This is a follow-up of our recent article Deng et al. (2004). In Deng et al. (2004), we derive some local geometric conditions on vortex filaments which can prevent finite time blowup of the 3D incompressible Euler equation. In this article, we derive improved geometric conditions which can be applied to the scenario when velocity blows up at the same time… (More)
By exploring a local geometric property of the vorticity field along a vortex filament, we establish a sharp relationship between the geometric properties of the vorticity field and the maximum vortex stretching. This new understanding leads to an improved result of the global existence of the 3D Euler equation under mild assumptions.
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the associated mass-action system. Furthermore, an index formula is given for the set of equilibria in a given stoichiometric… (More)
We explore a level set representation of vorticity in the study of the singularity problems for incompressible fluid models. This representation exists for all initial vorticity fields. We further apply it to study the 3D Lagrangian averaged Euler equations and the 3D Euler equations, and obtain new global existence conditions.
BACKGROUND Several systematic reviews and meta-analyses demonstrated the association between depression and the risk of coronary heart disease (CHD), but the previous reviews had some limitations. Moreover, a number of additional studies have been published since the publication of these reviews. We conducted an updated meta-analysis of prospective studies… (More)
Incentive schemes are designed to promote cooperation in distributed systems, in which peers are free to decide how much to contribute. A variety of incentive schemes have been proposed in peer-to-peer file-sharing systems, touted to have special advantages in certain scenarios. However, only little research has been done on comparing these incentive… (More)
Real Time Cell Analysis (RTCA) technology is used to monitor cellular changes continuously over the entire exposure period. Combining with different testing concentrations, the profiles have potential in probing the mode of action (MOA) of the testing substances. In this paper, we present machine learning approaches for MOA assessment. Computational tools… (More)
Artificial vegetation restoration can induce variations in accumulation and distribution of soil carbon (C), nitrogen (N) and phosphorus (P). However, little is known about variations in soil C, N and P nutrient fraction stratification following artificial vegetation in Loess Plateau China. Based on the hypothesis that re-vegetated can improve soil quality… (More)
—Nonlinear model order reduction has always been a challenging but important task in various science and engineering fields. In this paper, a novel symmetric tensor-based order-reduction method (STORM) is presented for simulating large-scale nonlinear systems. The multidimensional data structure of symmetric tensors, as the higher order generalization of… (More)