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In geometry, the rhombille tiling, [1] also known as tumbling blocks, [2] reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets ...
In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n-dimensional lattice that produces a third function, also of n-dimensions. Multidimensional discrete convolution is the discrete analog of the multidimensional convolution of functions on Euclidean space.
The oblique lattice is one of the five two-dimensional Bravais lattice types. [1] The symmetry category of the lattice is wallpaper group p2. The primitive translation vectors of the oblique lattice form an angle other than 90° and are of unequal lengths.
In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in n-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1. The E 8 lattice and the Leech lattice are two famous examples.
A three-dimensional lattice filled with two molecules A and B, here shown as black and white spheres. Lattices such as this are used - for example - in the Flory–Huggins solution theory 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 ...
The rectangular lattice and rhombic lattice (or centered rectangular lattice) constitute two of the five two-dimensional Bravais lattice types. [1] The symmetry categories of these lattices are wallpaper groups pmm and cmm respectively. The conventional translation vectors of the rectangular lattices form an angle of 90° and are of unequal ...
In some cases, the Schrödinger equation can be solved analytically on a one-dimensional lattice of finite length [6] [7] using the theory of periodic differential equations. [8] The length of the lattice is assumed to be L = N a {\displaystyle L=Na} , where a {\displaystyle a} is the potential period and the number of periods N {\displaystyle ...
The group GL(2, Z) is the linear maps preserving the standard lattice Z 2, and SL(2, Z) is the orientation-preserving maps preserving this lattice; they thus descend to self-homeomorphisms of the torus (SL mapping to orientation-preserving maps), and in fact map isomorphically to the (extended) mapping class group of the torus, meaning that ...