Lorentz detuning and tuning system study of 3+1/2cell DC-SC photo-injector for PKU-FEL

A 3+1/2cell DC-SC photo-injector for PKU-FEL facility is under development, which is an upgrade design of the successful 1+1/2cell DC-SC photo-injector. The Lorentz detuning and tuning structure for the 3+1/2cell superconducting cavity is presented in this paper. The Lorentz force detuning coefficient is 7.2 Hz/(MV/m)2 with double stiffening rings for the half cell and single stiffening rings between the adjacent TESLA cells. With the special stiffening structure, the 3+1/2cell whole cavity needs only one tuner. The influences of the tuning on frequency shift, field flatness and average gradient are discussed in this paper. The simulation results show that the stiffening rings' design is successful.     

半质环的交换性条件

本文对满足可变恒等式的半质环在某种有界条件下给出了一个判断环Ｒ交换性的简便准则，使文献［２－２７］中所有相应结果均成为其直接推论．此外，对不限有界的情况，也得到较为广泛的结论．     

弱$r$-Clean环

As generalization of r-clean rings and weakly clean rings, we define a ring R is weakly r-clean if for any a∈R there exist an idempotent e and a regular element r such that a = r + e or a = r-e. Some properties and examples of weakly r-clean rings are given. Furthermore, we prove the weakly clean rings and weakly r-clean rings are equivalent for abelian rings.     

The Fascination of Vortex Rings

We present inviscid and viscous models for the formation and propagation of single, and co-axial pairs of, vortex rings. Inviscid flows are based on both thin rings, and thick rings treated by a contour dynamics approach, whilst viscous flows are determined from numerical solutions of the Navier–Stokes equations. A kaleidoscope of different flow behaviours for these axisymmetric flows is presented.     

Dispersion Curves for Harmonic Waves Propagating Along the Directrix of a Cylindrical Shell Reinforced with Rings

A method is proposed to study the influence of discrete ribs on the dispersion curves for harmonic waves propagating along the directrix of a simply supported cylindrical shell reinforced with rings. A numerical example is considered to demonstrate the necessity of accounting for this factor, the possibility of using a simplified formulation of the problem, and the necessity of accounting for the asymmetry of rib arrangement about the median surface of the shell     

拟-中心半交换环

环$R$称为拟-中心半交换的(简称QCS环)如果对$a,b\in R$, $ab=0$蕴含$aRb\subseteq Q(R)$, 其中$Q(R)$为$R$的拟中心.证明了如果$R$ 为QCS环, 那么$R$的幂零元集恰好是它的Wedderburn根, 且对$n\geq 2$, 上三角矩阵环$R=T_n(S)$ 是QCS 环当且仅当$n=2$ 且$S$ 是duo 环, 而$T_{2k+2}^k$是QCS环如果$R$是约化的duo环.     

On certain homological finiteness conditions

In this paper, we show that the injective dimension of all projective modules over a countable ring is bounded by the self-injective dimension of the ring. We also examine the extent to which the flat length of all injective modules is bounded by the flat length of an injective cogenerator. To that end, we study the relation between these finiteness conditions on the ring and certain properties of the (strict) Mittag–Le?er modules. We also examine the relation between the self-injective dimension of the integral group ring of a group and Ikenaga’s generalized (co-)homological dimension.