Search results for "Map"
showing 10 items of 3484 documents
Hardy spaces and quasiconformal maps in the Heisenberg group
2023
We define Hardy spaces $H^p$, $00$ such that every $K$-quasiconformal map $f:B \to f(B) \subset \mathbb{H}^1$ belongs to $H^p$ for all $0<p<p_0(K)$. Second, we give two equivalent conditions for the $H^p$ membership of a quasiconformal map $f$, one in terms of the radial limits of $f$, and one using a nontangential maximal function of $f$. As an application, we characterize Carleson measures on $B$ via integral inequalities for quasiconformal mappings on $B$ and their radial limits. Our paper thus extends results by Astala and Koskela, Jerison and Weitsman, Nolder, and Zinsmeister, from $\mathbb{R}^n$ to $\mathbb{H}^1$. A crucial difference between the proofs in $\mathbb{R}^n$ and $\mathbb{…
$n$-harmonic coordinates and the regularity of conformal mappings
2014
This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with $C^r$ metric tensors ($r > 1$) is a $C^{r+1}$ conformal (local) diffeomorphism. This result was proved in [12, 27, 33], but we give a new proof of this fact. The proof is based on $n$-harmonic coordinates, a generalization of the standard harmonic coordinates that is particularly suited to studying conformal mappings. We establish the existence of a $p$-harmonic coordinate system for $1 < p < \infty$ on any Riemannian manifold.
Conformality and $Q$-harmonicity in sub-Riemannian manifolds
2016
We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.
Comments on the paper "COINCIDENCE THEOREMS FOR SOME MULTIVALUED MAPPINGS" by B. E. RHOADES, S. L. SINGH AND CHITRA KULSHRESTHA
2011
The aim of this note is to point out an error in the proof of Theorem 1 in the paper entitled “Coincidence theorems for some multivalued mappings” by B. E. Rhoades, S. L. Singh and Chitra Kulshrestha [Internat. J. Math. & Math. Sci., 7 (1984), 429-434], and to indicate a way to repair it.
Assessment of the interpretability of data mining for the spatial modelling of water erosion using game theory
2021
Abstract This study undertook a comprehensive application of 15 data mining (DM) models, most of which have, thus far, not been commonly used in environmental sciences, to predict land susceptibility to water erosion hazard in the Kahorestan catchment, southern Iran. The DM models were BGLM, BGAM, Cforest, CITree, GAMS, LRSS, NCPQR, PLS, PLSGLM, QR, RLM, SGB, SVM, BCART and BTR. We identified 18 factors usually considered as key controls for water erosion, comprising 10 factors extracted from a digital elevation model (DEM), three indices extracted from Landsat 8 images, a sediment connectivity index (SCI) and three other intrinsic factors. Three indicators consisting of MAE, MBE, RMSE, and…
Geo-hazards of the San Vito peninsula offshore (southwestern Tyrrhenian Sea)
2021
Geomorphological Tools for Mapping Natural Hazards.-- 12 pages, 7 figures, supplemental material https://doi.org/10.1080/17445647.2020.1866703.-- Software: The geomorphological main map and the Figures in the text were compiled using GLOBAL MAPPER, Surfer and Quantum-G GIS Software and redesigned to print with Adobe Illustrator
Pluvial flooding in urban areas: the role of surface drainage efficiency
2018
Pluvial flooding in urban areas may derive from the limited or temporarily reduced efficiency of surface drainage, even when the underlying storm sewers are properly designed. This study focuses on the impact of uncertainties in the operational condition of the surface drainage system on pluvial flood hazard. The flood propagation model FLURB-2D is implemented on a selected study area in the town of Genoa (Italy). Synthetic hyetographs based on the Chicago and bivariate copula methods with suitable return periods are used as input. While simulating the design rainfall, inlet operational conditions are varied stochastically using a Monte Carlo approach. Results confirm that microtopography h…
Fully automatic, real-time detection of facial gestures from generic video
2005
A technique for the detection of facial gestures from low resolution video sequences is presented. The technique builds upon the automatic 3D head tracker formulation of [M. La Cascia et al., 2000]. The tracker is based on the registration of a texture-mapped cylindrical model. Facial gesture analysis is performed in the texture map by assuming that the residual registration error can be modeled as a linear combination of facial motion templates. Two formulations are proposed and tested. In one formulation, the head and facial motion are estimated in a single, combined linear system. In the other formulation, head motion and then facial motion are estimated in a two-step process. The two-st…
Fast, Reliable Head Tracking Under Varying Illumination
2003
An improved technique for 3D head tracking under varying illumination conditions is proposed. The head is modeled as a texture mapped cylinder. Tracking is formulated as an image registration problem in the cylinder's texture map image. To solve the registration problem in the presence of lighting variation and head motion, the residual error of registration is modeled as a linear combination of texture warping templates and orthogonal illumination templates. Fast and stable on-line tracking is then achieved via regularized weighted least squares minimization of the registration error. The regularization term tends to limit potential ambiguities that arise in the warping and illumination te…
Head Tracking via Robust Registration in Texture Map Images.
1998
A novel method for 3D head tracking in the presence of large head rotations and facial expression changes is described. Tracking is formulated in terms of color image registration in the texture map of a 3D surface model. Model appearance is recursively updated via image mosaicking in the texture map as the head orientation varies. The resulting dynamic texture map provides a stabilized view of the face that can be used as input to many existing 2D techniques for face recognition, facial expressions analysis, lip reading, and eye tracking. Parameters are estimated via a robust minimization procedure; this provides robustness to occlusions, wrinkles, shadows and specular highlights. The syst…