Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach mod...Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.展开更多
本文是介绍解决资源开发,运输决策等社会现象的问题中归纳出来的“调配问题”及经济数学的一组公式sum from i=1 to n(S_iT_a_i)≥sum from i=1 to n(S_iT_(n-i+1));sum from i=1 to n(S_iT_i)≥sum from i=1 to n(S_iT_a_i)
In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of...In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging. The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07% higher than the one of the space-time ordinary Kriging. Therefore, a space-time CoKriging interpolation with air humidity as a covariate improves the interpolation accuracy.展开更多
Observations of atmospheric carbon dioxide (CO2 ) from satellites offer new data sources to understand global carbon cycling. The correlation structure of satellite-observed CO2 can be analyzed and modeled by geostati...Observations of atmospheric carbon dioxide (CO2 ) from satellites offer new data sources to understand global carbon cycling. The correlation structure of satellite-observed CO2 can be analyzed and modeled by geostatistical methods, and CO2 values at unsampled locations can be predicted with a correlation model. Conventional geostatistical analysis only investigates the spatial correlation of CO2 , and does not consider temporal variation in the satellite-observed CO2 data. In this paper, a spatiotemporal geostatistical method that incorporates temporal variability is implemented and assessed for analyzing the spatiotemporal correlation structure and prediction of monthly CO2 in China. The spatiotemporal correlation is estimated and modeled by a product-sum variogram model with a global nugget component. The variogram result indicates a significant degree of temporal correlation within satellite-observed CO2 data sets in China. Prediction of monthly CO2 using the spatiotemporal variogram model and spacetime kriging procedure is implemented. The prediction is compared with a spatial-only geostatistical prediction approach using a cross-validation technique. The spatiotemporal approach gives better results, with higher correlation coefficient (r2 ), and less mean absolute prediction error and root mean square error. Moreover, the monthly mapping result generated from the spatiotemporal approach has less prediction uncertainty and more detailed spatial variation of CO2 than those from the spatial-only approach.展开更多
基金supported by the National Natural Science Foundation of China (10671013,60972089,11171022)
文摘Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.
文摘本文是介绍解决资源开发,运输决策等社会现象的问题中归纳出来的“调配问题”及经济数学的一组公式sum from i=1 to n(S_iT_a_i)≥sum from i=1 to n(S_iT_(n-i+1));sum from i=1 to n(S_iT_i)≥sum from i=1 to n(S_iT_a_i)
基金Project(17D02)supported by the Open Fund of State Laboratory of Information Engineering in Surveying,Mapping and Remote Sensing,Wuhan University,ChinaProject supported by the State Key Laboratory of Satellite Navigation System and Equipment Technology,China
文摘In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging. The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07% higher than the one of the space-time ordinary Kriging. Therefore, a space-time CoKriging interpolation with air humidity as a covariate improves the interpolation accuracy.
基金supported by the National Natural Science Foundation of China (41071234)the Strategic Priority Research Program-Climate Change: Carbon Budget and Relevant Issues of the Chinese Academy of Sciences (XDA05040401)
文摘Observations of atmospheric carbon dioxide (CO2 ) from satellites offer new data sources to understand global carbon cycling. The correlation structure of satellite-observed CO2 can be analyzed and modeled by geostatistical methods, and CO2 values at unsampled locations can be predicted with a correlation model. Conventional geostatistical analysis only investigates the spatial correlation of CO2 , and does not consider temporal variation in the satellite-observed CO2 data. In this paper, a spatiotemporal geostatistical method that incorporates temporal variability is implemented and assessed for analyzing the spatiotemporal correlation structure and prediction of monthly CO2 in China. The spatiotemporal correlation is estimated and modeled by a product-sum variogram model with a global nugget component. The variogram result indicates a significant degree of temporal correlation within satellite-observed CO2 data sets in China. Prediction of monthly CO2 using the spatiotemporal variogram model and spacetime kriging procedure is implemented. The prediction is compared with a spatial-only geostatistical prediction approach using a cross-validation technique. The spatiotemporal approach gives better results, with higher correlation coefficient (r2 ), and less mean absolute prediction error and root mean square error. Moreover, the monthly mapping result generated from the spatiotemporal approach has less prediction uncertainty and more detailed spatial variation of CO2 than those from the spatial-only approach.
