Algebraic groupIn mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example, orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties.
Equivalence classIn mathematics, when the elements of some set have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set into equivalence classes. These equivalence classes are constructed so that elements and belong to the same equivalence class if, and only if, they are equivalent. Formally, given a set and an equivalence relation on the of an element in denoted by is the set of elements which are equivalent to It may be proven, from the defining properties of equivalence relations, that the equivalence classes form a partition of This partition—the set of equivalence classes—is sometimes called the quotient set or the quotient space of by and is denoted by .
Common EraCommon Era (CE) and Before the Common Era (BCE) are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the original Anno Domini (AD) and Before Christ (BC) notations used for the same calendar era. The two notation systems are numerically equivalent: " CE" and "AD " each describe the current year; "400 BCE" and "400 BC" are the same year.
Natural capitalNatural capital is the world's stock of natural resources, which includes geology, soils, air, water and all living organisms. Some natural capital assets provide people with free goods and services, often called ecosystem services. All of these underpin our economy and society, and thus make human life possible. It is an extension of the economic notion of capital (resources which enable the production of more resources) to goods and services provided by the natural environment.
Natural resource managementNatural resource management (NRM) is the management of natural resources such as land, water, soil, plants and animals, with a particular focus on how management affects the quality of life for both present and future generations (stewardship). Natural resource management deals with managing the way in which people and natural landscapes interact. It brings together natural heritage management, land use planning, water management, bio-diversity conservation, and the future sustainability of industries like agriculture, mining, tourism, fisheries and forestry.
