Recurrence relationIn mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation. If the values of the first numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In linear recurrences, the nth term is equated to a linear function of the previous terms.
Gamma matricesIn mathematical physics, the gamma matrices, also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts.
Tisha B'AvTisha B'Av (תִּשְׁעָה בְּאָב Tīšʿā Bəʾāv; tiʃʕa beˈʔav, the ninth of Av) is an annual fast day in Judaism, on which a number of disasters in Jewish history occurred, primarily the destruction of both Solomon's Temple by the Neo-Babylonian Empire and the Second Temple by the Roman Empire in Jerusalem. Tisha B'Av marks the end of the three weeks between dire straits and is regarded as the saddest day in the Jewish calendar, and it is thus believed to be a day which is destined for tragedy.
AvAv (also Menachem Av, ) is the eleventh month of the civil year and the fifth month of the ecclesiastical year on the Hebrew calendar. It is a month of 30 days, and usually occurs in July–August on the Gregorian calendar. The Babylonian Talmud states that "when we enter [the month of] Av, our joy is diminished". This is because the darkest events in Jewish history occurred during the first week and a half of this month, particularly the Nine Days which culminate in Tisha B'Av, the 9th day of Av.
Kim Il SungKim Il Sung (ˈkɪm_ˈɪlˈsʌŋ,_-ˈsʊŋ; , kimils͈ʌŋ; 15 April 1912 – 8 July 1994) was a Korean politician and the founder of North Korea. He ruled the country from the country's establishment in 1948 until his death in 1994. Afterwards, he was declared its eternal president. His birth name was Kim Song Ju (). He held the posts of the Premier from 1948 to 1972 and President from 1972 to 1994. He was the leader of the Workers' Party of Korea (WPK) from 1949 to 1994 (titled as Chairman from 1949 to 1966 and as General Secretary after 1966).
Linear recurrence with constant coefficientsIn mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence. The polynomial's linearity means that each of its terms has degree 0 or 1.
Nicholas SparksNicholas Charles Sparks (born December 31, 1965) is an American romance novelist, screenwriter, and film producer. He has published twenty-three novels, all New York Times bestsellers, and two works of non-fiction, with over 115 million copies sold worldwide in more than 50 languages. Among his works are The Notebook, A Walk to Remember, and Message in a Bottle which, along with eight other books, have been adapted as feature films. Sparks lives in North Carolina, where many of his novels are set.
Notebook for Anna Magdalena BachThe title Notebook for Anna Magdalena Bach (Notenbüchlein für Anna Magdalena Bach) refers to either of two manuscript notebooks that the German Baroque composer Johann Sebastian Bach presented to his second wife, Anna Magdalena. Keyboard music (minuets, rondeaux, polonaises, chorales, sonatas, preludes, musettes, marches, gavottes) makes up most of both notebooks, and a few pieces for voice (songs, and arias) are included. The Notebooks provide a glimpse into the domestic music of the 18th century and the musical tastes of the Bach family.
Kim Jong IlKim Jong Il (,kɪm_ʤɒŋˈɪl; ; kim.dzɔŋ.il; also transcribed as Kim Jong-il and born Yuri Irsenovich Kim; 16 February 1941 or 1942 – 17 December 2011) was a North Korean politician who was the second supreme leader of North Korea from 1994 to 2011. He led North Korea from the 1994 death of his father Kim Il Sung, the first Supreme Leader, until his own death in 2011, when he was succeeded by his son, Kim Jong Un. In the early 1980s, Kim had become the heir apparent for the leadership of the Democratic People's Republic of Korea (DPRK) and assumed important posts in the party and army organs.
Teenage Mutant Ninja Turtles: Mutant MayhemTeenage Mutant Ninja Turtles: Mutant Mayhem is a 2023 American computer-animated superhero film directed by Jeff Rowe, who co-wrote the screenplay with Seth Rogen, Evan Goldberg, Dan Hernandez, and Benji Samit. It is the seventh theatrical Teenage Mutant Ninja Turtles film and a reboot of the Turtles series. The film stars Micah Abbey, Shamon Brown Jr., Nicolas Cantu, and Brady Noon in the lead voice roles. The ensemble voice cast also includes Ayo Edebiri, Maya Rudolph, John Cena, Rogen, Rose Byrne, Natasia Demetriou, Giancarlo Esposito, Jackie Chan, Ice Cube, Paul Rudd, Post Malone, and Hannibal Buress.
Recurrence quantification analysisRecurrence quantification analysis (RQA) is a method of nonlinear data analysis (cf. chaos theory) for the investigation of dynamical systems. It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory. The recurrence quantification analysis (RQA) was developed in order to quantify differently appearing recurrence plots (RPs), based on the small-scale structures therein.
Recurrence plotIn descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for each moment in time, the times at which the state of a dynamical system returns to the previous state at , i.e., when the phase space trajectory visits roughly the same area in the phase space as at time . In other words, it is a plot of showing on a horizontal axis and on a vertical axis, where is the state of the system (or its phase space trajectory). Natural processes can have a distinct recurrent behaviour, e.g.
