Using remote sensing(RS)data and geographical information system(GIS),eco-environmental vulnerability and its changes were analyzed for the Yellow River Basin,China.The objective of this study was to improve our under...Using remote sensing(RS)data and geographical information system(GIS),eco-environmental vulnerability and its changes were analyzed for the Yellow River Basin,China.The objective of this study was to improve our understanding of eco-environmental changes so that a strategy of sustainable land use could be established.An environmental numerical model was developed using spatial principal component analysis(SPCA)model.The model contains twelve factors that include variables of land use,soil erosion,topography,climate,and vegetation.Using this model,synthetic eco- environmental vulnerability index(SEVI)was computed for 1990 and 2000 for the Yellow River Basin.The SEVI was classified into six levels,potential,slight,light,medium,heavy,and very heavy,following the natural breaks classification. The eco-environmental vulnerability distribution and its changes over the ten years from 1990 to 2000 were analyzed and the driving factors of eco-environmental changes were investigated.The results show that the eco-environmental vulnerability in the study area was at medium level,and the eco-environmental quality had been gradually improved on the whole.However,the eco-environmental quality had become worse over the ten years in some regions.In the study area,population growth,vegetation degradation,and governmental policies for eco-environmental protection were found to be the major factors that caused the eco-environmental changes over the ten years.展开更多
In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficie...In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficiently smooth.In this case,the proposed method leads to a fully discrete linear system.We show that the fully discrete integral operator is stable in both infinite and weighted square norms.Furthermore,we establish that the approximate solution arrives at an optimal convergence order under the two norms.Finally,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.展开更多
基金the National Key Basic Research Support Foundation of China(973 Program)(No.2005CB422003)the National Natural Science Foundation of China(No.40571037)
文摘Using remote sensing(RS)data and geographical information system(GIS),eco-environmental vulnerability and its changes were analyzed for the Yellow River Basin,China.The objective of this study was to improve our understanding of eco-environmental changes so that a strategy of sustainable land use could be established.An environmental numerical model was developed using spatial principal component analysis(SPCA)model.The model contains twelve factors that include variables of land use,soil erosion,topography,climate,and vegetation.Using this model,synthetic eco- environmental vulnerability index(SEVI)was computed for 1990 and 2000 for the Yellow River Basin.The SEVI was classified into six levels,potential,slight,light,medium,heavy,and very heavy,following the natural breaks classification. The eco-environmental vulnerability distribution and its changes over the ten years from 1990 to 2000 were analyzed and the driving factors of eco-environmental changes were investigated.The results show that the eco-environmental vulnerability in the study area was at medium level,and the eco-environmental quality had been gradually improved on the whole.However,the eco-environmental quality had become worse over the ten years in some regions.In the study area,population growth,vegetation degradation,and governmental policies for eco-environmental protection were found to be the major factors that caused the eco-environmental changes over the ten years.
基金supported by National Natural Science Foundation of China(Grant No.10901093)National Science Foundation of Shandong Province(Grant No.ZR2013AM006)
文摘In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficiently smooth.In this case,the proposed method leads to a fully discrete linear system.We show that the fully discrete integral operator is stable in both infinite and weighted square norms.Furthermore,we establish that the approximate solution arrives at an optimal convergence order under the two norms.Finally,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.
