Characterizing a proton beam with two different methods in beam halo experiments

In beam halo experiments, it is very important to correctly characterize the RFQ output proton beam. In order to simulate the beam dynamics properly, we must first know the correct initial beam parameters. We have used two different methods, quadrupole scans and multi-wire scanners to determine the transverse phase-space properties of the proton beam. The experimental data were analyzed by fitting to the 3-D nonlinear simulation code IMPACT. For the quadrupole scan method, we found that the RMS beam radius and the measured beam-core profiles agreed very well with the simulations. For the multi-wire scanner method, we choose the case of a matched beam. By fitting the IMPACT simulation results to the measured data, we obtained the Courant-Snyder parameters and the emittance of the beam. The difference between the two methods is about eight percent, which is acceptable in our experiments.     

$C_3$型的退化Ringel-Hall代数的Gr\"{o}bner-Shirshov基

The Gr?bner-Shirshov basis of the degenerate Ringel-Hall Algebras of type C₃ is obtained by studying the generic extension monoid algebra.     

Cr(Ⅲ)-羧基配位状态稳定性的理论研究

本文采用模型实验结合密度泛函理论B3LYP方法,研究了单核单齿配位、单核螯合配位、多核单齿配位以及多核双点配位Cr(Ⅲ)的氧化还原稳定性。结果显示,单核单齿配位体系的氧化还原稳定性低于单核螯合配位体系。模型实验与理论预测活性得出的结论一致。在此基础上,计算分析了多核Cr(Ⅲ)离子与羧基形成单齿配位结合和双点单齿配位结合后理论参数的差异。前线轨道能差表明这些配合物中Cr(Ⅲ)的氧化还原稳定性顺序为:单核螯合配位>单核单齿配位>四核双点单齿配位>三核单齿配位>二核单齿配位。研究结果将有益于控制皮革中Cr(Ⅵ)的产生。     

一类拋物线与圆相切问题的解法探究

通过对一道经典试题的多角度思考,探究解决抛物线与圆相切问题的策略和方案,在此基础上拓展变式,并链接竞赛试题.