p-harmonic functions by way of intrinsic mean value properties

Let Ω be a bounded domain in ℝ n {\mathbb{R}^{n}} . Under appropriate conditions on Ω, we prove existence and uniqueness of continuous functions solving the Dirichlet problem associated to certain nonlinear mean value properties in Ω with respect to balls of variable radius. We also show that, when properly normalized, such functions converge to the p-harmonic solution of the Dirichlet problem in Ω for p ⩾ 2 {p\geqslant 2} . Existence is obtained via iteration, a fundamental tool being the construction of explicit universal barriers in Ω.

Circuit Determinants of Ventricular Tachycardia Cycle Length: Characterization of Fast and Unstable Human VT

Background: Fast ventricular tachycardias (VTs) have been historically attributed to shorter path lengths with smaller reentrant circuit dimensions in animal models. The relationship between the dimensions of the reentrant VT circuit and tachycardia cycle length (TCL) has not been examined in humans. This study aimed to analyze the determinants of the rate of human VT with comparison of circuit dimensions and conduction velocity (CV) across a wide range of both stable and unstable VTs delineated by high-resolution mapping. Methods: 54 VTs with complete circuit delineation (>90% TCL) by high-resolution multielectrode mapping were analyzed in 49 patients (male 88%, 65 years [58-71], nonischemic 47%). Fast VT was defined as TCL <333 ms (rate >180 bpm). Unstable VT was defined by hemodynamic deterioration with an intrinsic mean arterial pressure <60 mmHg during a sustained episode. Results: The median TCL of VT was 365 ms (306-443 ms) and 24 fast VTs with TCL<333ms (180 bpm) were characterized. A wide range of CV was observed within the entrance (0.03-0.55 m/s), common pathway (0.03-0.77 m/s), exit (0.03-0.53m/s), and outer loop (0.17-1.13 m/s). There were no significant differences in the median dimensions of the isthmus and path length between fast versus slow VTs and unstable versus stable VTs. The outer loop CV was the only circuit component that correlated with TCL both in ischemic cardiomyopathy (r=-0.5, p=0.006) and nonischemic cardiomyopathy(r=-0.45, p=0.028). The duration of the longest diastolic electrogram was inversely correlated with the dimensions of common pathway (length: r=-0.46, p=0.001, width: r=-0.3, p=0.047) and predictive of VT termination by a single radiofrequency application (r=-0.41, p=0.023). Conclusions: Due to a wide spectrum of CV observed within the reentrant path during human VT, the dimensions of the circuit were not predictive of VT cycle length. For the first time, we demonstrate that the CV of the outer loop, rather than isthmus, is the principal determinant of the rate of VT. The size of the circuit was similar between fast versus slow VTs and unstable versus stable VTs. Long, continuous electrograms were indicative of spatially confined isthmus dimensions, confirmed by rapid termination of VT during radiofrequency delivery.

SCENE CLASSIFICATION BASED ON THE INTRINSIC MEAN OF LIE GROUP

Remote Sensing scene classification aims to identify semantic objects with similar characteristics from high resolution images. Even though existing methods have achieved satisfactory performance, the features used for classification modeling are still limited to some kinds of vector representation within a Euclidean space. As a result, their models are not robust to reflect the essential scene characteristics, hardly to promote classification accuracy higher. In this study, we propose a novel scene classification method based on the intrinsic mean on a Lie Group manifold. By introducing Lie Group machine learning into scene classification, the new method uses the geodesic distance on the Lie Group manifold, instead of Euclidean distance, solving the problem that non-euclidean space samples could not be calculated by Euclidean distance directly. The experiments show that our method produces satisfactory performance on two public and challenging remote sensing scene datasets, UC Merced and SIRI-WHU, respectively.

Localized and Distributed Energy in Wave–Current Flow

Evaluation of localized and distributed in time spectral energy in wave–current coexisting environment is investigated in this study. In order to understand the inherent characteristics of the flow under consideration, the Hilbert-Huang transform (HHT) is introduced to determine the instantaneous frequency corresponding to the maximum energy carrying by the velocity field. This frequency is associated with the timescale of the most energetic velocity fluctuations. The intrinsic mean frequency of the intrinsic mode function (IMF) is reduced with the increase in the IMF number. It was shown that the maximum energy is concentrated close to the center of the IMF series. The spectral characteristics obtained by the HHT are carefully compared with those obtained by more conventional Fourier and wavelet transform (FFT and WT, respectively). Addition of the surface wave component to the velocity field of the current-only case leads to the extension of the frequency range containing the dominant portion of the energy.

The MUSE-Faint survey

Aims. It has been shown that the ultra-faint dwarf galaxy Eridanus 2 may host a stellar cluster in its centre. If this cluster is shown to exist, it can be used to set constraints on the mass and abundance of massive astrophysical compact halo objects (MACHOs) as a form of dark matter. Previous research has shown promising expectations in the mass range of 10−100 M⊙, but lacked spectroscopic measurements of the cluster. We aim to provide spectroscopic evidence regarding the nature of the putative star cluster in Eridanus 2 and to place constraints on MACHOs as a constituent of dark matter. Methods. We present spectroscopic observations of the central square arcminute of Eridanus 2 from MUSE-Faint, a survey of ultra-faint dwarf galaxies with the Multi Unit Spectroscopic Explorer on the Very Large Telescope. We derived line-of-sight velocities for possible member stars of the putative cluster and for stars in the centre of Eridanus 2. We discuss the existence of the cluster and determine new constraints for MACHOs using the Fokker–Planck diffusion approximation. Results. Out of 182 extracted spectra, we identify 26 member stars of Eridanus 2, seven of which are possible cluster members. We find intrinsic mean line-of-sight velocities of 79.7+3.1−3.8 km s−1 and 76.0+3.2−3.7 km s−1 for the cluster and the bulk of Eridanus 2, respectively, as well as intrinsic velocity dispersions of < 7.6 km s−1 (68% upper limit) and 10.3+3.9−3.2 km s−1, respectively. This indicates that the cluster most likely exists as a distinct dynamical population hosted by Eridanus 2 and that it does not have a surplus of dark matter over the background distribution. Among the member stars in the bulk of Eridanus 2, we find possible carbon stars, alluding to the existence of an intermediate-age population. We derived constraints on the fraction of dark matter that can consist of MACHOs with a given mass between 1 and 105 M⊙. For dark matter consisting purely of MACHOs, the mass of the MACHOs must be less than ∼7.6 M⊙ and ∼44 M⊙ at a 68- and 95% confidence level, respectively.

Experiment-based modelling of the mechanical behaviour of non-hazardous waste incineration bottom ashes treated by hydraulic binder

Instrumented indentation tests have been carried out on an isolated 25 mm diameter particle of Non-Hazardous Waste Incineration bottom ash. These tests have enabled one to assess the intrinsic mean reduced modulus of elasticity “Er” of the particles. This result is used as input data for a 3D numerical model of Representative Elementary Volumes (REV) of a road gravel made with this kind of by-products. This numerical model is based on a multi-scale hierarchical modelling strategy. The aggregates treated with cement have been decomposed into two REV at the sub-mesoscopic and mesoscopic scales. The numerical simulations campaign (“virtual laboratory”) lead to the following results. At the sub-mesoscopic scale, we determined the input parameters for the Concrete Damaged Plasticity Model (CDPM) used at the mesoscopic scale. At the mesoscopic scale, the mechanical characteristics of the road aggregates usually determined through experiments have been found. The non-hazardous waste incineration bottom ashes treated by hydraulic binder was classified into mechanical classe 3.