In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the con...This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained.展开更多
The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for s...The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.展开更多
基金Sponsored by the National NSFC under grant No.19771063
文摘In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
文摘This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained.
文摘The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.
