An algorithm of analysis tools on points distribution in high dimension space: The distance of a point and an infinite sub-space

This paper discusses the algorithm on the distance from a point and an infinite sub-space in high dimensional space With the development of Information Geometry([1]), the analysis tools of points distribution in high dimension space, as a measure of calculability, draw more attention of experts of pattern recognition. By the assistance of these tools, Geometrical properties of sets of samples in high-dimensional structures are studied, under guidance of the established properties and theorems in high-dimensional geometry.

Linear spatio-temporal instability analysis of ice growth under a falling water film

A linear spatio-temporal stability analysis is conducted for the ice growth under a falling water film along an inclined ice plane. The full system of linear stability equations is solved by using the Chebyshev collocation method. By plotting the boundary curve between the linear absolute and convective instabilities (AI/CI) of the ice mode in the parameter plane of the Reynolds number and incline angle, it is found that the linear absolute instability exists and occurs above a minimum Reynolds number and below a maximum inclined angle. Furthermore, by plotting the critical Reynolds number curves with respect to the inclined angle for the downstream and upstream branches, the convectively unstable region is determined and divided into three parts, one of which has both downstream and upstream convectively unstable wavepackets and the other two have only downstream or upstream convectively unstable wavepacket. Finally, the effect of the Stefan number and the thickness of the ice layer on the AI/CI boundary curve is investigated.

Numerical Study on the Spatial and Temporal Characteristics of Water Quality in the Taihu Lake of China

Taihu Lake is the third largest fresh water lake in China. With the fast economic development, abundant industrial and agricultural waste water has been discharged into Taihu Lake, causing the eutrophication of the water quality, which greatly affected the water utility. In the past decades, the treatment of Taihu Lake has witnessed limited success. Therefore, it is practically and theoretically significant to study the eutrophication of Taihu Lake. This research has focused on the issue of water quality including the characteristics of spatial and temporal distributions, and the rules of nutrient diffusion in the Taihu lake area. Based on the monitoring data, the basis distribution characteristics of water quality in Taihu Lake are analyzed. Comparing Taihu Lake with other Lakes shows that one important reason for Taihu eutrophication is the long period of water retention. A transporting and diffusing model of Taihu nutrient is developed by combining with the hydrodynamics model. Using the model, the concentration field of the total phosphorus (TP) and the influence of wind-driven current are numerically investigated, which leads to the conclusion that the flow field has a great influence on the spatial and temporal distributions of TP in Taihu Lake. Furthermore, the effect for improving the water quality by the project of water diversion from the Yangtze River to Taihu Lake was analyzed by simulation. The results demonstrate that short-term water diversion cannot improve the water quality of the heavily-polluted Meiliang Bay and the western bank areas of Taihu Lake.