Direct Transformation of Arenols Based on C—O Activation

In the view of substrate availability, atomic efficiency and cost, directly using arenols as coupling partners in cross‐coupling, would be one of the most attractive goals. Up to date, many efforts have been made to activate the C—O bond of phenols with different strategies, for example, through in‐situ formed intermediates, through a catalytic reductive dearomatization‐condensation‐rearomatization sequence or catalytic deoxygenation. In this review, we summarized recent advances in cross‐couplings of arenols as the electrophiles via C—O activation.     

Structure determination of KScS2, RbScS2 and KLnS2 (Ln = Nd,Sm, Tb,Dy, Ho,Er, Tm and Yb) and crystal–chemical discussion

The title structures of KScS₂ (potassium scandium sulfide), RbScS₂ (rubidium scandium sulfide) and KLnS₂ [Ln = Nd (potassium neodymium sufide), Sm (potassium samarium sulfide), Tb (potassium terbium sulfide), Dy (potassium dysprosium sulfide), Ho (potassium holmium sulfide), Er (potassium erbium sulfide), Tm (potassium thulium sulfide) and Yb (potassium ytterbium sulfide)] are either newly determined (KScS₂, RbScS₂ and KTbS₂) or redetermined. All of them belong to the α‐NaFeO₂ structure type in agreement with the ratio of the ionic radii r³⁺/r⁺. KScS₂, the member of this structural family with the smallest trivalent cation, is an extreme representative of these structures with rare earth trivalent cations. The title structures are compared with isostructural alkali rare earth sulfides in plots showing the dependence of several relevant parameters on the trivalent cation crystal radius; the parameters thus compared are c, a and c/a, the thicknesses of the S—S layers which contain the respective constituent cations, the sulfur fractional coordinates z(S²⁻) and the bond‐valence sums.     

关于一类二次哈密尔顿系统在二次扰动下的极限环个数问题

本文研究了一类具有两个鞍点和一个中心的通用二次哈密尔顿向量场在二次扰动下的三参数开折，证明极限环的最小上界为２。     

Double Michael Additions of Lithium Enolate of 1,4-Dioxaspiro[4.5]dec-6-en-8-One to Acrylates

Double Michael additions of lithium enolaie of 1,4-dioxaspiro[4.5]dec-6-en-8-one to four acrylates afforded bicyclo[2.2.2]octan-2-ones with high regio- and stereoselectivities in moderate yields.     

Banach空间二阶非线性微分方程的弱Carathéodory解

本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果     

Surface structures formed by individual adsorption and coadsorption of Mn and Bi on Cu(0 0 1), studied by LEED

We have studied the individual adsorption of Mn and Bi, and their coadsorption on Cu(0 0 1) by low-energy electron diffraction (LEED). For Mn, we have determined the c(2 × 2) structure formed at 300 K, whose structure had been determined by several methods. We reconfirmed by a tensor LEED analysis that it is a substitutional structure and that a previously reported large corrugation (0.30 Å) between substitutional Mn and remaining surface Cu atoms coincides perfectly with the present value. In the individual adsorption of Bi, we have found a c(4 × 2) structure, which is formed by cooling below ∼250 K a surface prepared by Bi deposition of ∼0.25 ML coverage at 300 K where streaky half-order LEED spots appear. The c(4 × 2) structure has been determined by the tensor LEED analysis at 130 K and it is a substitutional structure. In the coadsorption, we found a c(6 × 4) structure, which has been determined by the tensor LEED analysis. It is very similar to the previously determined structure of the c(6 × 4) formed by coadsorption of Mg and Bi, and embedded MnBi₄ clusters are arranged in the top Cu layer instead of MgBi₄. Large lateral displacements of Bi atoms in the c(6 × 4)-(Mn + Bi) suggest that the Mn atoms undergo the size-enhancement caused by their large magnetic moment.     

Germanium growth on Br-terminated Si(1 0 0)

The consequences of Ge deposition on Br-terminated Si(1 0 0) were studied with scanning tunneling microscopy at ambient temperature after annealing at 650 K. One monolayer of Br was sufficient to prevent the formation of Ge huts beyond the critical thickness of 3 ML. This is possible because Br acts as a surfactant whose presence lowered the diffusivity of Ge adatoms. Hindered mobility was manifest at low coverage through the formation of short Ge chains. Further deposition resulted in the extension and connection of the Ge chains and gave rise to the buildup of incomplete layers. The deposition of 7 ML of Ge resulted in a rough surface characterized by irregularly shaped clusters. A short 800 K anneal desorbed the Br and allowed Ge atoms to reorganize into the more energetically favorable “hut” structures produced by conventional Ge overlayer growth on Si(1 0 0).     

On the duration of the total eclipse of a satellite of a body

This paper solves the problem of the duration of the total eclipseof a satellite of a body, provided that (a) the body is sphericalin shape and the mass distribution inside the body is sphericallysymmetrical; (b) the satellite is a very small object; (c) thesatellite's orbit around a body is circular and the satellitecan pass through the centre of its shadow; (d) a source of lightis the source of the conical body's shadow (umbra) and it doesnot change its apparent position in the sky; (e) there are noperturbations on the satellite's orbit. The solution presentedrepresents the general discussion of the problem based on utilizationof some parts of the theory of contraction mappings.