Meaning of quasiregular | Babel Free

Definitions

1. Having some regular characteristics.
   not-comparable
2. That is semiregular with regular faces of precisely two types that alternate around each vertex.
   not-comparable
3. Such that 1 − r is a unit (has a multiplicative inverse).
   not-comparable
4. Having certain properties in common with holomorphic functions of a single complex variable.
   not-comparable
5. That is the result of a required adjustment of an induced representation that would, unadjusted, give rise to (only) a quasi-invariant measure.
   not-comparable

Examples

“The lattice points that lie in this plane are the vertices of the regular tessellation {3, 4} of equilateral triangles, and the other points just mentioned are the vertices of the quasiregular tessellation #92;begin#123;Bmatrix#125;3#92;#92;4#92;end#123;Bmatrix#125; of triangles and hexagons [9, p. 60].”

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

“2007, V. A. Blatov, O. Delgado-Friedrichs, M. O'Keeffe, D. M. Proserpio, Periodic nets and tilings: possibilities tor analysis and design of porous materials: Proceedings of the 15th International Zeolite Conference, Ruren Xu, Jiesheng Chen, Zi Gao, Wenfu Yan (editors), From Zeolites to Porous MOF Materials, page 1642, If we allow the coordination figure to be a quasiregular polyhedron (a polyhedron with one kind of vertex and edge, but two kinds of face) there is just one possibility compatible with translational symmetry – a cuboctahedron.”

“Two semiregular polyhedra are classified as so-called quasiregular polyhedra. They have two kinds of faces, and each face of one kind is entirely surrounded by faces of the other kind.”

“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:[…].”

“Given two orientable Riemannian manifolds V₁ and V₂, one may ask whether a non-constant quasiregular map 𝑓 : V₁ → V₂ exists.”

“1999, S. Mueller, Variational models for microstructure and phase transitions, F. Bethuel, G. Huisken, S. Mueller, K. Steffen (editors),Calculus of Variations and Geometric Evolution Problems, Springer, Lecture Notes in Mathematics, Volume 1713, page 108, An alternative proof that features an interesting connection with the theory of quasiconformal (or more precisely quasiregular) maps proceeds as follows.”

“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.”

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

“1998, Vladimir F. Molchanov, Discrete series and analyticity, Joachim Hilgert, Jimmie D. Lawson, Karl-Hermann Leeb, Ernest B. Vinberg (editors), Positivity in Lie Theory: Open Problems,De Gruyter Expositions in Mathematics, Volume 26, page 188, As it is known (see [11], [13], [21], [22]), the quasiregular representation on the hyperboloid decomposes into two series of irreducible unitary representations: continuous and discrete.”

“2008, André Unterberger, Alternative Pseudodifferential Analysis: With an Application to Modular Forms, Springer, Lecture Notes in Mathematics, Volume 1935, page 6, Note that the representation Met⁽²⁾, contrary to the quasiregular representation of the same group, does not act by changes of coordinates only […] .”

CEFR level