The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and it...The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and its extensions （MF^＊ and ME^＊ ） are not strong complete; and generally, ff a consistent formal system is not strong complete, then any consistent extensions of this forreal system are not strong complete either.展开更多
In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the c...In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].展开更多
In this paper, it is shown that if a local convex space is weakly complete, then it is complete. Moreover, it shows that a local convex space with the axiom （To） is weakly complete（or weakly＊ complete） if and onl...In this paper, it is shown that if a local convex space is weakly complete, then it is complete. Moreover, it shows that a local convex space with the axiom （To） is weakly complete（or weakly＊ complete） if and only if it is finite dimensional.展开更多
In the paper we introduce the notions of the separation factor ~ and give a representive of metric projection on an n-codimension subspace （or an affine set） under certain conditions in Banach space. Further, we obt...In the paper we introduce the notions of the separation factor ~ and give a representive of metric projection on an n-codimension subspace （or an affine set） under certain conditions in Banach space. Further, we obtain the distance formula from any point x to a finite n-codimension subspace. Results extend and improve the corresponding results in Hilbert space.展开更多
By using partial order method. some existing theorems of solutions for two-point bouniary value problem of second order ordinary differenlial equations in Banach spaces are given.
In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the prope...In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained.展开更多
文摘The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and its extensions （MF^＊ and ME^＊ ） are not strong complete; and generally, ff a consistent formal system is not strong complete, then any consistent extensions of this forreal system are not strong complete either.
文摘In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].
基金Supported by the Scientific Research Fund of Colleges of Inner Mongolia(NJ09180)
文摘In this paper, it is shown that if a local convex space is weakly complete, then it is complete. Moreover, it shows that a local convex space with the axiom （To） is weakly complete（or weakly＊ complete） if and only if it is finite dimensional.
文摘In the paper we introduce the notions of the separation factor ~ and give a representive of metric projection on an n-codimension subspace （or an affine set） under certain conditions in Banach space. Further, we obtain the distance formula from any point x to a finite n-codimension subspace. Results extend and improve the corresponding results in Hilbert space.
文摘By using partial order method. some existing theorems of solutions for two-point bouniary value problem of second order ordinary differenlial equations in Banach spaces are given.
基金Supported by Specific Academic Discipline Project of Shanghai Municipal Education Commission (Grant No. A-3500-11-10)
文摘In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained.
