Some unsolvable conjectures in finite p-groups

We survey some unsolvable conjectures in finite p-groups and their research progress.     

基于模糊综合评判的大学数学考核方式改革

独立高校数学课程的开设旨在让学生掌握数学知识的基础上,提高数学应用能力.然而现行的考核方式存在重考试结果,轻学习过程等问题.从传统考核方式入手,指出其不足之处,基于模糊综合评判法建立新型评价体系和数学模型,通过试点运行验证了新的考核方式的可行性、客观性、合理性和科学性.     

交错跃迁Hofstadter梯子的量子流相

为玻色Hofstadter梯子模型引入交错跃迁,来扩展模型支持的量子流相.基于精确对角化和密度矩阵重整化群计算发现,无相互作用时,系统中包含横流相、涡旋相和纵流相;横流相来自均匀跃迁时Hofstadter梯子模型的Meissner相,纵流相是交错跃迁时才可见的流相.强相互作用极限下系统的超流区也包含横流相、纵流相和涡旋相,但存在更多的相变级数;超流区的横流相、纵流相之间存在相变但Mott区的不存在,把Mott区的"横、纵流相"称为Mott-均匀相,在Mott区只存在均匀相和涡旋相.跃迁的交错会压缩涡旋相存在的区域,使Mott区最终只剩下均匀相;跃迁的交错不仅能驱动Mott-超流相变,还使磁通的改变也能够驱动系统的Mott-超流相变.对这一系统的研究丰富了磁通系统中的量子流相,同时为研究拓扑流特性提供了模型支持.     

A giant enhancement of magnetic moment in a ternary three-shell icosahedral cluster: Fe@Mn12@Au20

ABSTRACT

The average magnetic moment per atom of Mn₁₃ cluster is expected to be enhanced by doping or coating with a shell. Several ternary core–shell icosahedral clusters TM@Mn₁₂@Au₂₀ were constructed by combining substituting the central Mn with VIII elements (Fe, Co, Ni, Ru, Rh, Pd and Pt) and coating with a icosahedral Au₂₀ shell, and systematically studied by using the first-principles density functional method. Compared to Mn₁₃, Fe@Mn₁₂@Au₂₀ cluster shows a giant enhancement on total magnetic moment (52?µ_B) which can be greatly attributed to the ferromagnetic coupling between spin moments of atoms. Coating with Au₂₀ shell enlarged the average distances of TM-Mn and Mn-Mn and is a useful way to change the magnetic coupling style. By analysis of density of states and electron localisation functional, we can conclude that the weak hybridisation between Fe and Mn in Fe@Mn₁₂@Au₂₀ is propitious to maintain their original direction of spin moments of atoms and then form ferromagnetic coupling.     

思维导图促进分析化学课堂思政教学的探索——以“酸碱滴定法基本原理”为例

在分析化学课程的教学中,通过充分发掘其中的思政元素,将其与教学内容进行有机结合,达到育人的目的。通过引入思维导图教学法,搭建思政元素与教学内容的桥梁,学生可以快速把握所学知识。通过学生的表现,分析教学效果,存在的问题等,为课堂思政与本科化学教学有机结合提供一定的借鉴。     

对《关于〈一维圆环上双原子链的马德隆常数〉的解析解》的讨论

本文绘制了一维等距离子晶体的累加法、埃夫琴法和平均值法的各级马德隆常数的曲线.本文推导了二聚化直线离子晶体马德隆常数的求和式,比较了两种解析式的优劣.本文详细地推导了圆环上等距和二聚化离子晶体的马德隆常数的解析式,使读者更易于理解.本文修正了《关于〈一维圆环上双原子链的马德隆常数〉的解析解》的两个笔误,还建议修正二聚化马德隆常数的定义式,使其物理意义更明显.     

The effects of pre-equilibrium emission and secondary decay on the determination of freeze-out volume at intermediate energies

The effects of pre-equilibrium emission and secondary decay on the determination of the freeze-out volume are investigated using the isospin-dependent quantum molecular dynamics model accompanied by the statistical decay model GEMINI. Small-mass projectiles and large-mass targets with central collisions are studied at intermediate energies. It is revealed that the proton yields of pre-equilibrium emission are smaller than those of secondary decay. However, the determination of the freeze-out volume from the proton yields is more easily affected by pre-equilibrium emission. Moreover, the percentage of proton yields in the freeze-out stage is found to be approximately 50%.