In algebra, which is a broad division of mathematics, abstract algebra is a common name for the sub-area that studies algebraic structures in their own right. Such structures include groups, rings, fields, modules, vector spaces, and algebras. The specific term abstract algebra was coined at the beginning of the 20th century to distinguish this area from the other parts of algebra. The term modern algebra has also been used to denote abstract algebra.
Two mathematical subject areas that study the properties of algebraic structures viewed as a whole are universal algebra and category theory. Algebraic structures, together with the associated homomorphisms, form categories. Category theory is a powerful formalism for studying and comparing different algebraic structures.
In mathematics, an inverse function is a function that reverses another function: if the function f applied to an input x gives a result of y, then applying the inverse function g to y gives the result x, and vice versa. i.e. f(x) = y, and g(y) = x. More directly, g(f(x)) = x, meaning g composed with f form an identity.
A function f that has an inverse is defined as invertible; the inverse function is then uniquely determined by f and is denoted by f −1, read f inverse. Superscripted "−1" does not refer to numerical exponentiation: see composition monoid for explanation of this notation.
In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication. The intuition is of an element that can 'undo' the effect of combination with another given element. While the precise definition of an inverse element varies depending on the algebraic structure involved, these definitions coincide in a group.
The word 'inverse' is derived from Latin: inversus that means 'turned upside down', 'overturned'.
Salvia divinorum (also known as Diviner's Sage, Ska María Pastora, Seer's Sage, and by its genus name Salvia) is a psychoactive plant which can induce dissociative effects and is a potent producer of "visions" and other hallucinatory experiences. Its native habitat is in cloud forest in the isolated Sierra Mazateca of Oaxaca, Mexico, where it grows in shady and moist locations. The plant grows to over a meter high, has hollow square stems, large leaves, and occasional white flowers with violet calyxes. Botanists have not determined whether Salvia divinorum is a cultigen or a hybrid; native plants reproduce vegetatively, rarely producing viable seed.
Mazatec shamans have a long and continuous tradition of religious use of Salvia divinorum, using it to facilitate visionary states of consciousness during spiritual healing sessions. Most of the plant's local common names allude to the Mazatec belief that the plant is an incarnation of the Virgin Mary, with its ritual use also invoking that relationship. Its chief active psychoactive constituent is a structurally unique diterpenoid called salvinorin A, a potent κ-opioid and receptor2D agonist. Salvia divinorum is generally understood to be of low toxicity (high 50LD) and low addictive potential since it is a κ-opioid agonist and a great deal of research has indicated that κ-opioid agonist activation of the kappa opioid receptor as shown by salvia may, in fact, serve as a potent addiction treatment therapy.
The legal status of Salvia divinorum in the United States varies with some states banning it and others are considering proposals for banning its use.
In late 2002 Rep. Joe Baca (D- California) introduced a bill (Congress bill HR 5607) to schedule Salvia as a controlled substance at the national level. Those opposed to Joe Baca's bill include Daniel Siebert, who sent a letter to Congress arguing against the proposed legislation, and the Center for Cognitive Liberty & Ethics (CCLE), who sent key members of the US Congress a report on Salvia divinorum and its active principle, along with letters from an array of scientists who expressed concern that scheduling Salvia divinorum would negatively impact important research on the plant. Baca's bill did not pass.
In journalism, a human interest story is a feature story that discusses a person or people in an emotional way. It presents people and their problems, concerns, or achievements in a way that brings about interest, sympathy or motivation in the reader or viewer.
Human interest stories may be "the story behind the story" about an event, organization, or otherwise faceless historical happening, such as about the life of an individual soldier during wartime, an interview with a survivor of a natural disaster, a random act of kindness or profile of someone known for a career achievement.