The$H$^{$p$}corona problem is the following: Let$g$_{1}, ...,$g$_{$m$}be bounded holomorphic functions with 0<δ≤Σ‖$g$_{$i$}‖. Can we, for any$H$^{$p$}function ϕ, find$H$^{$p$}functions$u$_{1}, ...,$u$_{$m$}such that Σ$g$_{$i$}$u$_{$i$}=ϕ? It is known that the answer is affirmative in the polydisc, and the aim of this paper is to prove that it is in non-degenerate analytic polyhedra. To prove this, we construct a solution using a certain integral representation formula. The$H$^{$p$}estimate for the solution is then obtained by localization and some harmonic analysis results in the polydisc.

Laser scanning is an effective tool for acquiring geometric attributes of trees and vegetation, which lays a solid foundation for 3-dimensional tree modelling. Existing studies on tree modelling from laser scanning data are vast. However, some works cannot guarantee sufficient modelling accuracy, while some other works are mainly rule-based and therefore highly depend on user inputs. In this paper, we propose a novel method to accurately and automatically reconstruct detailed 3D tree models from laser scans. We first extract an initial tree skeleton from the input point cloud by establishing a minimum spanning tree using the Dijkstra shortest-path algorithm. Then, the initial tree skeleton is pruned by iteratively removing redundant components. After that, an optimization-based approach is performed to fit a sequence of cylinders to approximate the geometry of the tree branches. Experiments on various types of trees from different data sources demonstrate the effectiveness and robustness of our method. The overall fitting error (i.e., the distance between the input points and the output model) is less than 10 cm. The reconstructed tree models can be further applied in the precise estimation of tree attributes, urban landscape visualization, etc. The source code of this work is freely available at https://github.com/tudelft3d/adtree

The superradiant scattering of a scalar field with frequency and angular momentum (ω, m) by a near-extreme Kerr black hole with mass and spin (M, J) was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In this paper we show that for frequencies scaled to the superradiant bound the full functional dependence on (ω, m, M, J) of the scattering amplitudes is precisely reproduced by a dual two-dimensional conformal field theory in which the black hole corresponds to a specific thermal state and the scalar field to a specific operator. This striking agreement corroborates a conjectured Kerr/CFT correspondence.

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We present novel algorithms for compressible flows that\n\nare efficient for all Mach numbers. The approach is based on several\n\ningredients: semi-implicit schemes, the gauge decomposition\n\nof the velocity field and a second order formulation of the density\n\nequation (in the isentropic case) and of the energy equation (in\n\nthe full Navier-Stokes case). Additionally, we show that our approach\n\ncorresponds to a micro-macro decomposition of the model,\n\nwhere the macro field corresponds to the incompressible component\n\nsatisfying a perturbed low Mach number limit equation and\n\nthe micro field is the potential component of the velocity. Finally,\n\nwe also use the conservative variables in order to obtain a proper\n\nconservative formulation of the equations when the Mach number\n\nis order unity. We successively consider the isentropic case, the\n\nfull Navier-Stokes case, and the isentropic Navier-Stokes-Poisson\n\ncase. In this work, we only concentrate on the question of the\n\ntime discretization and show that the proposed method leads to\n\nAsymptotic Preserving schemes for compressible flows in the low\n\nMach number limit.