镓一镁二元相图研究

本文用两种差热分析方法即“一步法”和“二步法”以及多晶X-射线衍射法对镓-镁二元系相图进行了研究.修正了前人的工作. 为了考察该二元体系的金属间化合物是否以镓原子多面体簇状结构存在,作者对富镓部分相图(镓原子百分含量大于71.4％)进行了较为细致的研究.在三种不同比例下(含镓量分别为85at.％、90at.％、95at.％)合成,分离得到了颗粒状晶体.对这些晶体进行了差热分析和多晶X-射线研究.分析结果表明:从这三种不同比例的合金中分离得到的晶体为同一金属间化合物Mg_2Ga_5,也是该二元系镓含量最高的金属间化合物.考察Ga-Mg体系中存在的五种金属间化合物的结构,未能发现镓原子以多面体簇状结构存在的现象.     

团簇Aun+1-1、AunCr-1 (n=1-10)吸附CO的密度泛函理论研究

采用密度泛函理论对CO在阴离子团簇Aun+1-1、AunCr-1(n=1-10))表面的吸附做了系统研究.结果表明,团簇Aun+1CO-1、AunCrCO-1的基态结构是在团簇Aun+1-1、AunCr-1最低能量结构的基础上吸附CO形成; 吸附后的CO键长变长,振动频率减小,表明CO分子被活化;取值相同时,AunCrCO-1的平均结合能高,表明团簇Aun+1CO-1掺杂Cr后稳定性升高.HOMO-LOMO能隙结果表明Aun+1CO-1替代掺杂Cr原子后团簇的化学活性得到了提升,AunCrCO-1、Aun+1CO-1团簇能隙具有奇偶振荡的现象;轨道电荷分析表明CO与团簇相互作用实质是C原子与成键Au原子或Cr原子间转移电荷,CO在与团簇相互作用过程中O原子轨道电荷分布几乎没有发生变化.     

GI／G／1单重休假随机服务系统的马氏骨架方法

文献[1]引入一类具有广泛应用前景的随机过程-Markov骨架过程。借助Markov骨架过程的方法研究GI/G/1单重休假服务系统队长，及t时刻到达顾客等待时间的瞬时概率分布。     

The generalized Roper-Suffridge extension operator

Let f(z) be a normalized convex (starlike) function on the unit disc D. Let , where z=(z₁,z₂,…,z_n), z₁∈D, , p_i?1, i=2,…,n, are real numbers. In this note, we prove that Φ(f)(z)=(f(z₁),f′(z₁)^1/p₂z₂,…,f′(z₁)^1/p_nz_n) is a normalized convex (starlike) mapping on Ω, where we choose the power function such that (f′(z₁))^1/p_i|_z1=0=1, i=2,…,n. Some other related results are proved.     

拓扑遍历与拓扑双重遍历

令X为紧致度量空间,f:X→X为连续映射,U,V为X的任意非空开集,若{n>0|fn(U)∩V≠ )为正上密度集,则称f拓扑遍历.f拓扑双重遍历意味着f×f拓扑遍历.本文在[2]的基础上进一步讨论拓扑遍历与拓扑双重遍历映射的性质.     

混合单调算子的两点拉伸型不动点定理

本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究.     

The tame kernel of imaginary quadratic fields with class number 2 or 3

This paper presents improved bounds for the norms of exceptional finite places of the group , where is an imaginary quadratic field of class number 2 or 3. As an application we show that .

     

Study on application of independent component analysis in the CSNS/RCS

The China Spallation Neutron Source (CSNS) accelerators consist of a low energy H linac and a high energy proton Rapid Cycling Synchrotron (RCS). The proton beam is accumulated in the RCS and accelerated from 80MeV to 1.6GeV with a repetition of 25Hz. Independent component analysis (ICA) is a robust method for processing the collected data (samples) recorded by the turn-by-turn beam position monitor (BPM), which was recently applied to the accelerator. The samples are decomposed to source signals, or the so-called independent components, which correspond to the inherent motion of samples, such as betatron motion and synchrotron motion. A study on the application of the ICA method to CSNS/RCS has been made. It shows that the beta function, phase advance, and dispersion can be well reconstructed by using ICA in CSNS/RCS. The effects of BPM errors on the ICA results are also studied. By comparing the different solving methods in ICA, the so-called SOBI has more advantages for isolating the independent components on the application of ICA to CSNS/RCS. Beam emittance dilution in the process of exciting the turn-by-turn samples is considered,and thus an RF kicker is adopted to avoid such emittance growth.     

Structured mirror array for two-dimensional collimation of a chromium beam in atom lithography

Direct-write atom lithography,one of the potential nanofabrication techniques,is restricted by some difficulties in producing optical masks for the deposition of complex structures.In order to make further progress,a structured mirror array is developed to transversely collimate the chromium atomic beam in two dimensions.The best collimation is obtained when the laser red detunes by natural line-width of transition 7S3 → 7P40 of the chromium atom.The collimation ratio is 0.45 vertically(in x axis),and it is 0.55 horizontally(in y axis).The theoretical model is also simulated,and success of our structured mirror array is achieved.