Banach空间中寻求(α,β)-适度混合集值映像吸引点的一般迭代格式

引入（α，β）-适度混合集值映像与条件I^*的概念，提出了用于寻求（α，β）-适度混合集值映像吸引点的一般迭代法.在一致凸Banach空间中，利用条件I^*与半紧性质，建立了所提（α，β）-适度混合集值映像的迭代格式的强收敛性.结论改进与修正了之前文献中已发布的相应结果.     

‐Theory for Schrödinger systems

In this article, we study for the ‐realization of the vector‐valued Schrödinger operator . Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the ‐realization of , defined on the intersection of the natural domains of the differential and multiplication operators which form , generates a strongly continuous contraction semigroup on . We also study additional properties of the semigroup such as extension to L¹, positivity, ultracontractivity and prove that the generator has compact resolvent.     

Corrigendum to: on the inheritance of the strongly π-extending property

In this corrigendum, we provide correct versions of Theorem 2.8 and Corollary 3.2, retract two consequences of the previous form of the Theorem 2.8. To this end, the main results of the article remain after the aforementioned changes.     

Probe‐assisted spin manipulation in one‐dimensional quantum dots

We study a spin structure that arises in a one‐dimensional quantum dot with zero total spin under the action of a charged tip of a scanning probe microscope in the presence of a weak magnetic field. The evolution of spin structure with changing the probe position is traced to show that the movable probe can be an effective tool to manipulate the spin. The spin structures are formed when the probe is located in certain regions along the dot due to Coulomb interaction of electrons as they are redistributed between the two sections in which the quantum dot is divided by the potential barrier created by the probe. There are two main states: spin‐polarized and non‐polarized ones. The transition between them is accompanied by a spin precession governed by the Rashba spin–orbit interaction induced by the electric field of the probe. In the transition region the spin density changes strongly while charge distribution remains nearly unchanged. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Kinetics and thermodynamics of rebaudioside A adsorption on a strongly acidic cation exchange resin

To explain the mechanism underlying the adsorption of stevia's polar component rebaudioside A in hydrophilic interaction liquid chromatography mode, the characteristics of rebaudioside A adsorption on various resins in an organic‐solvent‐rich system were studied. Among the tested resins, the strongly acidic cation resin FPC11 showed the best adsorption behavior for rebaudioside A. The factors affecting the adsorption kinetics of the resin for rebaudioside A are discussed. The results showed that the pseudo‐second‐order reaction model and intra‐particle diffusion model best described the adsorption kinetics of rebaudioside A on the resin. The adsorption rate was controlled by physical sorption, mainly via electron sharing or electron transfer between the adsorbent and the adsorbate. The adsorption process with multiple stages involved weak initial adsorption behavior. Thermodynamic studies showed that the adsorption of rebaudioside A on the resin was not an ideal monolayer adsorption, but mutual adsorption effects between the adsorbates. The adsorption was a spontaneous, entropy‐increasing endothermic process. The synergistic effect of hydrogen bonding and ion–dipole was a possible driving force.     

一类随机环境中的随机游动

研究了在环境平稳遍历时,右半直线上可逗留的随机环境中的随机游动的常返性和非常返性,给出非常返、正常返、零常返的充要条件,并讨论了极限性质.作为推论,给出P独立同分布时的相应结论.     

强亚正交矩阵及其性质

推广正交矩阵得到了强亚正交矩阵的概念并讨论了它的性质.     

d-界距离正则图中一类格的特征多项式

设Г是一个直径d≥3的d-界距离正则图,x∈V(Г),P(x)是Г中包含x的所有强闭包子图的集合,并且P(x,i)是P(x)中所有直径为i的强闭包子图的集合.设￡(x,i)是P(x,i)中元素的交生成的集合.按反包含关系规定￡(x,i)的偏序,￡(x,i)记为￡R(x,i).利用M(o)bius反演公式计算了￡R((x,i)上的特征多项式X(PR(x),t).     

Banach空间中Ishikawa迭代过程的收敛定理

用新的方法和技巧研究了Banach空间中Ishikawa迭代过程的收敛性,改进了相关结果.