Dissociations of O_2 molecules on ultrathin Pb(111) films:first-principles plane wave calculations

Using first-principles calculations, we systematically study the dissociations of 02 molecules on different ultrathin Pb（lll） films. According to our previous work revealing the molecular adsorption precursor states for O2, we further explore why there are two nearly degenerate adsorption states on Pb（lll） ultrathin films, but no precursor adsorption states existing at all on Mg（0001） and Al（lll） surfaces. The reason is concluded to be the different surface electronic structures. For the O2 dissociation, we consider both the reaction channels from gas-like and molecularly adsorbed O2 molecules. We find that the energy barrier for O2 dissociation from the molecular adsorption precursor states is always smaller than that from O2 gas. The most energetically favorable dissociation process is found to be the same on different Pb（lll） fihns, and the energy barriers are found to be influenced by the quantum size effects of Pb（lll） films.

洛瓦兹局部引理的新变种及其应用

洛瓦兹局部引理是组合数学和概率论中的重要工具,其最主要的用途之一是证明当约束之间"弱相关"时,满足复杂约束的组合对象存在.自从1975年Erdos和Lovasz提出洛瓦兹局部引理以来,局部引理在组合数学、理论计算机和物理学等领域已经有了很多应用.近年来,为了扩展局部引理的应用范围,人们提出了很多新版的局部引理,尤其是在构造版本局部引理上取得了重大的突破.本文将综述局部引理近年来最新的研究进展,包括几种最主要的局部引理变种以及它们在计算机科学和物理学中的应用.特别的,我们将给出抽象版本、Lopsided版本、变量版本和量子版本局部引理紧的条件,并讨论抽象版本紧的条件同统计物理、量子版本紧的条件同量子物理之间的联系.同时,我们还将以布尔可满足性问题和量子可满足性问题为例,说明局部引理在证明问题有解、找到问题的解以及对问题的解进行计数和采样等方面的应用.