Up to

In mathematics, the phrase up to indicates that its grammatical object is some equivalence class, to be regarded as a single entity, or disregarded as a single entity. If this object is a class of transformations (such as "isomorphism" or "permutation"), it implies the equivalence of objects one of which is the image of the other under such a transformation.

If X is some property or process, the phrase "up to X" means "disregarding a possible difference in X". For instance we might follow the statement "an integer's prime factorization is unique up to ordering", meaning that the prime factorization is unique if we disregard the order of the factors; or we might say "the solution to an indefinite integral is f(x), up to addition by a constant", meaning that the added constant is not the focus here, the solution f(x) is, and that the addition of a constant is to be regarded as a background, of secondary focus. Further examples concerning up to isomorphism, up to permutations and up to rotations are described below.

Mark Ronson

Mark Daniel Ronson (born 4 September 1975) is an English musician, DJ, singer, songwriter, and record producer. Although his debut album Here Comes the Fuzz failed to make an impact on the charts, his second album Version reached number two in the UK and included three top 10 singles. This success won him a Brit Award for Best British Male Solo Artist in 2008. His third studio album, Record Collection, was released on 27 September 2010, peaking at number two in the UK.

In 2014, Ronson achieved his first UK and US number one single with the Grammy-nominated "Uptown Funk," which featured vocals from Bruno Mars. In 2015 it won Ronson the Brit Award for British Single of the Year. His fourth studio album, the Grammy-nominated Uptown Special, was released in January 2015, and became his first UK number one album. Ronson has also produced multi-platinum, Grammy-winning albums for Amy Winehouse and Adele.

Early life

Ronson was born at the Wellington Hospital, St John's Wood, London, the son of Laurence Ronson, a real-estate speculator and music manager, and Anne Dexter. His parents are both Ashkenazi Jews (their ancestors being Jewish immigrants from Austria, Russia, and Lithuania); Ronson was brought up in Masorti Judaism and had a Bar Mitzvah. The family name was originally "Aaronson," but was shortened by Mark's grandfather Henry. He is the nephew of Gerald Ronson. Through his mother, he is also related to British Conservative politicians Sir Malcolm Rifkind and Leon Lord Brittan, as well as Odeon Cinemas founder Oscar Deutsch. He is not related to the late English guitarist Mick Ronson, who coincidentally fathered a son named Mark in 1975.

Korean language

Korean (한국어/조선말, see below) is the official language of both South Korea and North Korea, as well as one of the two official languages in China's Yanbian Korean Autonomous Prefecture. About 80 million people speak Korean worldwide.

Historical linguists classify Korean as a language isolate. The idea that Korean belongs to a putative Altaic language family has been generally discredited. The Korean language is agglutinative in its morphology and SOV in its syntax.

For over a millennium, Korean was written with adapted Chinese characters called hanja, complemented by phonetic systems such as hyangchal, gugyeol, and idu. In the 15th century, Sejong the Great commissioned a national writing system called Hangul, but it did not become a legal script to write Korean until the 20th century when the Japanese government in Korea was established. This happened because of the yangban aristocracy's preference for hanja.

History

Korean is descended from Proto-Korean, Old Korean, Middle Korean, and Modern Korean. Since the Korean War, through 70 year's of seperations North–South differences have developed in standard Korean, including variance in pronunciation, verb inflection, and vocabulary chosen.

Uptown Funk

"Uptown Funk" (stylised as "UpTown Funk!") is a song recorded by British producer Mark Ronson, with vocals from American singer Bruno Mars, for Ronson's fourth studio album, Uptown Special (2015). RCA Records released the song as the album's lead single on 10 November 2014.Jeff Bhasker assisted the artists in co-writing and co-producing the track, with additional writing from Philip Lawrence. This is Mars' fourth collaboration with Ronson (following Mars' own songs "Locked Out of Heaven", "Moonshine", and "Gorilla") and sixth with Bhasker (after "Talking to the Moon", "Young Girls" and the three previously mentioned songs).

Taylor Swift

Taylor Alison Swift (born December 13, 1989) is an American singer-songwriter. Raised in Wyomissing, Pennsylvania, she moved to Nashville, Tennessee, at the age of 14 to pursue a career in country music. She signed with the independent label Big Machine Records and became the youngest songwriter ever signed by the Sony/ATV Music publishing house. The release of Swift's eponymous debut album in 2006 marked the start of her career as a country music singer. Her third single, "Our Song", made her the youngest person to single-handedly write and perform a number-one song on the Hot Country Songs chart.

Swift's second album, Fearless, was released in 2008. Buoyed by the pop crossover success of the singles "Love Story" and "You Belong with Me", Fearless became the best-selling album of 2009 in the United States. The album won four Grammy Awards, making Swift the youngest ever Album of the Year winner. Swift's third and fourth albums, 2010's Speak Now and 2012's Red, both sold more than one million copies within the first week of their U.S release. Speak Now's "Mean" won two Grammy Awards, while Red's singles "We Are Never Ever Getting Back Together" and "I Knew You Were Trouble" were successful worldwide. Swift's fifth album, the pop-focused 1989, was released in 2014 and sold more copies in its opening week than any album in the previous 12 years, making Swift the first and only act to have three albums sell more than one million copies in the opening release week. Its singles "Shake It Off", "Blank Space", and "Bad Blood" reached number one on the Billboard Hot 100. The album would go on to win three awards at the 2016 Grammys including Album of the Year making Swift the first and thus far only female artist to receive the award twice.