Synthesis of substituted benzene derivatives by homo- and hetero-coupling of 2-bromobenzaldehyde and bromovinylaldehydes followed by McMurry coupling

A convenient synthetic approach to substituted benzene derivatives by modified Ullmann cross-coupling of 2-bromobenzaldehyde and bromovinylaldehydes followed by intramolecular McMurry coupling has been developed.     

�Թ�ŵ��������߻�����ż����C2��

在常温常压下采用新型旋转电极等离子体反应器，对辉光等离子体作用下的甲烷偶联反应制C2烃进行了研究。结果表明，甲烷偶联反应的主要产物为C2H2，占C2烃的80%以上，能量效率在5.6%～11.2%之间；增加H2含量可以提高CH4转化率和C2烃收率；在500～2200kJ•mol−1的能量密度范围内，CH4转化率随能量密度的增大而线性增加，C2烃收率随着能量密度的增加呈峰形变化趋势。     

Angular momenta and eigenvectors of the weakly coupled T ⊗ t Jahn‐Teller system

The eigenvalues of the weakly coupled T ? t Jahn‐Teller problem are known for several decades, and the same holds also true for the eigenstates. These, however, are only given in the traditional position representation, which proves inconvenient if one attempts to extend the weak‐coupling treatment into the region of stronger coupling. Here the solution of the T ? t eigenvalue problem at weak coupling is derived in terms of creation and annihilation operators. This reformulation of the problem is nontrivial, since the algebraic form of the oscillator eigenvectors, being simultaneous angular‐momentum eigenstates, has been worked out only recently and is probably still widely unknown. The electronic and oscillator eigenstates are then coupled to form eigenvectors of the total angular momentum. Finally, in preparation for an extension of the weak‐coupling treatment, the action of the boson creation and annihilation operators on the oscillator eigenvectors is calculated, thus completing the algebraic approach to the weakly coupled T ? t system.     

Resolvent estimates in W−1,p related to strongly coupled‐linear parabolic systems with coupled nonsmooth capacities

We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W^{?1, p} spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain L^p estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd.     

Coupling Losses for Resonators with Unequal Apertures for Extended Fresnel Numbers

Coupling losses have been calculated for laser resonators with unequal apertures and extended Fresnel Numbers. This was done using both, diffraction theory and a simple linear model.A close form expression was derived to calculate coupling losses with reasonable accuracies for a limited range of paramters. This should help in the preliminary design of hole coupling laser resonators.     

原子核的单粒子共振态

采用基于相对论平均场的耦合常数解析延拓方法研究球形核的单粒子共振态.具体计算了Zr同位素链中巨晕核的核芯核122Zr阈值附近的中子共振态的能量、宽度和波函数,其结果同相应的散射相移法的结果一致. Using analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory, the energies, widths and wave functions for single-particle resonant states close to the continuum threshold are evaluated. Predictions are also compared with corresponding results obtained by the scattering phase shift method.     

One- and Two-Mode Combination Squeezing Operator for Two Harmonic Oscillators with Coordinate-Momentum Coupling

By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinatemomentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H = p21/2m1 m1ω21x21/2 p22/2m2 m2ω22x22/2 - λx2p1, so its ground state is a one- and two-mode combination squeezed state.Quantum fluctuation in the ground state is calculated.     

压缩真空场与原子非线性作用过程中的纠缠与消纠缠

用Von Neumann熵研究了附加克尔介质的压缩真空场与二能级原子依赖强度耦合相互作用量子体系的量子纠缠特性.讨论了初始压缩真空场的压缩度以及克尔非线性作用的强度对该量子体系纠缠特性的影响.结果表明，克尔介质的非线性作用的强弱可以改变体系量子纠缠的周期性；在初始压缩度较大（r=5）时，克尔介质的非线性作用可导致原子与场持续地处于最大纠缠态，无消纠缠态或持续地处于消纠缠态. 关键词： 压缩真空态 克尔介质 依赖强度耦合J-C模型 Von Neumann熵 量子纠缠     

Oxidative Coupling of Thiols to Disulfides with Ti(IV) in the Presence of NaI under Air Atmosphere

Ti(IV) as TiCl₃(O₃SCF₃) and TiO(O₂CCF₃)₂ are used as efficient catalysts for oxidative coupling of aliphatic, aromatic and heteroaromatic thiols to their disulfides in the presence of NaI under air atmosphere.