quasiregular

Etymology

Definitions

1. 1

   Having some regular characteristics.

2. 2

   That is semiregular with regular faces of precisely two types that alternate around each…

   That is semiregular with regular faces of precisely two types that alternate around each vertex.

   • There are two quasiregular polyhedra not having identical regular faces: the cuboctahedron (dymaxion) and the icosidodecahedron.
3. 3

   Such that 1 − r is a unit (has a multiplicative inverse).

   • The element a can be uniquely represented in the form r + t, where [rt] = 0, t is nilpotent and r is a quasiregular element of G ([1]; p. 108).
   • A onesided ideal is quasiregular provided that it consists of quasiregular elements.
   • A norm #92;begin#123;Vmatrix#125;#92;end#123;Vmatrix#125; is called spectral if the group of quasiregular elements is open in the associated norm topology, equivalently if it satisfies Gelfand's spectral radius formula:[…].
4. ›+ 2 more definitionsshow fewer

   1. 4

      Having certain properties in common with holomorphic functions of a single complex…

      Having certain properties in common with holomorphic functions of a single complex variable.

      • Given two orientable Riemannian manifolds V₁ and V₂, one may ask whether a non-constant quasiregular map 𝑓 : V₁ → V₂ exists.
      • Quasiregular maps are a generalization of quasiconformal maps where the assumption of injectivity is relaxed. Heinonen and Holopainen [138] developed nonlinear potential theory and quasiregular maps on Carnot groups.
   2. 5

      That is the result of a required adjustment of an induced representation that would,…

      That is the result of a required adjustment of an induced representation that would, unadjusted, give rise to (only) a quasi-invariant measure.

      • in the fundamental affine space H = G/Z is called quasiregular.

The neighborhood

• neighborquasi-inverse
• neighborquasiregularity
• neighborquasiconformal