Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the ...Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.展开更多
Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-compos...Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.展开更多
It is proved that the Tsirelson’s space,which is not a strong subprojective space,is a local strong subprojective space.It is shown that every Riesz operator on a local strong subprojective spaoe,especially on the Ts...It is proved that the Tsirelson’s space,which is not a strong subprojective space,is a local strong subprojective space.It is shown that every Riesz operator on a local strong subprojective spaoe,especially on the Tsirelson’s space,has West decomposition.展开更多
Compared with discrete- time fuzzy supermartingales, the structure and the properties of trajectories for continuous-time fuzzy supermartingales are more complex. This paper focuses on Riesz decomposition for continuo...Compared with discrete- time fuzzy supermartingales, the structure and the properties of trajectories for continuous-time fuzzy supermartingales are more complex. This paper focuses on Riesz decomposition for continuous-time fuzzy supermartingales. The concepts of two types of Riesz decomposition (Riesz decomposition and level Riesz decomposition) are given and some necessary and sttfficient conditions of that a continuous time fuzzy supermartingale has Riesz decomposition are discussed in detail.展开更多
The paper proves the convergence theorem of set-valued Superpramart in the sense of weak convergence under the X<sup>*</sup> separable condition. Using support function and results about real-valued Superp...The paper proves the convergence theorem of set-valued Superpramart in the sense of weak convergence under the X<sup>*</sup> separable condition. Using support function and results about real-valued Superpramart, we give the Riesz decomposition of set-valued Superpramart.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12161030)by the Hainan Provincial Natural Science Foundation of China(Grant No.121RC537).
文摘Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.
文摘Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.
基金Project supported by the Science Foundation of Fujian Province.
文摘It is proved that the Tsirelson’s space,which is not a strong subprojective space,is a local strong subprojective space.It is shown that every Riesz operator on a local strong subprojective spaoe,especially on the Tsirelson’s space,has West decomposition.
文摘Compared with discrete- time fuzzy supermartingales, the structure and the properties of trajectories for continuous-time fuzzy supermartingales are more complex. This paper focuses on Riesz decomposition for continuous-time fuzzy supermartingales. The concepts of two types of Riesz decomposition (Riesz decomposition and level Riesz decomposition) are given and some necessary and sttfficient conditions of that a continuous time fuzzy supermartingale has Riesz decomposition are discussed in detail.
文摘The paper proves the convergence theorem of set-valued Superpramart in the sense of weak convergence under the X<sup>*</sup> separable condition. Using support function and results about real-valued Superpramart, we give the Riesz decomposition of set-valued Superpramart.
