Topological and differentiable rigidity of submanifolds in space forms

Let $F^{n+p}(c)$ be an $(n+p)$-dimensional simply connected space form with nonnegative constant curvature $c$. We prove that if $M^n(n\geq4)$ is a compact submanifold in $F^{n+p}(c)$, and if $Ric_M>(n-2)(c+H^2),$ where $H$ is the mean curvature of $M$, then $M$ is homeomorphic to a sphere. We also show that the pinching condition above is sharp. Moreover, we obtain a new differentiable sphere theorem for submanifolds with positive Ricci curvature.Comment: 12 page

Temperature effects on the nuclear symmetry energy and symmetry free energy with an isospin and momentum dependent interaction

Within a self-consistent thermal model using an isospin and momentum dependent interaction (MDI) constrained by the isospin diffusion data in heavy-ion collisions, we investigate the temperature dependence of the symmetry energy $E_{sym}(\rho, T)$ and symmetry free energy $F_{sym}(\rho, T)$ for hot, isospin asymmetric nuclear matter. It is shown that the symmetry energy $E_{sym}(\rho, T)$ generally decreases with increasing temperature while the symmetry free energy $F_{sym}(\rho, T)$ exhibits opposite temperature dependence. The decrement of the symmetry energy with temperature is essentially due to the decrement of the potential energy part of the symmetry energy with temperature. The difference between the symmetry energy and symmetry free energy is found to be quite small around the saturation density of nuclear matter. While at very low densities, they differ significantly from each other. In comparison with the experimental data of temperature dependent symmetry energy extracted from the isotopic scaling analysis of intermediate mass fragments (IMF's) in heavy-ion collisions, the resulting density and temperature dependent symmetry energy $E_{sym}(\rho, T)$ is then used to estimate the average freeze-out density of the IMF's.used to estimate the average freeze-out density of the IMF's.Comment: 9 pages, 7 figures, 1 figure added to show the temperature dependence of the potential and kinetic parts of the symmetry energy. Revised version to appear in PR

Ecological model to predict potential habitats of Oncomelania hupensis, the intermediate host of Schistosoma japonicum in the mountainous regions, China

Schistosomiasis japonica is a parasitic disease that remains endemic in seven provinces in the People's Republic of China (P.R. China). One of the most important measures in the process of schistosomiasis elimination in P.R. China is control of Oncomelania hupensis, the unique intermediate host snail of Schistosoma japonicum. Compared with plains/swamp and lake regions, the hilly/mountainous regions of schistosomiasis endemic areas are more complicated, which makes the snail survey difficult to conduct precisely and efficiently. There is a pressing call to identify the snail habitats of mountainous regions in an efficient and cost-effective manner.; Twelve out of 56 administrative villages distributed with O. hupensis in Eryuan, Yunnan Province, were randomly selected to set up the ecological model. Thirty out of the rest of 78 villages (villages selected for building model were excluded from the villages for validation) in Eryuan and 30 out of 89 villages in Midu, Yunnan Province were selected via a chessboard method for model validation, respectively. Nine-year-average Normalized Difference Vegetation Index (NDVI) and Land Surface Temperature (LST) as well as Digital Elevation Model (DEM) covering Eryuan and Midu were extracted from MODIS and ASTER satellite images, respectively. Slope, elevation and the distance from every village to its nearest stream were derived from DEM. Suitable survival environment conditions for snails were defined by comparing historical snail presence data and remote sensing derived images. According to the suitable conditions for snails, environment factors, i.e. NDVI, LST, elevation, slope and the distance from every village to its nearest stream, were integrated into an ecological niche model to predict O. hupensis potential habitats in Eryuan and Midu. The evaluation of the model was assessed by comparing the model prediction and field investigation. Then, the consistency rate of model validation was calculated in Eryuan and Midu Counties, respectively. The final ecological niche model for potential O. hupensis habitats prediction comprised the following environmental factors, namely: NDVI (≥ 0.446), LST (≥ 22.70°C), elevation (≤ 2,300 m), slope (≤ 11°) and the distance to nearest stream (≤ 1,000 m). The potential O. hupensis habitats in Eryuan distributed in the Lancang River basin and O. hupensis in Midu shows a trend of clustering in the north and spotty distribution in the south. The consistency rates of the ecological niche model in Eryuan and Midu were 76.67% and 83.33%, respectively.; The ecological niche model integrated with NDVI, LST, elevation, slope and distance from every village to its nearest stream adequately predicted the snail habitats in the mountainous regions