The curvature estimate of the Yang-Mills-Higgs flow on Higgs bundles over compact Kähler manifolds is  studied. Under the assumptions that the Higgs bundle is non-semistable and the Harder-Narasimhan-Seshadri filtration has no singularities with length one, it is proved that the curvature of the evolved Hermitian metric is uniformly bounded.

The kernel density estimator for widely orthant dependent random variables is studied. The exponential inequalities and the exponential rate for the estimator of a density function with a uniform version over compact sets are investigated. Further, the consistency of the estimator is proved. The results are generalizations of some existing outcomes for both associated and negatively associated samples. The convergence rate of the kernel density estimator is illustrated via a simulation study. Moreover, a real data analysis is presented.

A heavy dust storm originating in Mongolia and Inner Mongolia traveled to Northeast China and met a midlatitude frontal system on May 3, 2017. The potential ice nuclei (IN) effects of mineral dust aerosols on the vertical structure of clouds, precipitation, and latent heat (LH) were studied using Global Precipitation Mission (GPM) satellite observations and Weather Research and Forecasting (WRF) model simulations. The WRF simulations correctly captured the main features of the system, and the surface rain rate distribution was positively correlated with data retrieved from the GPM Microwave Imager. Moreover, the correlation coefficient increased from 0.31 to 0.54 with increasing moving average window size. The WRF-simulated rainfall vertical profiles are generally comparable to the GPM Dual-Frequency Precipitation Radar (DPR) observations, particularly in low layers. The joint probability distribution functions of the rain rate at different altitudes from the WRF simulation and GPM observations show high positive correlation coefficients of ~0.80, indicating that the assumptions regarding the raindrop size distribution in the WRF model and DPR retrieval were consistent. Atmospheric circulation analysis and aerosol optical depth observations from the Himawari-8 satellite indicated that the dust storm entered only a narrow strip of the northwest edge of the frontal precipitation system. The WRF simulations showed that in carefully selected areas of heavy dust, dust can enhance the heterogeneous ice nucleation process and increase the cloud ice, snowfall, high-altitude precipitation rate, and LH rate in the upper layers. This effect is significant at temperatures of −15 °C to −38 °C and requires dust number concentrations exceeding 10⁶ m⁻³. It is important to accurately classify the dusty region in this type of case study. In the selected vertical cross section, the WRF-simulated and DPR-retrieved LH have comparable vertical shapes and amplitudes. Both results reflect the structure of the tilted frontal surface, with positive LH above it and negative LH below it. The simulated area-averaged LH profiles show positive heating in the entire column, which is a convective-dominated region, and this feature is not significantly affected by dust. DPR-based LH profiles show stratiform-dominated or convective-dominated shapes, depending on the DPR retrieval product.

Sheared   E   ×   B   flow has been frequently observed to excite instability in space plasma. In this study, two methods – the interpenetrating plasma and ring electrode methods – were developed in the Keda Space Plasma EXperiment (KSPEX) device to trigger sheared   E   ×   B   flow. Both methods produce sheared   E   ×   B   flow by generating a radial electric field. The results of the experiment indicated that plasma instabilities in the ion cyclotron range can be excited by these methods. Therefore, the methods reported here are important for research on the mechanism for generating sheared flow-driven plasma instabilities, which may enrich our understanding of geospace physics.

The evolution of the atmospheric oxygen content through Earth’s history is a key issue in paleoclimatic and paleoenvironmental research. There were at least two oxygenation events in the Precambrian that involved fundamental changes in both biotic innovation and the surface environment. However, a large dissolved organic carbon (DOC) pool maintained in deep oceans during the Neoproterozoic may have extended the time interval between the two oxygenation events. To test the DOC hypothesis, we conducted detailed micro-drilled analyses of carbonate carbon isotopes (δ¹³C_carb) of a long Ediacaran drill core (the Wangji drill core), for which whole-rock δ¹³C_carb and organic carbon isotope (δ¹³C_org) records were available. The micro-drilled δ¹³C_carb values obtained in this study are consistent with whole-rock δ¹³C_carb results, precluding the influence of severe authigenic carbonate incorporation. Importantly, the multiple negative δ¹³C_carb excursions in the Wangji drill core were likely linked with upwelling events, during which DOC was supplied to the surface water and oxidized. Using box models, we estimate that ~3.6 × 10¹⁹ mol and ~2.0 × 10¹⁹ mol DOC were converted to bicarbonate during two negative δ¹³C_carb excursions spanning millions of years. The estimations are approximately 1000 times the modern marine DOC reservoir. Our results support a relatively high oxidation capacity (elevated atmospheric pO₂ and/or oceanic [

]) of the Earth’s surface during the early Ediacaran Period.

With its powerful real-time interaction and rich user experience, live streaming shopping has rapidly become consumers' new favorite. However, the frequent "rollover" incidents affecting the reputation of well-known streamers significantly reduce consumers' trust in the streamers. Academic research on trust in live streaming shopping has thus far mainly focused on purchase motivations. Few studies have focused on the factors influencing trust from the streamer's perspective, and they have ignored the moderating role of streamers and product factors, situational factors and individual characteristics of consumers. Therefore, this study introduces three new moderating variables – streamer-product matching, live streaming online reviews, and online shopping experience – to explore their moderating effects on streamers' reputation, popularity, and trust. The results show that streamers' reputation and popularity have a significant positive impact on trust in streamers, and streamer-product matching has a positive moderating effect on the relationship between streamers' reputation, streamers' popularity, and trust in streamers. Online reviews have a positive moderating effect on the relationship between streamers' popularity and trust, while online shopping experience has a positive moderating effect on the relationship between streamers' reputation and trust in streamers.