Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.     

环形装置中三维MHD平衡与稳定性的计算机模拟

一、引 言 在聚变研究中,环形等离子体的磁约束起着重要作用。目前托卡马克研究的进展令人鼓舞,其理论与实验比较符合,定标关系清楚。但是无论从聚变的最终目标来看,还是从实验的安排考虑,完全轴对称的几何形状给各方面部带来许多不便。人们希望知道如果把环形几何中加进直线段,或者把圆环改成不具有对称性的环形,会对等离子体约束产生何种影响?     

2-Nitroethanal conformations in solution: AnAb initio SCRF study

The structure of 2-nitroethanal has been studied at the MP2/6-31G^* level in the gas phase and in acetonitrile using a continuum model to represent the electrostatic solute-solvent interactions. The relative energies of the two stable conformations obtained are quite dependent on the media. Indeed, our computations predict a change of the most stable conformation from gas to polar solvent. These results are in agreement with experimental data for the axial/equatorial conformational equilibrium of 2-nitrocyclohexanone.     

基于双尺度渐近分析的有限元算法

1．引言正如文山所说，由于复合材料和周期结构的材料系数ail（x）在局部区域内间断且跳跃性很大，加上区域内含有周期性洞穴或裂缝，且周期长度很小．一般而言，直接采用有限元方法进行数值模拟，其计算量大得惊人，甚至难以实现．文山针对这种特征，提出了一种可计算的双尺度渐近分析模式，本文在此基础上给出了相应的有限元算法，它包括：1．周期解在一个基本构造上的有限元计算；2．边界层的有限元计算．同时，给出了相应的误差分析．2．周期解的有限元计算首先考虑下列形式的边值问题；其中把，代E尸（on叫，iii（0关于E—（EI，ZZ…     

腔长失调对光腔衰荡法测量精度的影响

 只考虑腔长失调因素下建立了反射率模拟测量的理论模型。根据高斯光束传输规律分析了腔长失调对衰荡腔模式耦合的影响，推导了腔长失调与谐振腔输出脉冲信号、衰荡信号与反射率之间的关系，模拟了腔长失调在±10mm范围内的光脉冲衰荡现象。结果表明：对于光敏面直径为0.2mm的高速探测器，为了保证10^-6的测量精度，腔长的失调量应控制在±1mm之间。在光路调节中采用具有对数变换功能的示波器和动态范围较大的探测器，可以提高测量精度。     

Influence of saddle-splay deformation on lyotropic chromonic liquid crystals confined between two coaxial cylinders

ABSTRACT

A striking feature of lyotropic chromonic liquid crystals confined in cylinder model exhibit double-twist director configurations. Evidence suggests that saddle-splay deformation is among the most important factors for the distortions of director. Previous researches limit the director to distort at a fixed plane (r-? plane) by using specific boundary conditions such as degenerate planar anchoring condition. In this work, we consider lyotropic chromonic liquid crystals confined between two coaxial cylinders with free-surface boundary conditions and Rapini-Papoular-type anchoring conditions. By using finite-difference iterative method to solve the numerical solution of Euler equation, we find that saddle-splay deformation leads to double-twist director configurations under free-surface boundary conditions, which consist of the result under degenerate planar anchoring conditions. Furthermore, at Rapini-Papoular-type anchoring conditions, saddle-splay deformation has a great influence on the director in the radial direction (r direction) and the director distorts in three-dimensional space. Remarkably, our method provides a more accurate theory basis for the measured values of saddle-splay elastic constant K_24。     

Schemes to generate and distinguish a type of genuine four-qubit entangled states in a cavity QED system

We propose a scheme to generate a type of genuine four-qubit entangled states, which were firstly introduced by Yeo et al. [Y. Yeo, W. K. Chua, Phys. Rev. Lett. 96 (2006) 060502]. These states have many interesting entanglement properties and possess possible applications in quantum information processing and in fundamental tests of quantum physics. We show that such a type of 16 orthonormal basis states can be deterministically distinguished by a cavity QED system.     

Configurational Lability at Tetrahedral Phosphorus: syn/anti-Isomerization of a P-Stereogenic Phosphiranium Cation by Intramolecular Epimerization at Phosphorus

Tetrahedral main-group compounds are normally configurationally stable, but P-epimerization of the chiral phosphiranium cations syn- or anti-[Mes*P(Me)CH₂CHPh][OTf] (Mes*=2,4,6-(t-Bu)₃C₆H₂) occurred under mild conditions at 60 °C in CD₂Cl₂, resulting in isomerization to give a syn-enriched equilibrium mixture. Ion exchange with excess [NBu₄][Δ-TRISPHAT] (Δ-TRISPHAT=Δ-P(o-C₆Cl₄O₂)₃) followed by chromatography on silica removed [NBu₄][OTf] and gave mixtures of syn- and anti-[Mes*P(Me)CH₂CHPh][Δ-TRISPHAT]?x[NBu₄][Δ-TRISPHAT]. NMR spectroscopy showed that isomerization proceeded with epimerization at P and retention at C. DFT calculations are consistent with a mechanism involving P-C cleavage to yield a hyperconjugation-stabilized carbocation, pyramidal inversion promoted by σ-interaction of the P lone pair with the neighboring β-carbocation, and ring closure with inversion of configuration at P.