A note on Rotfel’d Theorem in a sector

The main purpose of this work is to present a better bound than the recent result given by Zhang [Linear Multilinear Algebra. 2015;63:2511–2517].     

Synthesis, characterization, and catalytic activity of divalent organolanthanide complexes with new tetrahydro-2H-pyranyl-functionlized indenyl ligands

Two series of new divalent organolanthanide complexes with the general formula [η⁵:η¹-{1-R-3-(C₅H₉OCH₂)C₉H₅}]₂Ln^II (R = H, Ln = Yb (3); R = Me₃Si, Ln = Yb (4); R = H, Ln = Eu (5); R = Me₃Si, Ln = Eu (6)) were prepared by reactions of 2 equiv. of 1-R-3-(C₅H₉OCH₂)C₉H₆ (R = H (1), R = Me₃Si (2)) with the lanthanide(III) amides [(Me₃Si)₂N]₃Ln(μ-Cl)Li(THF)₃ (Ln = Yb, Eu) via a one-electron reductive elimination process. Recrystallization of 6 from n-hexane afforded [η⁵:η¹-(C₅H₉OCH₂C₉H₅SiMe₃)]₂Eu^II · (C₆H₁₄)_0.5 (7). All compounds were fully characterized by elemental analyses, and spectroscopic methods. The structures of complexes 4 and 7 were additionally determined by single-crystal X-ray analyses. The catalytic activity of the complexes on methyl methacrylate and ε-caprolactone polymerization was studied, and the temperatures, substituents on the indenyl ring, and solvents effects on the catalytic activity of the complexes were examined.     

Synthesis, characterization and catalytic activity of organolanthanide(II) complexes with heterocyclic-functionalized fluorenyl ligands

Two series of new organolanthanide(II) complexes with tetrahydro-2H-pyranyl- or N-piperidineethyl-functionalized fluorenyl ligands were synthesized via one-electron reductive elimination reaction. Treatments of [(Me₃Si)₂N]₃Ln^III(μ-Cl)Li(THF)₃ with 2 equiv. of C₅H₉OCH₂C₁₃H₉ (1) or C₅H₁₀NCH₂CH₂C₁₃H₉ (2), respectively, in toluene at about 80 °C produced, after workup, the corresponding organolanthanide(II) complexes with formula [η⁵:η¹-C₅H₉OCH₂C₁₃H₈]₂Ln^II (Ln = Yb (3), Ln = Eu (4)) and [η⁵:η¹-C₅H₁₀NCH₂CH₂C₁₃H₈]₂Ln^II (Ln = Yb (5), Ln = Eu (6)) in good yields. All the compounds were fully characterized by spectroscopic methods and elemental analyses. The structures of complexes 3, 4, and 6 were additionally determined by single-crystal X-ray analyses. It represents the first example of solvent-free organolanthanide(II) complexes with fluorenyl ligands. The catalytic properties of the organolanthanide(II) complexes on the polymerization of ε-caprolactone and methyl methacrylate have been studied. The temperatures, solvents and coordination effects on the catalytic activities of the complexes were examined.     

激光场线宽对四能级原子系统相干效应的影响

采用密度矩阵方程,在引入激光场线宽的条件下,计算了N型四能级原子系统中介质对探测场的吸收。结果表明:耦合场线宽的引入,消弱了四能级原子相干,对抑制吸收有增强作用,对增强吸收有抑制作用,即耦合场线宽的引入导致了退相干。控制场线宽的引入,在电磁感应透明中削弱了四能级原子相干性,降低了共振吸收,增强了光透明;在电磁感应吸收中,控制场线宽的增加使谱线中心两侧的吸收增强,削弱了谱线中心的吸收增强,从而使四能级系统的电磁感应吸收转换为电磁感应透明。     

Electrical properties and sulfur tolerance of La0.75Sr0.25Cr1−xMnxO3 under anodic conditions

Complex metal oxides with composition of La_0.75Sr_0.25Cr_1−xMn_xO₃(x=0.4,0.5,0.6) (LSCM) have been synthesized and examined as anode materials for solid oxide fuel cells (SOFCs). LSCM compositions show excellent tolerance to both reduction and oxidation but the crystal structure transforms from hexagonal in air to orthorhombic in H₂. The volume change associated with this phase transformation is only about 1%, thus having little effect on other properties. The total electrical conductivity increases with the content of Mn, whereas the resistance to sulfur poisoning increases with the content of Cr. Fuel cells using LSCM as the anode show very good performance when pure hydrogen is used as the fuel. However, they do not appear to be stable in fuels containing 10% of H₂S.     

四价钼体系催化丁二烯聚合动力学

本文报导了MoCl₂(n-C₈H₁7O)₂-(i-Bu)₂AlOph体系催化丁二烯聚合动力学研究结果,得到聚合速率方程式R=k(C)_O(2)[M]=k_pa(c)_o(M),表观活化能18.6千卡/摩尔,指数前因子1.6×10¹⁰分^-1,以及不同温度下的催化剂利用率,活性中心浓度,活性中心平均寿命等,还证明了等聚合速率的聚合时间t_O与活性中心平均寿命相近。     

Regio‐ and stereospecific synthesis of polysubstituted alkenes by carbozincation of acetylenic sulfones

Tri‐ or tetrasubstituted alkenes with various substituents can be constructed regio‐ and stereospecifically by treatment of acetylenic sulfones with organozinc reagents in tetrahydrofuran followed by hydrolysis or coupling with halohydrocarbon. Copyright © 2009 John Wiley & Sons, Ltd.     

HOMOMORPHISMS BETWEEN SYMPLECTIC GROUPS

Let F and F_1 be fields with |F| > 5, and n, n_1 integers satisfying $n\geq n_1$. The present paper determines the forms of homomorphisms from SP_{2n}(F) to SP_{2n}(F_1) and that from PSP_{2n}(F) to PSP{2n}(F_l).     

用易拉罐做的几个实验装置

本文介绍三种用易拉罐等旧物自制的简易实验装置。该装置具有取材方便，制作简单，造价低等优点。     

Alkyne coupling in rhenacarbaborane chemistry. Structure of [1,2-mu-NHBut-2,2-(CO)(2)-3,2-sigma:eta 2-(C(=CHBut)-CH=CHBut)-closo-2,1-ReCB10H9

The butadienyl moiety in the title compound is bound to both cage-boron and rhenium vertices, and arises from coupling of two alkyne molecules at the rhenium centre, unprecedented in metallacarbaborane chemistry.