Recently, a nonconvex relaxation of low-rank matrix recovery (LMR), called the Schatten- p quasi-norm minimization (0 <; p <; 1), was introduced instead of the previous nuclear norm minimization in order to approximate the problem of LMR closer. In this paper, we introduce a notion of the restricted p-isometry constants (0 <; p ≤ 1) and derive a p -RIP condition for exact reconstruction of LMR via Schatten-p quasi-norm minimization. In particular, we determine how many random, Gaussian measurements are needed for the p-RIP condition to hold with high probability, which gives a theoretical result that it needs fewer measurements with small p for exact recovery via Schatten-p quasi-norm minimization than when p=1.

In the context of climate warming, flash drought has become increasingly frequent, posing significant threats to agriculture, ecosystems, and the environment. Xinjiang, located in an arid and semi-arid region, necessitates a thorough investigation into the distinctions between flash drought and traditional drought, as well as an exploration of the driving forces behind both types of drought. In this study, soil moisture data from ERA5-Land were utilized to construct a framework for the identification of flash drought and traditional drought based on historical events. The Geodetector was employed to explore the factors that influence the spatial heterogeneity of these two drought forms. The findings illuminate that (1) in terms of spatial distribution, traditional drought predominated in southern Xinjiang, while flash drought exhibited greater prominence in northern Xinjiang. (2) Regarding changes in trends, both flash drought and traditional drought exhibited an increasing trend in frequency since the 1990s, with the frequency trend of flash drought passing the significance test (α ≤ 0.05). Additionally, the severity of both flash drought and traditional drought displayed a noteworthy and statistically significant increase within sliding windows ranging from 46 to 62 years. (3) Concerning the driving forces, precipitation emerged as the principal driving force behind both flash drought and traditional drought. Furthermore, human activities exerted a more substantial influence on traditional drought, and the interactions involving human activities had the potential to significantly amplify the explanatory power of the spatial heterogeneity for both drought types. (4) In terms of the drought risk, a notable variation in the risk of flash drought was observed across various ecological zones, with the highest risk occurring in mildly fragile ecological zones. Furthermore, when comparing the results from 1995 to 2019, the flash drought risk exhibited a marked increase in severely fragile ecological zones. This study enriches the understanding of the dynamics of flash drought and traditional drought in Xinjiang and carries important implications for enhancing the precision of drought monitoring and early warning systems.

A model of a two-stage $N$-person noncooperative game under uncertainty is studied, in which at the first stage each player solves a quadratic program parameterized by other players' decisions and ...

Quality has always been an important factor affecting the competitive advantages and financial performance of firms. Some research has examined the impacts of Malcolm Baldrige Award and European Quality Award announcements on the market value of winners. However, the effect of the China Quality Award on firm market value has rarely been studied and has not been fully elucidated. On the basis of 85 China Quality Award announcements, this study explores whether winners show significant abnormal stock returns on the award announcement day using an event study. Some firm characteristics, such as ownership type, industry type, registered address, first time winning the award or not, and whether related firms won the awards are further considered. A market adjustment model is also adopted to re-estimate the short-term market reaction to test the robustness of our findings. It is found that China Quality Award winners do not show a significant market reaction for the full sample in the short term. However, the China Quality Award has brought significantly positive benefits to firms located in eastern China, first-time winners, and firms winning the award themselves. The long-term stock price performance is significantly positive. The findings may expand the research on the relationship between quality awards and firm market value in various institutional contexts.

Drought displays dynamic and uncertain spatiotemporal characteristics, thus it is typically not confined to fixed temporal-spatial boundaries. Existing drought clustering methods often involve spatially clustering drought points or grids into patches, subsequently connected over time to form three-dimensional structures. Despite this process being able to extract three-dimensional drought clusters, it is likely to overlook mild or relatively small, isolated drought patches. To overcome this limitation, this paper presented an effective method (named STD-CLUSTER) for identifying drought clusters with complete three-dimensional structures. The method initially employed run theory to extract drought events as "lines" and subsequently clustered these events using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. A case study on the 2006 flash drought in the Yangtze River Basin demonstrated that STD-CLUSTER successfully clustered drought events and ensured the integrity of drought clusters by considering small, isolated, or disconnected patches. Additionally, an in-depth analysis using STD-CLUSTER examined seasonal drought events in China from 1991 to 2022, identifying a total of 35 drought clusters. These clusters began and ended with small-area patches, exhibiting features of expansion, contraction, spread, merging, and splitting over time. Furthermore, seasonal changes significantly influenced the evolution of drought clusters, with affected area and severity increasing in spring and summer and decreasing in autumn and winter. The applicability of the proposed method extends beyond various geographical regions and time scales, providing effective support for comprehensively investigating the spatiotemporal evolution of drought.