We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padr...We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2π-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures.展开更多
The spatial resolution of source data, the impact factor selection on the grid model and the size of the grid might be the main limitations of global land datasets applied on a regional scale. Quantitative studies of ...The spatial resolution of source data, the impact factor selection on the grid model and the size of the grid might be the main limitations of global land datasets applied on a regional scale. Quantitative studies of the impacts of rasterization on data accuracy can help improve data resolution and regional data accuracy. Through a case study of cropland data for Jiangsu and Anhui provinces in China, this research compared data accuracy with different data sources, rasterization methods, and grid sizes. First, we investigated the influence of different data sources on gridded data accuracy. The temporal trends of the History Database of the Global Environment （HYDE）, Chinese Historical Cropland Data （CHCD）, and Suwan Cropland Data （SWCD） datasets were more similar. However, differ- ent spatial resolutions of cropland source data in the CHCD and SWCD datasets revealed an average difference of 16.61% when provin- cial and county data were downscaled to a 10 x 10 km2 grid for comparison. Second, the influence of selection of the potential arable land reclamation rate and temperature factors, as well as the different processing methods for water factors, on accuracy of gridded datasets was investigated. Applying the reclamation rate of potential cropland to grid-processing increased the diversity of spatial distri- bution but resulted in only a slightly greater standard deviation, which increased by 4.05. Temperature factors only produced relative disparities within 10% and absolute disparities within 2 km2 over more than 90% of grid cells. For the different processing methods for water factors, the HYDE dataset distributed 70% more cropland in grid cells along riverbanks, at the abandoned Yellow River Estuary （located in Binhai County, Yancheng City, Jiangsu Province）, and around Hongze Lake, than did the SWCD dataset. Finally, we ex- plored the influence of different grid sizes. Absolute accuracy disparities by unit area for the year 2000 were within 0.1 km2 at a 1 km2 grid size, a 25% improvement over the 10 km2 grid size. Compared to the outcomes of other similar studies, this demonstrates that some model hypotheses and grid-processing methods in international land datasets are truly incongruent with actual land reclamation proc- esses, at least in China. Combining the model-based methods with historical empirical data may be a better way to improve the accuracy of regional scale datasets. Exploring methods for the above aspects improved the accuracy of historical crop/and gridded datasets for finer regional scales.展开更多
文摘We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2π-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures.
基金Under the auspices of National Natural Science Foundation of China(No.41471156,41501207)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDA05080102)Special Fund of National Science and Technology of China(No.2014FY130500)
文摘The spatial resolution of source data, the impact factor selection on the grid model and the size of the grid might be the main limitations of global land datasets applied on a regional scale. Quantitative studies of the impacts of rasterization on data accuracy can help improve data resolution and regional data accuracy. Through a case study of cropland data for Jiangsu and Anhui provinces in China, this research compared data accuracy with different data sources, rasterization methods, and grid sizes. First, we investigated the influence of different data sources on gridded data accuracy. The temporal trends of the History Database of the Global Environment （HYDE）, Chinese Historical Cropland Data （CHCD）, and Suwan Cropland Data （SWCD） datasets were more similar. However, differ- ent spatial resolutions of cropland source data in the CHCD and SWCD datasets revealed an average difference of 16.61% when provin- cial and county data were downscaled to a 10 x 10 km2 grid for comparison. Second, the influence of selection of the potential arable land reclamation rate and temperature factors, as well as the different processing methods for water factors, on accuracy of gridded datasets was investigated. Applying the reclamation rate of potential cropland to grid-processing increased the diversity of spatial distri- bution but resulted in only a slightly greater standard deviation, which increased by 4.05. Temperature factors only produced relative disparities within 10% and absolute disparities within 2 km2 over more than 90% of grid cells. For the different processing methods for water factors, the HYDE dataset distributed 70% more cropland in grid cells along riverbanks, at the abandoned Yellow River Estuary （located in Binhai County, Yancheng City, Jiangsu Province）, and around Hongze Lake, than did the SWCD dataset. Finally, we ex- plored the influence of different grid sizes. Absolute accuracy disparities by unit area for the year 2000 were within 0.1 km2 at a 1 km2 grid size, a 25% improvement over the 10 km2 grid size. Compared to the outcomes of other similar studies, this demonstrates that some model hypotheses and grid-processing methods in international land datasets are truly incongruent with actual land reclamation proc- esses, at least in China. Combining the model-based methods with historical empirical data may be a better way to improve the accuracy of regional scale datasets. Exploring methods for the above aspects improved the accuracy of historical crop/and gridded datasets for finer regional scales.
