A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation...A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given. Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period(frequency) of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.展开更多
For the Z-R relationship in radar-based rainfall estimation, the distribution of corresponding R values for a given Z value (or the corresponding Z value for a given R value) may be highly skewed. However, the traditi...For the Z-R relationship in radar-based rainfall estimation, the distribution of corresponding R values for a given Z value (or the corresponding Z value for a given R value) may be highly skewed. However, the traditional power-law model is physically deduced and fitted under the normal-distribution presumption of radar wave echoes associated with a rain rate value, and it may not be very appropriate. Considering this problem, the authors devised several generalized linear models with different forms and distribution presumptions to represent the Z-R relationship. Radar-reflectivity scans observed by a CINRAD/SC Doppler radar and 5-minute rainfall accumulation recorded by 10 ground gauges were used to fit these models. All data used in this study were collected during some large rainfalls of the period from 2005 to 2007. The radar and all gauges were installed in the catchment of the Yishu River, a branch of the Huaihe River in China. Three models based on normal distribution and a dBZ presumption of gamma distribution were fitted using maximum-likelihood techniques, which were resolved by genetic algorithms. Comparisons of estimated maximized likelihoods based on assumptions of gamma and normal distribution showed that all generalized linear models (GLMs) of presumed gamma distribution were better fitted than GLMs based on normal distribution. In a comparison of maximum-likelihood, the differences between these three models were small. Three error statistics were used to assess the agreement between radar estimated rainfall and gauge rainfall: relative bias (B), root mean square error (RMSE), and correlation coefficient (r). The results showed that no one model was excellent in all criteria. On the whole, the GLM-based models gave smaller relative bias than the traditional power-law model. It is suggested that validations conducted in many previous works should have been made against a specific criterion but overlooked others.展开更多
In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovest...In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.展开更多
For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is as...For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.展开更多
This paper analyzes whether the slowdown of China＇s trade in 2012-2015 was cyclical or structural, and further discusses the effects of structural factors, including trade structure, trade protectionism and global va...This paper analyzes whether the slowdown of China＇s trade in 2012-2015 was cyclical or structural, and further discusses the effects of structural factors, including trade structure, trade protectionism and global value chain participation, Using the national panel data from 2000 to 2015, based on the error correction model and import-intensity- adjusted demand model, our results show that the slowdown of China＇s trade growth in 2012-2015 was mainly a result of cyclical factors. Using 2000-2015 industry- level data, we also find that the structure of trade goods had an inhibitory effect on the import slowdown but a positive effect on the export slowdown. Trade protectionism had an adverse effect on the trade growth slowdown. The global value chain participation marginally contributed to the slowdown in trade growth. Therefore, the impacts of structural factors on trade growth slowdown cannot be ignored, and related policies should receive greater attention from policy-makers.展开更多
基金Funded by the National Natural Science Foundation of China (No. 50375113).
文摘A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given. Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period(frequency) of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.
基金financially supported by the National Natural Science Foundation of China (Grant No. 40971024)the National Basic Research Program of China (Grant No. 2006CB400502)the Special Meteorology Project (GYHY(QX)2007-6-1)
文摘For the Z-R relationship in radar-based rainfall estimation, the distribution of corresponding R values for a given Z value (or the corresponding Z value for a given R value) may be highly skewed. However, the traditional power-law model is physically deduced and fitted under the normal-distribution presumption of radar wave echoes associated with a rain rate value, and it may not be very appropriate. Considering this problem, the authors devised several generalized linear models with different forms and distribution presumptions to represent the Z-R relationship. Radar-reflectivity scans observed by a CINRAD/SC Doppler radar and 5-minute rainfall accumulation recorded by 10 ground gauges were used to fit these models. All data used in this study were collected during some large rainfalls of the period from 2005 to 2007. The radar and all gauges were installed in the catchment of the Yishu River, a branch of the Huaihe River in China. Three models based on normal distribution and a dBZ presumption of gamma distribution were fitted using maximum-likelihood techniques, which were resolved by genetic algorithms. Comparisons of estimated maximized likelihoods based on assumptions of gamma and normal distribution showed that all generalized linear models (GLMs) of presumed gamma distribution were better fitted than GLMs based on normal distribution. In a comparison of maximum-likelihood, the differences between these three models were small. Three error statistics were used to assess the agreement between radar estimated rainfall and gauge rainfall: relative bias (B), root mean square error (RMSE), and correlation coefficient (r). The results showed that no one model was excellent in all criteria. On the whole, the GLM-based models gave smaller relative bias than the traditional power-law model. It is suggested that validations conducted in many previous works should have been made against a specific criterion but overlooked others.
基金Supported by China Mathematics Tian Yuan Youth Foundation (10226024) and China Postdoctoral Science Foundation.
文摘In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.
基金Project supported by the National Natural Science Foundation of China.
文摘For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.
文摘This paper analyzes whether the slowdown of China＇s trade in 2012-2015 was cyclical or structural, and further discusses the effects of structural factors, including trade structure, trade protectionism and global value chain participation, Using the national panel data from 2000 to 2015, based on the error correction model and import-intensity- adjusted demand model, our results show that the slowdown of China＇s trade growth in 2012-2015 was mainly a result of cyclical factors. Using 2000-2015 industry- level data, we also find that the structure of trade goods had an inhibitory effect on the import slowdown but a positive effect on the export slowdown. Trade protectionism had an adverse effect on the trade growth slowdown. The global value chain participation marginally contributed to the slowdown in trade growth. Therefore, the impacts of structural factors on trade growth slowdown cannot be ignored, and related policies should receive greater attention from policy-makers.
