In mathematics, a Lie algebra is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. The Lie bracket of two vectors and is denoted . The vector space together with this operation is a non-associative algebra, meaning that the Lie bracket is not necessarily associative.
In mathematics, a Lie group is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be a group, for instance multiplication and the taking of inverses (division), or equivalently, the concept of addition and the taking of inverses (subtraction). Combining these two ideas, one obtains a continuous group where multiplying points and their inverses are continuous. If the multiplication and taking of inverses are smooth (differentiable) as well, one obtains a Lie group.
Rajasthan is a state in northern India. It covers 342,239 square kilometres (132,139 sq mi) or 10.4 per cent of India's total geographical area. It is the largest Indian state by area and the seventh largest by population. It is on India's northwestern side, where it comprises most of the wide and inhospitable Thar Desert and shares a border with the Pakistani provinces of Punjab to the northwest and Sindh to the west, along the Sutlej-Indus River valley. It is bordered by five other Indian states: Punjab to the north; Haryana and Uttar Pradesh to the northeast; Madhya Pradesh to the southeast; and Gujarat to the southwest. Its geographical location is 23.3 to 30.12 North latitude and 69.30 to 78.17 East longitude, with the Tropic of Cancer passing through its southernmost tip.
True Lies is a 1994 American action comedy film written and directed by James Cameron. It was executive produced by Lawrence Kasanoff and stars Arnold Schwarzenegger, Jamie Lee Curtis, Tom Arnold, Art Malik, Tia Carrere, Bill Paxton, Eliza Dushku, Grant Heslov and Charlton Heston. It is based on the 1991 French comedy film La Totale! The film follows U.S. government agent Harry Tasker (Schwarzenegger), who struggles to balance his double life as a spy with his familial duties.
A polygraph, popularly referred to as a lie detector test, is a device or procedure that measures and records several physiological indicators such as blood pressure, pulse, respiration, and skin conductivity while a person is asked and answers a series of questions. The belief underpinning the use of the polygraph is that deceptive answers will produce physiological responses that can be differentiated from those associated with non-deceptive answers; however, there are no specific physiological reactions associated with lying, making it difficult to identify factors that separate those who are lying from those who are telling the truth. Polygraph examiners also prefer to use their own individual scoring method, as opposed to computerized techniques, as they may more easily defend their own evaluations.
The Western Hemisphere is the half of Earth which lies west of the prime meridian and east of the antimeridian. The other half is called the Eastern Hemisphere. In geopolitical terms, the context in which the term is most often used, the Encyclopedia Britannica defines it as "North and South America and the surrounding waters. Longitudes 20°W and 160°E are often considered its boundaries." It may be used in a cultural or geopolitical sense as a synonym for the "New World".
A sex position is a position of the body that people use for sexual intercourse or other sexual activities. Sexual acts are generally described by the positions the participants adopt in order to perform those acts. Though sexual intercourse generally involves penetration of the body of one person by another, sex positions commonly involve penetrative or non-penetrative sexual activities.
The big lie is a gross distortion or misrepresentation of the truth, used especially as a propaganda technique. The German expression was coined by Adolf Hitler, when he dictated his 1925 book Mein Kampf, to describe the use of a lie so colossal that no one would believe that someone "could have the impudence to distort the truth so infamously." Hitler claimed that the technique had been used by Jews to blame Germany's loss in World War I on German general Erich Ludendorff, who was a prominent nationalist political leader in the Weimar Republic.
A lie is an assertion that is believed to be false, typically used with the purpose of deceiving someone. The practice of communicating lies is called lying. A person who communicates a lie may be termed a liar. Lies may serve a variety of instrumental, interpersonal, or psychological functions for the individuals who use them.
In mathematics, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian symmetric spaces.
A midfielder is an association football position. Midfielders are generally positioned on the field between their team's defenders and forwards. Some midfielders play a strictly-defined defensive role, breaking up attacks, and are otherwise known as defensive midfielders. Others blur the boundaries, being more mobile and efficient in passing: they are commonly referred to as deep-lying midfielders, play-makers, box-to-box, or holding midfielders. The number of midfielders on a team and their assigned roles depends on the team's formation; the collective group of these players on the field is sometimes referred to as the midfield.
Elfen Lied is a Japanese manga series written and illustrated by Lynn Okamoto. It was originally serialized in Shueisha's Weekly Young Jump from June 2002 to August 2005, with the 107 chapters collected into twelve tankōbon volumes. Elfen Lied revolves around the interactions, views, emotions, and differences between human beings and the Diclonii, a mutant species similar to humans in build but distinguishable by two horns on their heads and "vectors", transparent telekinetically controlled arms that have the power to manipulate and cut objects within their reach. The series is centered on the teenage Diclonius girl "Lucy" who was rejected by human beings and subsequently wants revenge.
Pathological lying, also known as mythomania and pseudologia fantastica, is a chronic behavior in which the person habitually or compulsively lies. These lies often serve no obvious purpose other than to paint oneself as a hero or victim, depending on the circumstance.
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations. The theory of matrices and linear operators is well-understood, so representations of more abstract objects in terms of familiar linear algebra objects helps glean properties and sometimes simplify calculations on more abstract theories.
Lie to Me is an American crime drama television series. It originally ran on the Fox network from January 21, 2009, to January 31, 2011. In the show, Dr. Cal Lightman and his colleagues in The Lightman Group accept assignments from third parties, and assist in investigations, reaching the truth through applied psychology: interpreting microexpressions, through the Facial Action Coding System, and body language. In May 2009, the show was renewed for a second season consisting of 13 episodes; season two premiered on September 28, 2009. On November 24, 2009, Fox ordered an extra nine episodes for season two, bringing the season order to 22 episodes.
PolitiFact.com is an American nonprofit project operated by the Poynter Institute in St. Petersburg, Florida, with offices there and in Washington, D.C. It began in 2007 as a project of the Tampa Bay Times, with reporters and editors from the newspaper and its affiliated news media partners reporting on the accuracy of statements made by elected officials, candidates, their staffs, lobbyists, interest groups and others involved in U.S. politics. Its journalists select original statements to evaluate and then publish their findings on the PolitiFact.com website, where each statement receives a "Truth-O-Meter" rating. The ratings range from "True" for statements the journalists deem as accurate to "Pants on Fire" for claims the journalists deem as false or ludicrous.
In Western classical music tradition, lied is a term for setting poetry to classical music to create a piece of polyphonic music. The term is used for any kind of song in contemporary German, but among English and French speakers, "lied" is often used interchangeably with "art song" to encompass works that the tradition has inspired in other languages as well. The poems that have been made into lieder often center on pastoral themes or themes of romantic love.
"Love the Way You Lie" is a song recorded by American rapper Eminem, featuring Barbadian singer Rihanna, from Eminem's seventh studio album Recovery (2010). The singer and songwriter Skylar Grey wrote and recorded a demo of the song alongside the producer Alex da Kid when she felt she was in an abusive romantic relationship with the music industry. Eminem wrote the verses and chose Rihanna to sing the chorus, resulting in a collaboration influenced by their past experiences in difficult relationships. Recording sessions were held in Ferndale, Michigan, and Dublin, Ireland. Backed by guitar, piano and violin, the track is a midtempo hip-hop ballad with a pop refrain, sung by Rihanna, and describes two lovers who refuse to separate despite being in a dangerous love–hate relationship.
Your Lie in April is a Japanese romantic drama manga series that was written and illustrated by Naoshi Arakawa, and has been adapted into an anime television series and multiple stage productions. The manga was serialized in Kodansha's shōnen manga magazine Monthly Shōnen Magazine from April 2011 to May 2015. The story follows a young pianist named Kо̄sei Arima, who loses the ability to hear the piano after his mother's death and his experiences after he meets violinist Kaori Miyazono.
Big Little Lies is an American drama television series based on the 2014 novel of the same name by Liane Moriarty. Created and written by David E. Kelley, it aired on HBO from February 19, 2017, to July 21, 2019, encompassing 14 episodes and two seasons. Originally billed as a miniseries, Jean-Marc Vallée directed the first season, while Andrea Arnold directed the second season.
