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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 ...
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).
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 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.
The mathematics behind formal concept analysis therefore is the theory of complete lattices. Another representation is obtained as follows: A subset of a complete lattice is itself a complete lattice (when ordered with the induced order) if and only if it is the image of an increasing and idempotent (but not necessarily extensive) self-map. The ...
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
Let be a locally compact group and a discrete subgroup (this means that there exists a neighbourhood of the identity element of such that = {}).Then is called a lattice in if in addition there exists a Borel measure on the quotient space / which is finite (i.e. (/) < +) and -invariant (meaning that for any and any open subset / the equality () = is satisfied).
In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted , is the lattice in the Euclidean space whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice , or grid lattice.
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