In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting p...In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.展开更多
模拟投料环境,探索温度、时间、氧化剂NaClO、弱碱NaHCO_(3)、弱酸NaHSO_(3)对DTD分解情况的影响。结果表明:温度低于15℃时DTD分解缓慢,高于15℃时DTD分解迅速,且随时间的延长分解加剧。氧化剂NaClO会造成产物的迅速分解,4 h DTD分解剩...模拟投料环境,探索温度、时间、氧化剂NaClO、弱碱NaHCO_(3)、弱酸NaHSO_(3)对DTD分解情况的影响。结果表明:温度低于15℃时DTD分解缓慢,高于15℃时DTD分解迅速,且随时间的延长分解加剧。氧化剂NaClO会造成产物的迅速分解,4 h DTD分解剩余24.53%。NaHCO_(3)、NaHSO_(3)的加入对DTD的分解影响较小。为避免长时间对收率的影响,合成结束后需迅速进行后处理,对后期工业化生产具有重要的指导意义。展开更多
It is discussed in this paper the spaces with σ-point-discrete N_0-weak bases. The main results are： （1） A space X has a σ-compact-finite N_0-weak base if and only if X is a k-space with a σ-point-discrete N_0-w...It is discussed in this paper the spaces with σ-point-discrete N_0-weak bases. The main results are： （1） A space X has a σ-compact-finite N_0-weak base if and only if X is a k-space with a σ-point-discrete N_0-weak base; （2） Under （CH）, every separable space with a σ-point-discrete N_0-weak base has a countable N_0-weak base.展开更多
The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function...The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.展开更多
In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
基金supported by the National Natural Science Foundation of China(12271344)the Natural Science Foundation of Shanghai(23ZR1425800)。
文摘In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.
文摘模拟投料环境,探索温度、时间、氧化剂NaClO、弱碱NaHCO_(3)、弱酸NaHSO_(3)对DTD分解情况的影响。结果表明:温度低于15℃时DTD分解缓慢,高于15℃时DTD分解迅速,且随时间的延长分解加剧。氧化剂NaClO会造成产物的迅速分解,4 h DTD分解剩余24.53%。NaHCO_(3)、NaHSO_(3)的加入对DTD的分解影响较小。为避免长时间对收率的影响,合成结束后需迅速进行后处理,对后期工业化生产具有重要的指导意义。
基金Supported by the National Natural Science Foundation of China (10971185, 11171162, 11201053)China Postdoctoral Science Foundation funded project (20090461093, 201003571)+1 种基金Jiangsu Planned Projects for Teachers Overseas Research FundsTaizhou Teachers College Research Funds
文摘It is discussed in this paper the spaces with σ-point-discrete N_0-weak bases. The main results are： （1） A space X has a σ-compact-finite N_0-weak base if and only if X is a k-space with a σ-point-discrete N_0-weak base; （2） Under （CH）, every separable space with a σ-point-discrete N_0-weak base has a countable N_0-weak base.
基金supported by the National Natural Science Foundation of China(11471043,11671271)the Beijing Natural Science Foundation(1172004)
文摘The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
