Search results for "Conformal"
showing 10 items of 234 documents
Dimension gap under conformal mappings
2012
Abstract We give an estimate for the Hausdorff gauge dimension of the boundary of a simply connected planar domain under p -integrability of the hyperbolic metric, p > 1 . This estimate does not degenerate when p tends to one; for p = 1 the boundary can even have positive area. The same phenomenon is extended to general planar domains in terms of the quasihyperbolic metric. We also give an example which shows that our estimates are essentially sharp.
Generalized evolutes, vertices and conformal invariants of curves in Rn + 1
1999
Abstract We define the generalized evolute of a curve in ( n + 1)-space and find a duality relation between them. We also prove that the conformal torsion is a function of the speed of the generalized evolute and that the singular points of the generalized evolute (vertices) are conformal invariants.
Conformal curvatures of curves in
2001
Abstract We define a complete set of conformal invariants for pairs of spheres in and obtain from these the expressions of the conformal curvatures of curves in (n + 1)-space in terms of the Euclidean invariants.
Pointwise characterizations of Besov and Triebel–Lizorkin spaces and quasiconformal mappings
2011
Abstract In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces B ˙ p , q s and Triebel–Lizorkin spaces F ˙ p , q s for all s ∈ ( 0 , 1 ) and p , q ∈ ( n / ( n + s ) , ∞ ] , both in R n and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve F ˙ n / s , q s on R n for all s ∈ ( 0 , 1 ) and q ∈ ( n / ( n + s ) , ∞ ] . A metric measure space version of the above morphism property is also established.
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
2019
AbstractThe conformal mapping $$f(z)=(z+1)^2 $$ f ( z ) = ( z + 1 ) 2 from $${\mathbb {D}}$$ D onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 .$$ R 2 . We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $${\mathbb {D}}$$ D onto cardioid-type domains.
Dimension gap under Sobolev mappings
2015
Abstract We prove an essentially sharp estimate in terms of generalized Hausdorff measures for the images of boundaries of Holder domains under continuous Sobolev mappings, satisfying suitable Orlicz–Sobolev conditions. This estimate marks a dimension gap, which was first observed in [2] for conformal mappings.
Bounded compositions on scaling invariant Besov spaces
2012
For $0 < s < 1 < q < \infty$, we characterize the homeomorphisms $��: \real^n \to \real^n$ for which the composition operator $f \mapsto f \circ ��$ is bounded on the homogeneous, scaling invariant Besov space $\dot{B}^s_{n/s,q}(\real^n)$, where the emphasis is on the case $q\not=n/s$, left open in the previous literature. We also establish an analogous result for Besov-type function spaces on a wide class of metric measure spaces as well, and make some new remarks considering the scaling invariant Triebel-Lizorkin spaces $\dot{F}^s_{n/s,q}(\real^n)$ with $0 < s < 1$ and $0 < q \leq \infty$.
Generalization of the model-independent Laurent–Pietarinen single-channel pole-extraction formalism to multiple channels
2016
A method to extract resonance pole information from single-channel partial-wave amplitudes based on a Laurent (Mittag-Leffler) expansion and conformal mapping techniques has recently been developed. This method has been applied to a number of reactions and provides a model-independent extraction procedure which is particularly useful in cases where a set of amplitudes is available only at discrete energies. This method has been generalized and applied to the case of a multi-channel fit, where several sets of amplitudes are analyzed simultaneously. The importance of unitarity constraints is discussed. The final result provides a powerful, model-independent tool for analyzing partial-wave amp…
Absolute volume of the rectum and AUC from rectal DVH between 25Gy and 50Gy predict acute gastrointestinal toxicity with IG-IMRT in prostate cancer
2016
International audience; Background: To determine whether dose/volume specific endpoints (DVSE) or Area under the rectal DVH curve (rAUC) better predict acute gastrointestinal (GI) toxicity in prostate cancer patients treated with IMRT in the era of daily image guidance (IG-IMRT). Methods: A set of DVSE was recorded from V25 to V75 (increments of 5Gy) (both in % and in cc) for 180 men. The rAUC was calculated for doses ranging between 25Gy and 50Gy (rAUC(25-50)). Univariate and multivariate logistic regressions were performed to determine the relationship between DVSE or rAUC(25-50) and the appearance of any acute GI toxicity. Results: The rates of acute grade 1 (G1), G2 and G3 GI toxicities…
Minimization of a rectangular patch using genetic algorithms
2002
In recent years, the miniaturization of antennas have become more and more important, especially in connection with subscriber transceivers for cellular systems. Due to the multiple scattering environments and the almost indefinable operating scenario, the crosspolarization characteristics of the antenna are less important, however its physical size is critical. The attempts to reduce the physical size of the antenna made in the past, used classical methods, such as embedding the antenna in a dielectric medium of a high permittivity, adding a resistive element in series with the antenna, etc., but little effort was invested in simply generating other geometries, which by their intrinsic pro…