quasiregular
Language: English
Part of speech: adj
Etymology: From quasi- + regular.
Senses: glosses: Having some regular characteristics.
examples: text: 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].
ref: 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 Festschrift, page 151:
text: There are two quasiregular polyhedra not having identical regular faces: the cuboctahedron (dymaxion) and the icosidodecahedron.
ref: 1996, Wolfgang Schueller, The Design of Building Structures, page 540:
text: 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.
text: 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.
ref: 2007, Istvan Hargittai, Magdolna Hargittai, Symmetry through the Eyes of a Chemist, page 89:
topics: geometry
mathematics
sciences
glosses: That is semiregular with regular faces of precisely two types that alternate around each vertex.
raw_tags: of a polyhedron or tessellation
examples: text: 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).
ref: 1966, Translations: Lie groups, American Mathematical Society, Series 1, Volume 9, page 215:
text: A onesided ideal is quasiregular provided that it consists of quasiregular elements.
ref: 1976, Carl Faith, Algebra II: Ring Theory, page 33:
text: 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:[…].
ref: 1989, Proceedings of the Royal Irish Academy: Mathematical and physical sciences, page 128:
topics: mathematics
sciences
qualifier: ring theory
glosses: Such that 1 − r is a unit (has a multiplicative inverse).
raw_tags: of an element r of a ring
examples: text: Given two orientable Riemannian manifolds V₁ and V₂, one may ask whether a non-constant quasiregular map 𝑓 : V₁ → V₂ exists.
ref: 1999, Israel Mathematical Conference Proceedings, volumes 12-14, page 61:
text: 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.
text: 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.
ref: 2007, Luca Capogna, Donatella Danielli, Scott D. Pauls, Jeremy Tyson, An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem, page 142:
topics: mathematical-analysis
mathematics
sciences
glosses: Having certain properties in common with holomorphic functions of a single complex variable.
raw_tags: of a mapping from a multi-dimensional space or manifold to an equivalent space
examples: text: in the fundamental affine space H = G/Z is called quasiregular.
ref: 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, Volume II, page 357, We first decompose the quasiregular representations of a complex semi-simple Lie group into irreducible ones. A representation of the group G given by the formula T_g𝑓(h) = 𝑓(hg)
text: 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.
text: 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 […] .
topics: mathematics
sciences
qualifier: representation theory; topological algebra; representation theory; topological algebra
glosses: That is the result of a required adjustment of an induced representation that would, unadjusted, give rise to (only) a quasi-invariant measure.
raw_tags: of a representation
Related terms: quasi-inverse
quasiregularity
quasiconformal