What is a sublattice? - ResearchGate
网页A sublattice, correctly defined, is a group of translation operations that have a subgroup relation to another lattice. The group-subgroup relation implies that the number of operations in the ...
Lattice (order) - Wikipedia
网页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).
子格 - 百度百科
网页子格(sublattice)是 格论 的基本概念之一，设(L，∨，∧)是一格，T是L的非空子集，如果T关于两种运算都是封闭的，则称(T，∨，∧)是(L，∨
格 (数学) - 维基百科，自由的百科全书
网页在 数学 中， 格 （英語： Lattice）是其非空有限 子集 都有一个 上确界 （称为 并）和一个 下确界 （称为 交）的 偏序集合 （poset）。 格也可以特征化为满足特定公理 恒等式 的 代数结构。 因为两个定义是等价的，格理论从 序理论 和 泛代数 二者提取内容。 半格 包括了格，依次包括 海廷代数 和 布尔代数。 这些"格样式"的结构都允许序理论和抽象代数的描述。 需要注意的是，本条目介绍的是序理论中的“格”，并非几何与 群论 中的“ 格（群论） ”（点 …
Sublattice - Encyclopedia of Mathematics
网页2015年12月20日 — A subset $A$ of a lattice that is closed under the operations $+$ and $\cdot$, i.e. a subset $A$ such that $a+b \in A$ and $ab \in A$ for any $a$ and $b$ from $A$. Therefore, a sublattice is a subalgebra of the lattice considered as a universal algebra with two binary operations.
Sublattice - an overview | ScienceDirect Topics
网页Sublattice modelling is now one of the most predominant methods used to describe solution and compound phases. It is flexible and can account for a variety of different phase types ranging from interstitial phases such as austenite and ferrite in steels to intermetallic phases, such as sigma and Laves, which have wide homogeneity ranges.
13.2: Lattices - Mathematics LibreTexts
网页2021年8月17日 — What is a reasonable definition of the term sublattice? Answer. One reasonable definition would be this: Let \([L; \lor, \land ]\) be a lattice and let \(K\) be a nonempty subset of \(L\text{.}\) Then \(K\) is a sublattice of \(L\) if and only if \(K\) is closed under both \(\lor\) and \(\land\)
Sublattice - Vocab, Definition, and Must Know Facts - Fiveable
网页A sublattice is a subset of a lattice that is itself a lattice under the same operations of join and meet. This means that for any two elements in the sublattice, their least upper bound (join) and greatest lower bound (meet) also belong to the sublattice, preserving the structure of the original lattice.
Section 9.3.6. Sublattices - Wiley Online Library
网页Sublattices are defined in a natural way in those lattices that have centred conventional cells, being generated by the vertices of these cells (`decentring'). They are primitive and belong to the same crystal family as the given lattice.
Sublattice - Chemistry LibreTexts
网页A lattice L' obtained by another lattice L by removing one or more sets of nodes is called a sublattice of L. The translation subgroup T' of L' is a subgroup of the translation subgroup T of L. The unit cell of L' is larger than the unit cell of L and is therefore called a supercell.