In the context of tower measured radiation datasets.following the correction principle meeting a diagnostic equation in data quality control and in terms of a technique for model construction on data and ANN(artificia...In the context of tower measured radiation datasets.following the correction principle meeting a diagnostic equation in data quality control and in terms of a technique for model construction on data and ANN(artificial neural network)retrieval for BP correction of radiation measurements with rough errors available,a BP model is presented.Evidence suggests that the developed model works well and is superior to a convenient multivariate linear regression model,indicating its wide applications.展开更多
In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth ...In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial discretization.In addition,two stabilization terms in different forms are added for the sake of the numerical stability.We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined estimate.By regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete?^(∞)bound of the numerical solution,as a result of the rough error estimate.Subsequently,the refined error estimate is derived to obtain the optimal rate of convergence,following the established?∞bound of the numerical solution.Moreover,the energy stability is also rigorously proved with respect to a modified energy.The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.展开更多
基金This work is supported jointly by the Project of Funds for University-Level Remarkable Teachers,Education Ministry of China by the Program of 2000 South-China Sea Flux Observations.
文摘In the context of tower measured radiation datasets.following the correction principle meeting a diagnostic equation in data quality control and in terms of a technique for model construction on data and ANN(artificial neural network)retrieval for BP correction of radiation measurements with rough errors available,a BP model is presented.Evidence suggests that the developed model works well and is superior to a convenient multivariate linear regression model,indicating its wide applications.
基金supported by the Chinese Academy of Sciences(CAS)Academy of Mathematics and Systems Science(AMSS)the Hong Kong Polytechnic University(PolyU)Joint Laboratory of Applied Mathematics+4 种基金supported by the Hong Kong Research Council General Research Fund(Grant No.15300821)the Hong Kong Polytechnic University Grants(Grant Nos.1-BD8N,4-ZZMK and 1-ZVWW)supported by the Hong Kong Research Council Research Fellow Scheme(Grant No.RFS2021-5S03)General Research Fund(Grant No.15302919)supported by US National Science Foundation(Grant No.DMS-2012269)。
文摘In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial discretization.In addition,two stabilization terms in different forms are added for the sake of the numerical stability.We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined estimate.By regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete?^(∞)bound of the numerical solution,as a result of the rough error estimate.Subsequently,the refined error estimate is derived to obtain the optimal rate of convergence,following the established?∞bound of the numerical solution.Moreover,the energy stability is also rigorously proved with respect to a modified energy.The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.
