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In mathematics, an ordered pair, denoted (a, b), is a pair of objects in which their order is significant. The ordered pair (a, b) is different from the ordered pair (b, a), unless a = b. In contrast, the unordered pair, denoted {a, b}, equals the unordered pair {b, a}. Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a ...
e. A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R ; S from two given binary relations R and S. In the calculus of relations, the composition of relations is called relative multiplication, [1] and its result is called a relative product. [2]: 40 Function composition is the special ...
Wick's theorem is a method of reducing high-order derivatives to a combinatorics problem. [1] It is named after Italian physicist Gian-Carlo Wick. [2] It is used extensively in quantum field theory to reduce arbitrary products of creation and annihilation operators to sums of products of pairs of these operators.
Conjugate variables. Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, [1][2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle —between them.
Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space. [1][2][3][4] Interatomic potentials are widely used as the physical basis of molecular mechanics and molecular dynamics simulations in computational chemistry, computational physics and computational materials ...
Object composition refers to the logical or conceptual structure of the information, not the implementation or physical data structure used to represent it [citation needed]. For example, a sequence differs from a set because (among other things) the order of the composed items matters for the former but not the latter.
Gelfand pair. In mathematics, a Gelfand pair is a pair (G, K ) consisting of a group G and a subgroup K (called a Euler subgroup of G) that satisfies a certain property on restricted representations. The theory of Gelfand pairs is closely related to the topic of spherical functions in the classical theory of special functions, and to the theory ...