Group extensionIn mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If and are two groups, then is an extension of by if there is a short exact sequence If is an extension of by , then is a group, is a normal subgroup of and the quotient group is isomorphic to the group . Group extensions arise in the context of the extension problem, where the groups and are known and the properties of are to be determined.
TerrainTerrain or relief (also topographical relief) involves the vertical and horizontal dimensions of land surface. The term bathymetry is used to describe underwater relief, while hypsometry studies terrain relative to sea level. The Latin word terra (the root of terrain) means "earth." In physical geography, terrain is the lay of the land. This is usually expressed in terms of the elevation, slope, and orientation of terrain features. Terrain affects surface water flow and distribution.
Volume elementIn mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form where the are the coordinates, so that the volume of any set can be computed by For example, in spherical coordinates , and so . The notion of a volume element is not limited to three dimensions: in two dimensions it is often known as the area element, and in this setting it is useful for doing surface integrals.
Centre-left politicsCentre-left politics is the range of left-wing political ideologies that lean closer to the political centre. Major ideologies of the centre-left include social democracy, social liberalism and progressivism. Ideas commonly supported by the centre-left include welfare capitalism, social justice, liberal internationalism, and multiculturalism. Economically, the centre-left supports a mixed economy in a democratic capitalist system, often including economic interventionism, progressive taxation, and the right to unionize.
Left-libertarianismLeft-libertarianism, also known as left-wing libertarianism, or social libertarianism, is a political philosophy and type of libertarianism that stresses both individual freedom and social equality. Left-libertarianism represents several related yet distinct approaches to political and social theory. Its classical usage refers to anti-authoritarian varieties of left-wing politics such as anarchism, especially social anarchism, communalism, and libertarian Marxism, collectively termed libertarian socialism.
Greatest element and least elementIn mathematics, especially in order theory, the greatest element of a subset of a partially ordered set (poset) is an element of that is greater than every other element of . The term least element is defined dually, that is, it is an element of that is smaller than every other element of Let be a preordered set and let An element is said to be if and if it also satisfies: for all By switching the side of the relation that is on in the above definition, the definition of a least element of is obtained.
French LeftThe Left in France (gauche française) was represented at the beginning of the 20th century by two main political parties, namely the Republican, Radical and Radical-Socialist Party and the French Section of the Workers' International (SFIO), created in 1905 as a merger of various Marxist parties. In 1914, after the assassination of the leader of the SFIO, Jean Jaurès, who had upheld an internationalist and anti-militarist line, the SFIO accepted to join the Union sacrée national front.
Absorbing elementIn mathematics, an absorbing element (or annihilating element) is a special type of element of a set with respect to a binary operation on that set. The result of combining an absorbing element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because there is no risk of confusion with other notions of zero, with the notable exception: under additive notation zero may, quite naturally, denote the neutral element of a monoid.
Identity elementIn mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity element is often shortened to identity (as in the case of additive identity and multiplicative identity) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.
Left-wing politicsLeft-wing politics describes the range of political ideologies that support and seek to achieve social equality and egalitarianism, often in opposition to social hierarchy as a whole or certain social hierarchies. Left-wing politics typically involve a concern for those in society whom its adherents perceive as disadvantaged relative to others as well as a belief that there are unjustified inequalities that need to be reduced or abolished through radical means that change the nature of the society they are implemented in.
