The weighted log canonical threshold

In this note, we show how to apply the original $L^2$-extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic function. In this way, we are able to reprove the strong openness conjecture and to obtain an effective version of the semicontinuity theorem for weighted log canonical thresholds.Comment: Final versio

Singularity invariants of plurisubharmonic functions

In this paper, we combine tools in pluripotential theory and commutative algebra to study singularity invariants of plurisubharmonic functions. We obtain some relationships between singularity invariants of plurisubharmonic functions and holomorphic functions. These results lead a sharp lower bound for the log canonical threshold of a plurisubharmonic function. It simultaneously improves the main result in Demailly and Pham (Acta. Math 212: 1-9, 2014), the classical result due to Skoda (Bull. Soc. Math. France 100: 353-408, 1972), as well as the lower estimate in Fernex, Ein and Mustata (Math. Res. Lett: 10 219-236, 2003) which has received crucial applications to birational geometry in recent years.Comment: 17 page

Factors Affecting Prosocial Sharing Health-related Information on Social Media During a Health Crisis

During a health crisis, prosocial sharing of health-related information (HRI) on social media can help to deliver early warnings about new diseases, raise social awareness, exchange support, and spread health policies. Current literature has mainly focused on the factors of general sharing of HRI under normal conditions but neglected those motivations under the health crisis context. This research aims to investigate factors that influence online users’ prosocial sharing of HRI during a health crisis. To obtain the objective, this study developed a dual helping-protecting motivation model from the fear appeal model and social exchange theory. The partial least squares analysis, carried out on the surveyed data of 326 participants, revealed that prosocial sharing intention is affected by protecting factors (i.e., sharing efficacy, response efficacy) and helping factors (i.e., reciprocity expectation). Additionally, both perceived health risk and perceived information quality risk were found to influence the sharing intention via motivational factors