The Peetre K-modulus and the generalized. Riesz summability operators on the sphere are introduced. The convergence and boundedness of the Riesz operators are discussed. The strong and weak equivalence relationships o...The Peetre K-modulus and the generalized. Riesz summability operators on the sphere are introduced. The convergence and boundedness of the Riesz operators are discussed. The strong and weak equivalence relationships of the K-moduli and the Riesz operators are presented. The Riesz operators can serve as a realization of the corresponding K-modulus.展开更多
The evolution of solar magnetic fields is significant for understanding and predicting solar activities.And our knowledge of solar magnetic fields largely depends on the photospheric magnetic field.In this paper,based...The evolution of solar magnetic fields is significant for understanding and predicting solar activities.And our knowledge of solar magnetic fields largely depends on the photospheric magnetic field.In this paper,based on the spherical harmonic expansion of the photospheric magnetic field observed by Wilcox Solar Observatory,we analyze the time series of spherical harmonic coefficients and predict Sunspot Number as well as synoptic maps for Solar Cycle 25.We find that solar maximum years have complex short-period disturbances,and the time series of coefficient g_(7)~0 is nearly in-phase with Sunspot Number,which may be related to solar meridional circulation.Utilizing Long Short-Term Memory networks(LSTM),our prediction suggests that the maximum of Solar Cycle 25 is likely to occur in June 2024 with an error of 8 months,the peak sunspot number may be 166.9±22.6,and the next solar minimum may occur around January 2031.By incorporating Empirical Mode Decomposition,we enhance our forecast of synoptic maps truncated to Order 5,validating their relative reliability.This prediction not only addresses a gap in forecasting the global distribution of the solar magnetic field but also holds potential reference value for forthcoming solar observation plans.展开更多
The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. The...The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory of the quantum scattering characteristics of the superlattice elementary cell (like e.g.transmission resonances) are shown in order. Two examples are treated with the analyticallycomputation of the diffusion constants.展开更多
文摘The Peetre K-modulus and the generalized. Riesz summability operators on the sphere are introduced. The convergence and boundedness of the Riesz operators are discussed. The strong and weak equivalence relationships of the K-moduli and the Riesz operators are presented. The Riesz operators can serve as a realization of the corresponding K-modulus.
基金supported by the National Natural Science Foundation of China(Grant Nos.42241118,42174194,42150105,42204166,42241106,42074207)the National Key R&D Program of China(Grant Nos.2021YFA0718600,2022YFF0503800)+1 种基金the CNSA(Grant No.D050106)supported by Youth Innovation Promotion Association of the Chinese Academy of Sciences(Grant No.2021064)。
文摘The evolution of solar magnetic fields is significant for understanding and predicting solar activities.And our knowledge of solar magnetic fields largely depends on the photospheric magnetic field.In this paper,based on the spherical harmonic expansion of the photospheric magnetic field observed by Wilcox Solar Observatory,we analyze the time series of spherical harmonic coefficients and predict Sunspot Number as well as synoptic maps for Solar Cycle 25.We find that solar maximum years have complex short-period disturbances,and the time series of coefficient g_(7)~0 is nearly in-phase with Sunspot Number,which may be related to solar meridional circulation.Utilizing Long Short-Term Memory networks(LSTM),our prediction suggests that the maximum of Solar Cycle 25 is likely to occur in June 2024 with an error of 8 months,the peak sunspot number may be 166.9±22.6,and the next solar minimum may occur around January 2031.By incorporating Empirical Mode Decomposition,we enhance our forecast of synoptic maps truncated to Order 5,validating their relative reliability.This prediction not only addresses a gap in forecasting the global distribution of the solar magnetic field but also holds potential reference value for forthcoming solar observation plans.
基金Project supported by the TMR network No.ERB FMBX CT97 0157 on‘Asymptotic methods in kinetic theory'of the European Community,the LIAMA(Laboratoire d'Informatique,Automatique et Mathematiques Appliquees),the PRA(Programme de Recherches Avancees),the Aust
文摘The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory of the quantum scattering characteristics of the superlattice elementary cell (like e.g.transmission resonances) are shown in order. Two examples are treated with the analyticallycomputation of the diffusion constants.
