Search results for "UAS"

Quasiconformal maps in metric spaces with controlled geometry

1998

This paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry. The principal message is that such a theory is both relevant and viable. The first main issue is the problem of definition, which we next describe. Quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount. This requirement makes sense in every metric space. Given a homeomorphism f from a metric space X to a metric space Y , then for x∈X and r>0 set

Asymptotic values and hölder continuity of quasiconformal mappings

1987

Cone conditions and quasiconformal mappings

1988

Let f be a quasiconformal mapping of the open unit ball B n = {x ∈ R n : | x | < l× in euclidean n-space R n onto a bounded domain D in that space. For dimension n= 2 the literature of geometric function theory abounds in results that correlate distinctive geometric properties of the domain D with special behavior, be it qualitative or quantitative, on the part of f or its inverse. There is a more modest, albeit growing, body of work that attempts to duplicate in dimensions three and above, where far fewer analytical tools are at a researcher’s disposal, some of the successes achieved in the plane along such lines. In this paper we contribute to that higher dimensional theory some observati…

Distortion of quasiconformal maps in terms of the quasihyperbolic metric

2013

Abstract We extend a theorem of Gehring and Osgood from 1979–relating to the distortion of the quasihyperbolic metric by a quasiconformal mapping between Euclidean domains–to the setting of metric measure spaces of Q -bounded geometry. When the underlying target space is bounded, we require that the boundary of the image has at least two points. We show that even in the manifold setting, this additional assumption is necessary.

Quasiconformal mappings and global integrability of the derivative

1991

Quasiextremal distance domains and extension of quasiconformal mappings

1985

Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings

2001

We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.

Second-order Raman scattering in CuO

2013

Polarized second-order Raman scattering spectra of CuO single crystals are reported. It is shown that for some scattering geometries the second-order processes dominate the inelastic light scattering spectra. Group-theoretical symmetry analysis of the selection rules for the first- and second-order scattering processes is performed and phonon dispersion relations are calculated within density functional theory. The main spectral features of the two-phonon spectra are assigned to overtones of the vibrational branches at various special points across the Brillouin zone.

Neutron scattering and crystal fields in Pr-hydrides

1978

The crystal field splittings of PrD2 and PrD2.5 have been determined by inelastic neutron scattering. While for PrD2 the crystal field experienced by the majority of Pr-ions is cubic, it is shown that in PrD2.5 the occupation of the octahedral interstitials occurs not in a statistical but rather in a well defined way which leads to an orthorhombic crystal field at the Pr-site.

Experimental studies of the liquid-glass transition in trimethylheptane

2000

The molecular glass former trimethylheptane was studied by calorimetric, dielectric, ultrasonic, neutron scattering, Brillouin scattering, and depolarized light-scattering techniques. The molecular structure appears to be nearly spherical optically as indicated by the low depolarization ratio and dielectric susceptibility values. A preliminary mode-coupling theory (MCT) analysis of the light-scattering and neutron-scattering data indicates that ${T}_{C}\ensuremath{\gtrsim}150 \mathrm{K},$ at least 25 K above ${T}_{G}.$ The susceptibility minima were analyzed with the MCT interpolation equation, and disagreement between the light and neutron results was observed despite the apparent isotropy…