Oriental Beauty,a deeply fermented variety of oolong tea,is famous for its fruity aroma and sweet taste.A targeted and untargeted metabolomics was used to comprehensively analyze the dynamic changes of taste and aroma...Oriental Beauty,a deeply fermented variety of oolong tea,is famous for its fruity aroma and sweet taste.A targeted and untargeted metabolomics was used to comprehensively analyze the dynamic changes of taste and aroma metabolites during the processing stage.During the enzyme reaction stage,the catechin components were oxidized and degraded into theaflavins and oolongtheanins.The total abundance of aroma increased from 259.24 to 564.52μg/L,and mainly monoterpenoids formed.During the nonenzymatic reaction stage,the total abundance of aroma decreased from 564.52 to 274.74μg/L,and linalool was thermally converted to hotrienol.In this study,metabolomics changes were conducive to better control of tea quality.展开更多
After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like structure.The theoretical analysis gives sufficient conditions ...After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like structure.The theoretical analysis gives sufficient conditions to guarantee the positive-definite property of the discretized matrix.Moreover,we develop a class of positive-definite operator splitting iteration methods for the numerical solution of fractional diffusion equations,which is unconditionally convergent for any positive constant.Meanwhile,the iteration methods introduce a new preconditioner for Krylov subspace methods.Numerical experiments verify the convergence of the positive-definite operator splitting iteration methods and show the efficiency of the proposed preconditioner,compared with the existing approaches.展开更多
A shift splitting concept is introduced and, correspondingly, a shift-splitting iteration scheme and a shift-splitting preconditioner are presented, for solving the large sparse system of linear equations of which the...A shift splitting concept is introduced and, correspondingly, a shift-splitting iteration scheme and a shift-splitting preconditioner are presented, for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned non-Hermitian positive definite matrix. The convergence property of the shift-splitting iteration method and the eigenvalue distribution of the shift-splitting preconditioned matrix are discussed in depth, and the best possible choice of the shift is investigated in detail. Numerical computations show that the shift-splitting preconditioner can induce accurate, robust and effective preconditioned Krylov subspace iteration methods for solving the large sparse non-Hermitian positive definite systems of linear equations.展开更多
In this paper,we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations.Theoretical analysis shows that with the deflation techni...In this paper,we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations.Theoretical analysis shows that with the deflation technique,the new residual of shifted restarted FOM is still collinear with each other.Hence,the new approach can solve the shifted systems simultaneously based on the same Krylov subspace.Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.展开更多
We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems.Applying the preconditioning technique we also construct the precond...We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems.Applying the preconditioning technique we also construct the preconditioned version of the proposed method.Theoretical analysis shows that the proposed method is unconditionally convergent even when the real part and the imaginary part of the coefficient matrix are non-symmetric.Meanwhile,when the real part and the imaginary part of the coefficient matrix are symmetric positive definite,we prove that the preconditioned variant modified skew-normal splitting iterative method will also unconditionally converge.Numerical experiments are presented to illustrate the efficiency of the proposed method and show better performance of it when compared with some other methods.展开更多
基金the Natural Science Foundation of Zhejiang(LQ20C160009)the National Natural Science Foundation of China(31872709)+3 种基金the Key Research and Development Program of Zhejiang(2022C02033)the Natural Science Foundation of Zhejiang(LQ20C160009)the Natural Science Foundation of Fujian Province(2020J01544)the Innovation Project for Chinese Academy of Agricultural Sciences.
文摘Oriental Beauty,a deeply fermented variety of oolong tea,is famous for its fruity aroma and sweet taste.A targeted and untargeted metabolomics was used to comprehensively analyze the dynamic changes of taste and aroma metabolites during the processing stage.During the enzyme reaction stage,the catechin components were oxidized and degraded into theaflavins and oolongtheanins.The total abundance of aroma increased from 259.24 to 564.52μg/L,and mainly monoterpenoids formed.During the nonenzymatic reaction stage,the total abundance of aroma decreased from 564.52 to 274.74μg/L,and linalool was thermally converted to hotrienol.In this study,metabolomics changes were conducive to better control of tea quality.
基金This work was supported by the National Natural Science Foundation of China(No.11971354)The author Yi-Shu Du acknowledges the financial support from the China Scholarship Council(File No.201906260146).
文摘After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like structure.The theoretical analysis gives sufficient conditions to guarantee the positive-definite property of the discretized matrix.Moreover,we develop a class of positive-definite operator splitting iteration methods for the numerical solution of fractional diffusion equations,which is unconditionally convergent for any positive constant.Meanwhile,the iteration methods introduce a new preconditioner for Krylov subspace methods.Numerical experiments verify the convergence of the positive-definite operator splitting iteration methods and show the efficiency of the proposed preconditioner,compared with the existing approaches.
基金Research supported by The China NNSF 0utstanding Young Scientist Foundation (No.10525102), The National Natural Science Foundation (No.10471146), and The National Basic Research Program (No.2005CB321702), P.R. China.
文摘A shift splitting concept is introduced and, correspondingly, a shift-splitting iteration scheme and a shift-splitting preconditioner are presented, for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned non-Hermitian positive definite matrix. The convergence property of the shift-splitting iteration method and the eigenvalue distribution of the shift-splitting preconditioned matrix are discussed in depth, and the best possible choice of the shift is investigated in detail. Numerical computations show that the shift-splitting preconditioner can induce accurate, robust and effective preconditioned Krylov subspace iteration methods for solving the large sparse non-Hermitian positive definite systems of linear equations.
文摘In this paper,we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations.Theoretical analysis shows that with the deflation technique,the new residual of shifted restarted FOM is still collinear with each other.Hence,the new approach can solve the shifted systems simultaneously based on the same Krylov subspace.Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.
基金R.Li is funded by the China Scholarship Council(File No.201808330668)the National Natural Science Foundation of China(Grant No.11701221)+1 种基金J.-F.Yin is funded by the National Natural Science Foundation of China(Grant No.11971354)Z.Li is partially supported by a Simon’s grant 63372.
文摘We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems.Applying the preconditioning technique we also construct the preconditioned version of the proposed method.Theoretical analysis shows that the proposed method is unconditionally convergent even when the real part and the imaginary part of the coefficient matrix are non-symmetric.Meanwhile,when the real part and the imaginary part of the coefficient matrix are symmetric positive definite,we prove that the preconditioned variant modified skew-normal splitting iterative method will also unconditionally converge.Numerical experiments are presented to illustrate the efficiency of the proposed method and show better performance of it when compared with some other methods.