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After considerable negotiation, AECL assumed full responsibility for the reactor in a settlement. [10] The MAPLE facility was granted an extension on its operating license on 25 October 2007, which would permit operations until 31 October 2011. [11] This (final) submission envisioned that the MAPLE I reactor would be operational in late 2008. [12]
Maple as the function IntegerRelations[LLL] Mathematica as the function LatticeReduce; Number Theory Library (NTL) as the function LLL; PARI/GP as the function qflll; Pymatgen as the function analysis.get_lll_reduced_lattice; SageMath as the method LLL driven by fpLLL and NTL; Isabelle/HOL in the 'archive of formal proofs' entry LLL_Basis ...
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.
In lattice field theory, the Wilson action is a discrete formulation of the Yang–Mills action, forming the foundation of lattice gauge theory.Rather than using Lie algebra valued gauge fields as the fundamental parameters of the theory, group valued link fields are used instead, which correspond to the smallest Wilson lines on the lattice.
In pointless topology we take these properties of the lattice as fundamental, without requiring that the lattice elements be sets of points of some underlying space and that the lattice operation be intersection and union. Rather, point-free topology is based on the concept of a "realistic spot" instead of a point without extent.
The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [1] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices. In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb ...
Example valuation function on the cube lattice which makes it a metric lattice. 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 ] v ( a ) + v ( b ) = v ( a ∧ b ) + v ( a ∨ b ) {\displaystyle v(a)+v(b)=v(a\wedge b)+v(a\vee ...