类氢U91+离子的辐射复合及其辐射退激发过程的理论研究

基于多组态Dirac-Fock理论方法,利用GRASP92和RATIP以及在此基础上最新发展的RERR06程序,对类氢U⁹¹⁺（1s）离子的辐射复合截面以及辐射退激发过程进行了详细的理论研究.系统地计算了具有确定能量的连续电子被处于基态的类氢U⁹¹⁺（1s）离子俘获到nl （1≤n≤8, 0≤l≤6）轨道形成类氦U⁹⁰⁺（1snl）离子的辐射复合截面,并研究了这辐射复合末态退激发谱的相对强度.研究发现,类氢U⁹¹⁺（1s）离子辐射复合到不同轨道的截面随其主量子数的增大而显著减小;同时,辐射复合末态的退激发对Kα谱线的相对强度有重要影响. 关键词： 辐射复合 多组态Dirac-Fock理论方法 辐射退激发     

Optical Properties of Neutral and Charged Low Band Gap Alternating Copolyfluorenes: TD-DFT Investigation

用含时的密度泛函(TD-DFT)方法研究了低带隙的中性和带电的交替共聚芴(Green 1),该化合物是由烷基取代芴和(1,2,5-噻吩基-3,4-硫重氮基)喹喔啉噻吩(T-TDQ-T)单元交替重复组成,对他们的激发态特性用二维(2D)和三维(3D)实空间分析方法做了进一步分析．对于中性的Green 1,分别得到其带隙、键能、激子结合能和核驰豫能．用3D跃迁密度方法对中性和带电的Green 1的跃迁偶极矩进行比较可显示出跃迁偶极矩的取向和强度;用3D电荷差异密度方法显示出激发后的中性和带电的Green 1电荷重新分布和比较,用2D实空间分析方法(跃迁密度矩阵)来研究中性和带电的Green1处于激发态时的电子空穴相干性．中性Green 1的激发态特性分别用TD-DFT和ZINDO两种方法进行了计算,比较得出电子-电子相互作用(在TD-DFT中)对激发态性质的重要影响．     

Reductions on equivalence relations generated by universal sets

Let X, Y be Polish spaces, , . We say A is universal for Γ provided that each x‐section of A is in Γ and each element of Γ occurs as an x‐section of A. An equivalence relation generated by a set is denoted by , where . The following results are shown:

• (1) If A is a set universal for all nonempty closed subsets of Y, then is a equivalence relation and .
• (2) If A is a set universal for all countable subsets of Y, then is a equivalence relation, and
  • (i) and ;
  • (ii) if , then ;
  • (iii) if every set is Lebesgue measurable or has the Baire property, then .
  • (iv) for , if every set has the Baire property, and E is any equivalence relation, then .

     

Upper Bounds on Liouville First-Passage Percolation and Watabiki's Prediction

Given a planar continuum Gaussian free field h^𝒰 in a domain 𝒰 with Dirichlet boundary condition and any δ > 0, we let be a real-valued smooth Gaussian process where is the average of h^𝒰 along a circle of radius δ with center v. For γ > 0, we study the Liouville first-passage percolation (in scale δ), i.e., the shortest path distance in 𝒰 where the weight of each path P is given by . We show that the distance between two typical points is for all sufficiently small but fixed γ > 0 and some constant c^* > 0. In addition, we obtain similar upper bounds on the Liouville first-passage percolation for discrete Gaussian free fields, as well as the Liouville graph distance, which roughly speaking is the minimal number of euclidean balls with comparable Liouville quantum gravity measure whose union contains a continuous path between two endpoints. Our results contradict some reasonable interpretations of Watabiki's prediction (1993) on the random distance of Liouville quantum gravity at high temperatures.© 2019 Wiley Periodicals, Inc.     

One-Pot Synthesis and Fungicidal Activities of Derivatives of Imidazo [2,1-b]-1,3,4-thiadiazol-5(6H)-one

The isothiocyanates 2, obtained from aza-Wittig reactions of vinyliminophosphoranes 1 with CS ₂ , reacted with hydrazine to give 3-amino-2-thioxo-4-imidazolidinones 4. One-pot reactions of 4, aromatic isocyanates, Ph ₃ P, C ₂ Cl ₆ , and Et ₃ N generated imidazo[2,1-b]-1,3,4-thiadiazol-5(6H)-ones 7. Compound 7 exhibited good fungicidal activities, especially against Sclerotinia sclerotiorum de Bary and Botrytis Cinerea Pers.     

An approach to the Paal–Knorr pyrroles synthesis in the presence of β-cyclodextrin in aqueous media

An efficient and facile method for the synthesis of N-substituted pyrroles in moderate to good yields by the Paal–Knorr reaction of γ-diketones with amines in the presence of β-cyclodextrin in aqueous media has been developed.Moreover,this process tolerated diamines(e.g.,para-,meta- or orthophenylenediamine)to construct bis-pyrrole or mono-pyrrole derivates.β-Cyclodextrin can be recovered easily after the reactions and reused without evident loss in activity.     

Renormalization and conjugacy of piecewise linear Lorenz maps

We investigate the uniform piecewise linearizing question for a family of Lorenz maps. Let f be a piecewise linear Lorenz map with different slopes and positive topological entropy, we show that f is conjugate to a linear mod one transformation and the conjugacy admits a dichotomy: it is either bi-Lipschitz or singular depending on whether f is renormalizable or not. f is renormalizable if and only if its rotation interval degenerates to be a rational point. Furthermore, if the endpoints are periodic points with the same rotation number, then the conjugacy is quasisymmetric.     

Two novel polycyclic spiro lignans from Gymnotheca involucrata

Two novel lignans, gymnothespirolignans A (1) and B (2), possessing a rare polycyclic spiro skeleton, were isolated from the endemic plant of Gymnotheca involucrata Pei. Their structures were determined by spectroscopic evidences and the absolute configurations were confirmed by single crystal X-ray diffraction analysis. Compounds 1 and 2 showed promising antiviral activities against RSV with an IC₅₀ value of 31.87 and 17.51 μM, respectively.