are smaller than the standard style of `` button '' ears , and are folded with the front edge against the side of the head .	`` Rose '' ears are smaller than the `` button '' ears and are folded up instead of on the side of the head .
These pugs had shorter legs and the modern-style pug nose .	Pugs have strong , straight legs and laid back shoulders .
The pug is a toy dog with a wrinkly , short-muzzled face and curled tail .	The pug is a type of dog with a wrinkly face .
The tail normally curls tightly over the hip .	The tail usually curls at the hip .
The breed is often described as multum in parvo , or `` much in little '' , alluding to the pug 's remarkable personality , despite its small size .	They have often been described as multum in parvo , which means `` much in little '' , referring to the pug 's character and size .
The lower teeth normally protrude further than their upper , resulting in an under-bite .	The lower teeth normally grow farther out than the upper teeth , so they meet in an under-bite .
Their ankles are strong , their feet are small , their toes are well split-up , and their nails are black .	They have toes that are split up perfectly , and their nails are all black .
Pugs have two distinct shapes for their ears , `` rose '' and `` button '' .	The pug has a square , muscular body with a large head , big eyes , and small ears .
John Michael Wright ( May 1617 - July 1694 ) was a portrait painter in the Baroque style .	John Michael Wright ( May 1617 - July 1694 ) was a British portrait painter in the Baroque style .
John Michael Wright , who at the height of his career would interchangeably sign himself `` Anglus '' or `` Scotus '' , is of uncertain origin .	John Michael Wright , who would later sign himself `` Anglus '' or `` Scotus '' , is of uncertain origin .
Wright 's paintings of royalty and aristocracy are included amongst the collections of many leading galleries today .	Wright 's paintings of royalty and aristocracy are in the collections of many great galleries today .
In the final years of the Stuart monarchy he returned to Rome as part of an embassy to Pope Innocent XI .	In the last years of the Stuart rule he went back to Rome as part of an embassy to Pope Innocent XI .
However , writing in 1700 , the English antiquarian Thomas Hearne claims Wright was born in Shoe Lane , London and , after an adolescent conversion to Roman Catholicism , was taken to Scotland by a priest .	But in 1700 , Thomas Hearne claimed that Wright was born in Shoe Lane , London .
A London birth certainly seems supported by a baptismal record , dated May 25 , 1617 , for a `` Mighell Wryghtt '' , son of James Wright , described as a tailor and a citizen of London , in St Bride 's Church , Fleet Street , London .	A baptismal record , dated 25 May 1617 , for a `` Mighell Wryghtt '' , son of James Wright , described as a tailor and a citizen of London , in London , seems to agree with this claim .
He was engaged by Archduke Leopold Wilhelm of Austria , the governor of the Spanish Netherlands , to acquire artworks in Oliver Cromwell 's England in 1655 .	He was hired by Archduke Leopold Wilhelm of Austria , the governor of the Spanish Netherlands in 1655 .
There he was admitted to the Accademia di San Luca , and was associated with some of the leading artists of his generation .	There , he entered the Accademia di San Luca , and came to know some of the most important artists of his time .
He took up permanent residence in England from 1656 , and served as court painter before and after the English Restoration .	He served there as a court painter before and after the English Restoration .
Described variously as English and Scottish , Wright trained in Edinburgh under the Scots painter George Jamesone , and acquired a considerable reputation as an artist and scholar during a long sojourn in Rome .	Wright was taught in Edinburgh by the Scots painter George Jamesone .
The diarist John Evelyn called him a Scotsman , an epithet repeated by Horace Walpole and tentatively accepted by his later biographer , Verne .	The diarist John Evelyn called him a Scotsman .
A convert to Roman Catholicism , he was a favorite of the restored Stuart court , a client of both Charles II and James II , and was a witness to many of the political maneuverings of the era .	Hired by both Charles II and James II , he saw many of the political experiences of the era .
He subsequently sang at Milan 's La Scala ( 1951 ) , the Glyndebourne Festival ( from 1954 on ) and London 's Royal Opera House , Covent Garden ( 1954 , 1956 and 1958 ) .	Then he sang at Milan 's La Scala ( 1951 ) , the Glyndebourne Festival ( from 1954 on ) and London 's Royal Opera House , Covent Garden ( 1954 , 1956 and 1958 ) .
From 1940 to 1946 , he taught at the Geneva Conservatory .	From 1940 to 1946 he taught at the Geneva Conservatory .
Cuénod resided with his life partner , Alfred Augustin ( 41 years his junior ) , in the Vaud region of Switzerland .	Cuénod lived with his male partner , Alfred Augustin , in the Vaud region of Switzerland .
His very last appearance on stage was in 1992 , aged 90 , when he sang M. Triquet in Tchaikovsky 's Eugene Onegin at the Théâtre du Jorat in Mézières .	He sang M. Triquet in Tchaikovsky 's Eugene Onegin when it was given by the Lausanne Opera at the Théâtre du Jorat in Mézières .
Born in Corseaux-sur-Vevey , Switzerland , of English ancestry through his grandmother , Cuénod received his training at the Ribaupierre Institute in Lausanne , at the conservatories in Geneva and Basel , and in Vienna .	Cuénod he studied at the Ribaupierre Institute in Lausanne , at the conservatories in Geneva and Basel , and in Vienna .
Cuénod was known for his roles as Basilio in Mozart 's The Marriage of Figaro , the Astrologer in Rimsky-Korsakov 's The Golden Cockerel , and Sellem in Stravinsky 's The Rake 's Progress .	He was famous for singing the part of Basilio in Mozart 's The Marriage of Figaro , the Astrologer in Rimsky-Korsakov 's The Golden Cockerel , and Sellem in Stravinsky 's The Rake 's Progress .
In 1943 he resumed his operatic career singing in Johann Strauss II 's Die Fledermaus in Geneva .	In 1943 he started singing in opera again , singing in Johann Strauss II 's Die Fledermaus in Geneva .
During the seasons 1937 to 1939 , he made an extensive concert tour of North America .	He made a concert tour of North America .
In 1928 , he made his stage debut in Ernst Krenek 's Jonny spielt auf in Paris , and in 1929 he sang for the first time in the United States in Noël Coward 's Bitter Sweet .	Then , in 1928 , he got a part in the jazz opera Jonny spielt auf by Ernst Krenek when it was performed in Paris .
He turned 108 on 26 June 2010 and died in Vevey on the following 6 December .	He died in Vevey on 6 December that year .
For her role in the series , she won two Golden Butterfly Awards , she is the first and only nominee to win the award for two consecutive years .	She won consecutive Golden Butterfly Awards for Best Actress for her performance .
In 2009 , she also acted in Serdar Akar 's film Gecenin Kanatları ( Wings of the Night ) , written by Mahsun Kırmızıgül .	Saat was the lead in director Serdar Akar 's movie Gecenin Kanatları ( Wings of the Night ) released in December 2009 .
Her character was introduced in the third season premiere .	Juliet 's character was introduced in the third season 's premiere .
Dr. Juliet Burke ( née Carlson ) is a fictional character on the ABC television series Lost played by Elizabeth Mitchell .	Juliet Burke is the name of a fictional character , a main character on the ABC 's TV series Lost .
Sony Vegas Pro is a video editing software package for non-linear editing systems ( NLE ) originally published by Sonic Foundry , now owned and run by Sony Creative Software .	Sony Vegas is a non-liner video editing software developed by Sony Creative Software .
The film stars Gregory Peck , Lee Remick , David Warner , Harvey Spencer Stephens , Billie Whitelaw , Patrick Troughton , Martin Benson and Leo McKern .	The movie stars Gregory Peck , Lee Remick , David Warner , Harvey Stephens , Billie Whitelaw , Patrick Troughton , Martin Benson , and Leo McKern .
The Omen is an 1976 British\/American suspense horror film directed by Richard Donner .	It was directed by Richard Donner .

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