This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers i...This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.展开更多
The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong c...The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).展开更多
A new class of reflected backward stochastic differential equations (RBSDEs) driven by Teugels martingales associated with Lévy process and Countable Brownian Motions are investigated. Via approximation, the exis...A new class of reflected backward stochastic differential equations (RBSDEs) driven by Teugels martingales associated with Lévy process and Countable Brownian Motions are investigated. Via approximation, the existence and uniqueness of solution to this kind of RBSDEs are obtained.展开更多
In the study of Poincaré inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space Rn, while the method in this paper is based on a countable set E and accord...In the study of Poincaré inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space Rn, while the method in this paper is based on a countable set E and accordingly the accurate expressions of Poincaré inequalities JB(=(f-μ(f))nJB)=_B≤cD(f, f) is presented to expand the research and application scope. As to inequalities for Ω={DK(x:0DK)≤x_i≤a, i=1,2,…,n}, the existing studies was usually made for n=2, but such an inequality was not the best. Therefore, the different values of n is discussed in this paper, and accordingly the accurate expressions of Poincaré inequalities is presented.展开更多
The concept of local s-countablity is introduced, and the relations between locally s-countable collections and star-countable collections are discussed.
在这份报纸，有一个局部地可计算的 sn 网络的空格被讨论。它空间与它是的局部地可计算的 sn 网络见被看那有局部地可计算的 k 网络的一个 snf 可计算的空格。作为它的应用程序，几乎打开和关上的 mappings (或 finite-to-one 并且印射...在这份报纸，有一个局部地可计算的 sn 网络的空格被讨论。它空间与它是的局部地可计算的 sn 网络见被看那有局部地可计算的 k 网络的一个 snf 可计算的空格。作为它的应用程序，几乎打开和关上的 mappings (或 finite-to-one 并且印射关上) 与一个局部地可计算的 sn 网络在空格保存局部地可计算的 sn 网络，和一条完美的 preimage 定理被建立。展开更多
The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In...The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true.展开更多
文摘This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.
文摘The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).
文摘A new class of reflected backward stochastic differential equations (RBSDEs) driven by Teugels martingales associated with Lévy process and Countable Brownian Motions are investigated. Via approximation, the existence and uniqueness of solution to this kind of RBSDEs are obtained.
文摘In the study of Poincaré inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space Rn, while the method in this paper is based on a countable set E and accordingly the accurate expressions of Poincaré inequalities JB(=(f-μ(f))nJB)=_B≤cD(f, f) is presented to expand the research and application scope. As to inequalities for Ω={DK(x:0DK)≤x_i≤a, i=1,2,…,n}, the existing studies was usually made for n=2, but such an inequality was not the best. Therefore, the different values of n is discussed in this paper, and accordingly the accurate expressions of Poincaré inequalities is presented.
基金Foundation item:The NSF(10171043,10271026)of China
文摘The concept of local s-countablity is introduced, and the relations between locally s-countable collections and star-countable collections are discussed.
基金Supported by the NNSF of China(1097118510971186)Supported by NSF of Fujian Province(2008F5066)
文摘在这份报纸，有一个局部地可计算的 sn 网络的空格被讨论。它空间与它是的局部地可计算的 sn 网络见被看那有局部地可计算的 k 网络的一个 snf 可计算的空格。作为它的应用程序，几乎打开和关上的 mappings (或 finite-to-one 并且印射关上) 与一个局部地可计算的 sn 网络在空格保存局部地可计算的 sn 网络，和一条完美的 preimage 定理被建立。
基金Supported by Research Fund of Kumoh National Institute of Technology(M1100)
文摘The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true.
