A new conservation theorem of the nonholonomic systems is studied. The conserved quantity is onlyconstructed in terms of a general Lie group of transformation vector of the dynamical equations. Firstly, we establish t...A new conservation theorem of the nonholonomic systems is studied. The conserved quantity is onlyconstructed in terms of a general Lie group of transformation vector of the dynamical equations. Firstly, we establish thedynamical equations of the nonholonomic systems and the determining equations of Lie symmetry. Next, the theore mof non-Noether conserved quantity is deduced. Finally, we give an example to illustrate the application of the result.展开更多
Vector-to-raster conversion is a process accompanied with errors.The errors are classified into predicted errors before rasterization and actual errors after that.Accurate prediction of the errors is beneficial to dev...Vector-to-raster conversion is a process accompanied with errors.The errors are classified into predicted errors before rasterization and actual errors after that.Accurate prediction of the errors is beneficial to developing reasonable rasterization technical schemes and to making products of high quality.Analyzing and establishing a quantitative relationship between the error and its affecting factors is the key to error prediction.In this study,land cover data of China at a scale of 1:250 000 were taken as an example for analyzing the relationship between rasterization errors and the density of arc length(DA),the density of polygon(DP) and the size of grid cells(SG).Significant correlations were found between the errors and DA,DP and SG.The correlation coefficient(R2) of a model established based on samples collected in a small region(Beijing) reaches 0.95,and the value of R2 is equal to 0.91 while the model was validated with samples from the whole nation.On the other hand,the R2 of a model established based on nationwide samples reaches 0.96,and R2 is equal to 0.91 while it was validated with the samples in Beijing.These models depict well the relationships between rasterization errors and their affecting factors(DA,DP and SG).The analyzing method established in this study can be applied to effectively predicting rasterization errors in other cases as well.展开更多
基金国家自然科学基金，the Science Research Foundation of the Education Bureau of Anhui Province of China
文摘A new conservation theorem of the nonholonomic systems is studied. The conserved quantity is onlyconstructed in terms of a general Lie group of transformation vector of the dynamical equations. Firstly, we establish thedynamical equations of the nonholonomic systems and the determining equations of Lie symmetry. Next, the theore mof non-Noether conserved quantity is deduced. Finally, we give an example to illustrate the application of the result.
基金Under the auspices of Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA05050000)Special Program for Informatization of Chinese Academy of Sciences(No.INF0-115-C01-SDB3-02)
文摘Vector-to-raster conversion is a process accompanied with errors.The errors are classified into predicted errors before rasterization and actual errors after that.Accurate prediction of the errors is beneficial to developing reasonable rasterization technical schemes and to making products of high quality.Analyzing and establishing a quantitative relationship between the error and its affecting factors is the key to error prediction.In this study,land cover data of China at a scale of 1:250 000 were taken as an example for analyzing the relationship between rasterization errors and the density of arc length(DA),the density of polygon(DP) and the size of grid cells(SG).Significant correlations were found between the errors and DA,DP and SG.The correlation coefficient(R2) of a model established based on samples collected in a small region(Beijing) reaches 0.95,and the value of R2 is equal to 0.91 while the model was validated with samples from the whole nation.On the other hand,the R2 of a model established based on nationwide samples reaches 0.96,and R2 is equal to 0.91 while it was validated with the samples in Beijing.These models depict well the relationships between rasterization errors and their affecting factors(DA,DP and SG).The analyzing method established in this study can be applied to effectively predicting rasterization errors in other cases as well.
