quasiregular

Adjective

quasiregular (not comparable)

1. Having some regular characteristics.
2. That is semiregular with regular faces of precisely two types that alternate around each vertex.
   • 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....1981, H. S. M. Coxeter, “The Derivation of Schoenberg's Star Polytopes from Schoute's Simplex Nets”, in Chandler Davis, Branko Grünbaum, F.A. Sherk, editors, The Geometric Vein: The Coxeter...
   • There are two quasiregular polyhedra not having identical regular faces: the cuboctahedron (dymaxion) and the icosidodecahedron.1996, Wolfgang Schueller, The Design of Building Structures, page 540
3. (ring theory) 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).1966, Translations: Lie groups, American Mathematical Society, Series 1, Volume 9, page 215
   • A onesided ideal is quasiregular provided that it consists of quasiregular elements.1976, Carl Faith, Algebra II: Ring Theory, page 33
4. 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.1999, Israel Mathematical Conference Proceedings, volumes 12-14, page 61
   • An alternative proof that features an interesting connection with the theory of quasiconformal (or more precisely quasiregular) maps proceeds as follows.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...
5. (representation theory, topological algebra) 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.1988, I. M. Gelfand, M. I. Graev, 3: Geometry of homogeneous spaces, representations of groups in homogeneous spaces and related questions of integral geometry, Izrail M. Gelfand, Collected Papers...
   • 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.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...