Real-Variable Theory for New Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Let $X$ be a ball quasi-Banach function space, $\alpha\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the new Herz-type Hardy spaces $\mathcal{H\dot{K}}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$ and $\mathcal{HK}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$ associated with ball quasi-Banach function space $X$, via the non-tangential grand maximal function. Then, under some mild assumptions on $X$, the authors establish the real-variable theory for $\mathcal{H\dot{K}}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$ and $\mathcal{HK}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$, in terms of maximal function characterizations, atomic and molecular decompositions, and obtain the boundedness of some sublinear operators from $\mathcal{H\dot{K}}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$ to $\mathcal{\dot{K}}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$ and from $\mathcal{HK}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$ to $\mathcal{K}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$. As appliccations, we give two concrete function spaces which are members of Herz-type Hardy spaces associated with ball quasi-Banach function spaces.Comment: 37 pages, submitte

Visual-UWB Navigation System for Unknown Environments

Navigation applications relying on the Global Navigation Satellite System (GNSS) are limited in indoor environments and GNSS-denied outdoor terrains such as dense urban or forests. In this paper, we present a novel accurate, robust and low-cost GNSS-independent navigation system, which is composed of a monocular camera and Ultra-wideband (UWB) transceivers. Visual techniques have gained excellent results when computing the incremental motion of the sensor, and UWB methods have proved to provide promising localization accuracy due to the high time resolution of the UWB ranging signals. However, the monocular visual techniques with scale ambiguity are not suitable for applications requiring metric results, and UWB methods assume that the positions of the UWB transceiver anchor are pre-calibrated and known, thus precluding their application in unknown and challenging environments. To this end, we advocate leveraging the monocular camera and UWB to create a map of visual features and UWB anchors. We propose a visual-UWB Simultaneous Localization and Mapping (SLAM) algorithm which tightly combines visual and UWB measurements to form a joint non-linear optimization problem on Lie-Manifold. The 6 Degrees of Freedom (DoF) state of the vehicles and the map are estimated by minimizing the UWB ranging errors and landmark reprojection errors. Our navigation system starts with an exploratory task which performs the real-time visual-UWB SLAM to obtain the global map, then the navigation task by reusing this global map. The tasks can be performed by different vehicles in terms of equipped sensors and payload capability in a heterogeneous team. We validate our system on the public datasets, achieving typical centimeter accuracy and 0.1% scale error.Comment: Proceedings of the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2018

Health monitoring of rolling element bearing using a spectrum searching strategy

Aiming at achieving early fault diagnosis and tracking the degradation process of bearings, we propose a novel monitoring methodology using a spectrum searching strategy in this paper. Firstly, a vibration signal is collected with appropriate sampling frequency and length. Secondly, the structural information of spectrum (SIOS) on a predefined frequency grid is constructed through a searching algorithm after deriving the single-sided FFT spectrum. Finally, the two-dimensional (2-D) line plot of the frequency grid versus the average power in SIOS is employed to conduct fault detection and the sum of the largest six total-power (SLSTP) of the frequency grid in SIOS is calculated as a health indication to demonstrate the changes in the bearing’s health status. The performance of the proposed scheme is validated with both simulation and bearing data. Experimental results show that the monitoring algorithm could manifest satisfactory behaviors in early fault diagnosis and health assessment of bearings

Multiband effects in thermoelectric and electrical transport properties of kagome superconductors AAV3_3Sb5_5 (AA = K, Rb, Cs)

We studied the effects of multiband electronic structure on the thermoelectric and electrical transport properties in the normal state of kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs). In all three members, the multiband nature is manifested by sign changes in the temperature dependence of the Seebeck and Hall resistivity, together with sublinear response of the isothermal Nernst and Hall effects to external magnetic fields in the charge ordered state. Moreover, ambipolar transport effects appear ubiquitously in all three systems, giving rise to sizable Nernst signal. Finally, possible origins of the sign reversal in the temperature dependence of the Hall effect are discussed.Comment: 8 pages, 5 figures. To appear in New Journal of Physic

Charge fluctuations above TCDWT_\mathrm{CDW} revealed by glasslike thermal transport in kagome metals AAV3_3Sb5_5 (AA = K, Rb, Cs)

We present heat capacity, electrical and thermal transport measurements of kagome metals $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs). In all three compounds, development of short-range charge fluctuations above the charge density wave (CDW) transition temperature $T_\mathrm{CDW}$ strongly scatters phonons via electron-phonon coupling, leading to glasslike phonon heat transport, i.e., phonon thermal conductivity decreases weakly upon cooling. Once the long-range charge order sets in below $T_\mathrm{CDW}$, short-range charge fluctuations are quenched, and the typical Umklapp scattering dominated phonon heat transport is recovered. The charge-fluctuations-induced glasslike phonon thermal conductivity implies sizable electron-phonon coupling in $A$V$_3$Sb$_5$.Comment: 8 pages, 5 figure

Colossal c-axis response and lack of rotational symmetry breaking within the kagome plane of the CsV3_3Sb5_5 superconductor

The kagome materials AV4$_3$Sb$_5$ (A = K, Rb, Cs) host an intriguing interplay between unconventional superconductivity and charge-density-waves. Here, we investigate CsV$_3$Sb$_5$ by combining high-resolution thermal-expansion, heat-capacity and electrical resistance under strain measurements. We directly unveil that the superconducting and charge-ordered states strongly compete, and that this competition is dramatically influenced by tuning the crystallographic c-axis. In addition, we report the absence of additional bulk phase transitions within the charge-ordered state, notably associated with rotational symmetry-breaking within the kagome planes. This suggests that any breaking of the C$_6$ invariance occurs via different stacking of C$_6$-symmetric kagome patterns. Finally, we find that the charge-density-wave phase exhibits an enhanced A$_{1g}$-symmetric elastoresistance coefficient, whose large increase at low temperature is driven by electronic degrees of freedom

Surface electrocardiographic characteristics in coronavirus disease 2019: repolarization abnormalities associated with cardiac involvement

AIMS The coronavirus disease 2019 (COVID-19) has spread rapidly around the globe, causing significant morbidity and mortality. This study aims to describe electrocardiographic (ECG) characteristics of COVID-19 patients and to identify ECG parameters that are associated with cardiac involvement. METHODS AND RESULTS The study included patients who were hospitalized with COVID-19 diagnosis and had cardiac biomarker assessments and simultaneous 12-lead surface ECGs. Sixty-three hospitalized patients (median 53 [inter-quartile range, 43-65] years, 76.2% male) were enrolled, including patients with (n = 23) and without (n = 40) cardiac injury. Patients with cardiac injury were older, had more pre-existing co-morbidities, and had higher mortality than those without cardiac injury. They also had prolonged QTc intervals and more T wave changes. Logistic regression model identified that the number of abnormal T waves (odds ratio (OR), 2.36 [95% confidence interval (CI), 1.38-4.04], P = 0.002) and QTc interval (OR, 1.31 [95% CI, 1.03-1.66], P = 0.027) were independent indicators for cardiac injury. The combination model of these two parameters along with age could well discriminate cardiac injury (area the under curve 0.881, P < 0.001) by receiver operating characteristic analysis. Cox regression model identified that the presence of T wave changes was an independent predictor of mortality (hazard ratio, 3.57 [1.40, 9.11], P = 0.008) after adjustment for age. CONCLUSIONS In COVID-19 patients, presence of cardiac injury at admission is associated with poor clinical outcomes. Repolarization abnormalities on surface ECG such as abnormal T waves and prolonged QTc intervals are more common in patients with cardiac involvement and can help in further risk stratification