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A totally ordered set is a distributive lattice. 21. A metric lattice is modular. [6] 22. A modular lattice is semi-modular. [7] 23. A projective lattice is modular. [8] 24. A projective lattice is geometric. (def) 25. A geometric lattice is semi-modular. [9] 26. A semi-modular lattice is atomic. [10] [disputed – discuss] 27. An atomic ...
Pertaining file extensions include:.docx – Word document.docm – Word macro-enabled document; same as docx, but may contain macros and scripts.dotx – Word template.dotm – Word macro-enabled template; same as dotx, but may contain macros and scripts; Other formats.pdf – PDF documents.wll – Word add-in.wwl – Word add-in
Physical lattice models frequently occur as an approximation to a continuum theory, either to give an ultraviolet cutoff to the theory to prevent divergences or to perform numerical computations. An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics.
In mathematics, a lattice word (or lattice permutation) is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1. A reverse lattice word , or Yamanouchi word (named after Takahiko Yamanouchi ), is a string whose reversal is a lattice word.
Bravais lattice, a repetitive arrangement of atoms; Lattice C, a compiler for the C programming language; 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
An example is the Knaster–Tarski theorem, which states that the set of fixed points of a monotone function on a complete lattice is again a complete lattice. This is easily seen to be a generalization of the above observation about the images of increasing and idempotent functions.
Examples in all admissible signatures are given by the II m,n and I m,n constructions, respectively. The theta function of a unimodular positive definite lattice is a modular form whose weight is one half the rank. If the lattice is even, the form has level 1, and if the lattice is odd the form has Γ 0 (4
The table shows an example computation to show that the words x∧z and x∧z∧(x∨y) denote the same value in every bounded lattice. The case of lattices that are not bounded is treated similarly, omitting rules 2. and 3. in the above construction. The solution of the word problem on free lattices has several interesting corollaries.