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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 mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice.
Lattice mast, a type of observation mast common on major warships in the early 20th century; Lattice model (physics), a model defined not on a continuum, but on a grid; Lattice tower, or truss tower is a type of freestanding framework tower; Lattice truss bridge, a type of truss bridge that uses many closely spaced diagonal elements
In the mathematical study of order, a metric lattice L is a lattice that admits a positive valuation: a function v ∈ L → ℝ satisfying, for any a, b ∈ L, [1] + = + and > > (). Relation to other notions
A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e.g. the atom or molecule positions in a crystal, or more generally, the orbit of a group action under translational symmetry, is a translation of the translation lattice: a coset, which need not contain the origin, and therefore need not be a lattice in ...
In mathematics, a supersolvable lattice is a graded lattice that has a maximal chain of elements, each of which obeys a certain modularity relationship. The definition encapsulates many of the nice properties of lattices of subgroups of supersolvable groups .
Lattice model (physics), a physical model that is defined on a periodic structure with a repeating elemental unit pattern, as opposed to the continuum of space or spacetime; Lattice model (finance), a "discrete-time" model of the varying price over time of the underlying financial instrument, during the life of the instrument
Consider a partially ordered set (P, ≤) that is a complete lattice.Then P is a complete Heyting algebra or frame if any of the following equivalent conditions hold: . P is a Heyting algebra, i.e. the operation () has a right adjoint (also called the lower adjoint of a (monotone) Galois connection), for each element x of P.
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