Harmonic maps on domains with piecewise Lipschitz continuous metrics

For a bounded domain equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from $(\Omega, g)$ to a compact Riemannian manifold $(N,h)\subset\mathbb R^k$ without boundary. We generalize the notion of stationary harmonic map and prove the partial regularity. We also discuss the global Lipschitz and piecewise $C^{1,\alpha}$-regularity of harmonic maps from $(\Omega, g)$ manifolds that support convex distance functions.Comment: 24 page

Mapping the Spatial-Temporal Dynamics of Vegetation Response Lag to Drought in a Semi-Arid Region

Drought, as an extreme climate event, affects the ecological environment for vegetation and agricultural production. Studies of the vegetative response to drought are paramount to providing scientific information for drought risk mitigation. In this paper, the spatial-temporal pattern of drought and the response lag of vegetation in Nebraska were analyzed from 2000 to 2015. Based on the long-term Daymet data set, the standard precipitation index (SPI) was computed to identify precipitation anomalies, and the Gaussian function was applied to obtain temperature anomalies. Vegetation anomaly was identified by dynamic time warping technique using a remote sensing Normalized Difference Vegetation Index (NDVI) time series. Finally, multilayer correlation analysis was applied to obtain the response lag of different vegetation types. The results show that Nebraska suffered severe drought events in 2002 and 2012. The response lag of vegetation to drought typically ranged from 30 to 45 days varying for different vegetation types and human activities (water use and management). Grasslands had the shortest response lag (~35 days), while forests had the longest lag period (~48 days). For specific crop types, the response lag of winter wheat varied among different regions of Nebraska (35–45 days), while soybeans, corn and alfalfa had similar response lag times of approximately 40 days

Improving lignocellulose thermal stability by chemical modification with boric acid for incorporating into polyamide

The preparation of bio-composites based on engineering plastic is always restricted by the low thermal stability of lignocellulose. In this study, the thermal stability of lignocellulose was improved by boric acid modification. Then, the borated lignocellulose was characterized to analyze the mechanism of involved in the improvement of thermal stability. Furthermore, the untreated and borated lignocellulose was combined with polyamide 6 to produce bio-composites. The effects of lignocellulose content and boric acid modification on the color, thermal stability and mechanical properties of the resulting composites were compared and analyzed. Boric acid protected lignocellulose from thermal degradation, increasing the lightness of the resulting composites. However, boric acid appeared to have a negative effect on the mechanical strength of the resulting composites. In summary, this study demonstrated that bio-composites based on engineering plastic could be prepared by improving the thermal stability of lignocellulose using a boric acid treatment