IlliteIllite is a group of closely related non-expanding clay minerals. Illite is a secondary mineral precipitate, and an example of a phyllosilicate, or layered alumino-silicate. Its structure is a 2:1 sandwich of silica tetrahedron (T) – alumina octahedron (O) – silica tetrahedron (T) layers. The space between this T-O-T sequence of layers is occupied by poorly hydrated potassium cations which are responsible for the absence of swelling.
Binary relationIn mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets X and Y is a new set of ordered pairs (x, y) consisting of elements x in X and y in Y. It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element x is related to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation.
Converse relationIn mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation, The notation is analogous with that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse.
Homogeneous relationIn mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product X × X. This is commonly phrased as "a relation on X" or "a (binary) relation over X". An example of a homogeneous relation is the relation of kinship, where the relation is between people. Common types of endorelations include orders, graphs, and equivalences. Specialized studies of order theory and graph theory have developed understanding of endorelations.
Reflexive relationIn mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself. An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.
Bayer processThe Bayer process is the principal industrial means of refining bauxite to produce alumina (aluminium oxide) and was developed by Carl Josef Bayer. Bauxite, the most important ore of aluminium, contains only 30–60% aluminium oxide (Al2O3), the rest being a mixture of silica, various iron oxides, and titanium dioxide. The aluminium oxide must be further purified before it can be refined into aluminium metal. The Bayer process is also the main source of gallium as a byproduct despite low extraction yields.
Total relationIn mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain {x : there is a y with xRy }. Conversely, R is called right total if Y equals the range {y : there is an x with xRy }. When f: X → Y is a function, the domain of f is all of X, hence f is a total relation. On the other hand, if f is a partial function, then the domain may be a proper subset of X, in which case f is not a total relation.
Calcite seaA calcite sea is a sea in which low-magnesium calcite is the primary inorganic marine calcium carbonate precipitate. An aragonite sea is the alternate seawater chemistry in which aragonite and high-magnesium calcite are the primary inorganic carbonate precipitates. The Early Paleozoic and the Middle to Late Mesozoic oceans were predominantly calcite seas, whereas the Middle Paleozoic through the Early Mesozoic and the Cenozoic (including today) are characterized by aragonite seas.
