The global dimensions of crossed products and crossed coproducts

In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^＊ are semisimple, then gl.dim（A#σH）=gl.dim（A）, where a is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A^#σH and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim（C α H）=gl.dim（C）.     

A Phase-Controlled Optical Parametric Amplifier Pumped by Two Phase-Distorted Laser Beams

We theoretically study the phase characteristic of optical parametric amplification （OPA） or chirped pulse OPA （OPCPA） pumped by two phase-distorted laser beams. In the two-beam-pumped optical parametric amplification （TBOPA）, due to spatial walk-off, both of the pump phase distortions will be partly transferred to signal in a single crystal so as to degrade the signal beam-quality, which will be more serious in high-energy OPCPA. An OPA configuration with a walkoff-compensated crystal pair is demonstrated for reducing the signal phase distortion experienced in the first stage and ensuring the signal phase independent of two pump phase distortions through the second crystal, hence maintaining the signal beam-quality. Such a TBOPA is similar to the conventional quantum laser amplifier by means of eliminating its sensitivity to the phase and number of the pump beams.     

物理学咬文嚼字之十六 荷（hè）

英文charge一词大致对应中文的荷（hè）、载等词,但具有相似意思的重要物理学词汇还包括load,vector,convection等等。相关词汇被译成中文时,一定程度上被扭曲或附会上了别的内容。     

碘甲烷分子内层轨道的电子动量谱学研究

本文利用电子动量谱仪在1200 eV电子碰撞能量下测量了碘甲烷分子内层轨道电子束缚能谱和电子动量分布. 在能谱上观测到自旋-轨道耦合作用导致的两个分裂峰,得到了它们对应的电子动量分布. 采用相对论密度泛函理论方法计算了自旋-轨道分裂成分的电子动量分布,计算结果在电子动量大于1.0 a.u.区域内与实验测量符合很好,但在动量小于1.0 a.u.区域内严重低估了实验. 扭曲波理论计算很好地解释了低动量区的实验结果.     

基于低双折射光子晶体光纤Sagnac干涉仪的超低温度系数扭曲传感器

研究了低双折射光子晶体光纤中由光纤扭曲造成的圆双折射效应,并应用Sagnac干涉仪结构设计了扭曲传感器.在Sagnac环中的光子晶体光纤上施加机械压力引入初始线双折射并产生正弦干涉光谱,再扭曲光纤产生圆双折射使干涉光谱随扭曲角度移动.光谱峰值波长随扭曲角度变化符合Sinc函数关系,理论分析与实验相符.传感器灵敏度为1....     

类铜Au50+离子电子碰撞激发特性的研究

利用全相对论扭曲波（RDW）方法,系统计算了类铜Au50+离子的外壳层电子4s激发到4l 、5l （ l= s、p、d、f,除去4s-4s ）和内壳层电子3l （l = s、p、d）激发到4l 、5l （l = s、p、d、f）的碰撞激发截面,研究了在不同入射电子能量下截面的变化规律,给出了3d-4f 和3d-5f 精细结构能级的碰撞激发截面。部分计算结果与其它理论及最新实验结果进行了比较,取得了很好的一致性。     

超滤函子余代数范畴

研究了超滤函子余代数范畴set_(F_u)的乘积和余积问题.首先构造了集合乘积上的超滤,讨论集合乘积上超滤的存在形式;接着利用超滤函子的性质给出了范畴set_(F_u)的有限乘积以及任意余积构造;最后证明了范畴set_(F_u)的终对象存在.改进了Gumm关于滤子函子的研究结果,深化了相关文献关于超滤函子余代数的研究.     

TWISTING STATICS AND DYNAMICS FOR CIRCULAR ELASTIC NANOSOLIDS BY NONLOCAL ELASTICITY THEORY

The torsional static and dynamic behaviors of circular nanosolids such as nanoshafts, nanorods and nanotubes are established based on a new nonlocal elastic stress field theory. Based on a new expression for strain energy with a nonlocal nanoscale parameter, new higher-order governing equations and the corresponding boundary conditions are first derived here via the variational principle because the classical equilibrium conditions and/or equations of motion can- not be directly applied to nonlocal nanostructures even if the stress and moment quantities are replaced by the corresponding nonlocal quantities. The static twist and torsional vibration of circular, nonlocal nanosolids are solved and discussed in detail. A comparison of the conventional and new nonlocal models is also presented for a fully fixed nanosolid, where a lower-order governing equation and reduced stiffness are found in the conventional model while the new model reports opposite solutions. Analytical solutions and numerical examples based on the new nonlocal stress theory demonstrate that nonlocal stress enhances stiffness of nanosolids, i.e. the angular displacement decreases with the increasing nonlocal nanoscale while the natural frequency increases with the increasing nonlocal nanoscale.     

相关扭曲Hopf模的基本同构定理与相关Yetter-Drinfel'd模

扭曲的方法在构造新的代数结构与余代数结构中起了重要的作用.本文首先把扭曲的方法运用到模与余模的构造中,得到扭曲模和扭曲余模;其次在更加一般的情形下给出相关扭曲Hopf模的基本同构定理;最后考虑在HopfYD模中如何使扭曲模构成相关Yetter-Drinfel'd模和相关Hopf模.