In the present paper,we generalize some classical results in convergence and integrability for trigonometric series with varying coefficients(may change signs),by introducing a new ultimate condition upon coefficient ...In the present paper,we generalize some classical results in convergence and integrability for trigonometric series with varying coefficients(may change signs),by introducing a new ultimate condition upon coefficient sequences.This is a comprehensive systematic work on the topic.展开更多
In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fou...In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting.In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.展开更多
An observation localization scheme is introduced into an ensemble-based three-dimensional variational （3DVar） assimilation method based on the singular value decomposition technique （SVD-En3DVar） to im- prove assi...An observation localization scheme is introduced into an ensemble-based three-dimensional variational （3DVar） assimilation method based on the singular value decomposition technique （SVD-En3DVar） to im- prove assimilation skill. A point-by-point analysis technique is adopted in which the weight of each obser- vation decreases with increasing distance between the analysis point and the observation point. A set of numerical experiments, in which simulated Doppler radar data are assimilated into the Weather Research and Forecasting （WRF） model, is designed to test the scheme. The results are compared with those ob- tained using the original global and local patch schemes in SVD-En3DVar, neither of which includes this type of observation localization. The observation localization scheme not only eliminates spurious analysis increments in areas of missing data, but also avoids the discontinuous analysis fields that arise from the local patch scheme. The new scheme provides better analysis fields and a more reasonable short-range rainfall forecast than the original schemes. Additional forecast experiments that assimilate real data from i0 radars indicate that the short-term precipitation forecast skill can be improved by assimilating radar data and the observation localization scheme provides a better forecast than the other two schemes.展开更多
文摘In the present paper,we generalize some classical results in convergence and integrability for trigonometric series with varying coefficients(may change signs),by introducing a new ultimate condition upon coefficient sequences.This is a comprehensive systematic work on the topic.
基金Supported by the European Research Council Advanced Grant(Grant No.267055)
文摘In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting.In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.
基金Supported by the Open Project Fund of the State Key Laboratory of Severe Weather of Chinese Academy of Meteorological Sciences, National Natural Science Foundation of China (40875063 and 41275102)Fundamental Research Fund for Central Universities of China (lzujbky-2010-9)
文摘An observation localization scheme is introduced into an ensemble-based three-dimensional variational （3DVar） assimilation method based on the singular value decomposition technique （SVD-En3DVar） to im- prove assimilation skill. A point-by-point analysis technique is adopted in which the weight of each obser- vation decreases with increasing distance between the analysis point and the observation point. A set of numerical experiments, in which simulated Doppler radar data are assimilated into the Weather Research and Forecasting （WRF） model, is designed to test the scheme. The results are compared with those ob- tained using the original global and local patch schemes in SVD-En3DVar, neither of which includes this type of observation localization. The observation localization scheme not only eliminates spurious analysis increments in areas of missing data, but also avoids the discontinuous analysis fields that arise from the local patch scheme. The new scheme provides better analysis fields and a more reasonable short-range rainfall forecast than the original schemes. Additional forecast experiments that assimilate real data from i0 radars indicate that the short-term precipitation forecast skill can be improved by assimilating radar data and the observation localization scheme provides a better forecast than the other two schemes.
