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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 Jordan–Wigner transformation is a transformation that maps spin operators onto fermionic creation and annihilation operators.It was proposed by Pascual Jordan and Eugene Wigner [1] for one-dimensional lattice models, but now two-dimensional analogues of the transformation have also been created.
In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in that is invariant under a rank-3 lattice of translations. These surfaces have the symmetries of a crystallographic group. Numerous examples are known with cubic, tetragonal, rhombohedral, and orthorhombic symmetries.
The seven lattice systems and their Bravais lattices in three dimensions. In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (), [1] is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
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 ...
A three-dimensional space lattice consists of a multiplicity of such Yee cells. An electromagnetic wave interaction structure is mapped into the space lattice by assigning appropriate values of permittivity to each electric field component, and permeability to each magnetic field component.
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).
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 ...