Herstein定理的推广

1955年Herstein将著名的Jacobson定理推广为:定理A.如果对R中任意x,y,存在可依赖于x,y的整系数多项式p(t),使[x-x2p(x),y]=0,则R是交换的.本文利用多项式的系数和定义了n元多项式,f(x1,x2…,xn)的Fk性质,并以此证明了一个环的交换性定理,当n=1时,即得到定理A.     

Multi-types of Skyrmions in SU(N) Quantum Hall System

The skyrmions in SU(N) quantum Hall (QH) system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU( N) QH system there can exist ( N - 1)types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the (N - 1) Cartan subalgebra local bases, we obtain the (N - 1) U(1) electromagnetic field tensors in the SU(N) gauge field of the QH system, and then derive (N - 1) types of skyrmion structures from these U(1) sub-field tensors. Furthermore, in light of the φ-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.     

New initial condition of the new agegraphic dark energy model

The initial condition Ω_de(z_ini)=n²(1+z_ini)^-2/4 at z_ini=2000 widely used to solve the differential equation of the density of the new agegraphic dark energy (NADE) Ω_de, makes the NADE model be a single-parameter dark-energy cosmological model. However, we find that this initial condition is only applicable in a flat universe with only dark energy and pressureless matter. In fact, in order to obtain more information from current observational data, such as the cosmic microwave background (CMB) and the baryon acoustic oscillations (BAO), we need to consider the contribution of radiation. For this situation, the initial condition mentioned above becomes invalid. To overcome this shortage, we investigate the evolutions of dark energy in the matter-dominated and the radiation-dominated epochs, and obtain a new initial condition Ω_de(z_ini)=n²(1+z_ini)^-2(1+√F(z_ini)²/4 at z_ini=2000, where F(z)≡Ω_r0(1+z)/[Ω_m0+Ω_r0(1+z)] with Ω_r0 and Ω_m0 being the current density parameters of radiation and pressureless matter, respectively. This revised initial condition is applicable for the differential equation of Ω_de obtained in the standard Friedmann-Robertson-Walker (FRW) universe with dark energy, pressureless matter, radiation, and even spatial curvature, and can still keep the NADE model being a single-parameter model. With the revised initial condition and the observational data of type Ia supernova (SNIa), CMB, and BAO, we finally constrain the NADE model. The results show that the single free parameter n of the NADE model can be constrained tightly.     

CVD金刚石中的氮对等离子体刻蚀的影响

采用非对称磁镜场电子回旋共振等离子体分别对沉积过程中掺氮和未掺氮的化学气相沉积金刚石膜进行了刻蚀研究, 结果表明: 掺氮制备的金刚石膜的刻蚀主要集中在晶棱处, 经过4h刻蚀后其表面粗糙度由刻蚀前的4.761 μm下降至3.701 μm, 刻蚀对金刚石膜的表面粗糙度的影响较小; 而未掺氮制备的金刚石膜的刻蚀表现为晶面的均匀刻蚀, 晶粒坍塌,刻蚀4h后其表面粗糙度由刻蚀前的3.061 μm下降至1.083 μm. 刻蚀导致表面粗糙度显著降低. 上述差别的主要原因在于金刚石膜沉积过程中掺氮导致氮缺陷在金刚石晶棱处富集, 晶棱处电子发射加强, 引导离子向晶棱运动并产生刻蚀, 从而加剧晶棱的刻蚀. 而未掺氮金刚石膜,其缺陷相对较少且分布较均匀 ,刻蚀时整体呈现为 (111) 晶面被均匀刻蚀继而晶粒坍塌的现象. 关键词： 掺氮 金刚石膜 刻蚀 非对称磁镜场     

利用数值再现实现彩虹全息色差评价

为了在计算机制彩色彩虹全息图输出之前定量得到再现像的色彩保真度,提出了一种采用数值再现进行色差评价的方法.首先对彩虹全息图进行了频谱分析,得到再现参量与频谱分布之间的关系;然后采用频域滤波算法实现彩色彩虹全息图数值再现,得到再现像的相对功率谱分布;最后采用CIE1976UCS均匀颜色空间对再现像色差情况进行了计算.设计了7个色块并制作了计算机制真彩色彩虹全息图,以金卤射灯作为照明光源进行了光学再现实验,给出实验结果及分析.研究证明了采用数值再现方法实现对计算彩虹全息再现像光谱分布和色差进行计算分析是一种快速经济的方法.     

水溶性CdTe:Mn量子点的双光子吸收

采用激发波长800 nm、脉宽50 fs、重复频率1 kHz的Ti:sapphire放大飞秒激光器作为激发光源,利用开孔Z扫描技术研究了不同粒径的CdTe:Mn量子点的非线性吸收性质。理论计算结果表明,同一生长时间CdTe:Mn量子点的双光子吸收系数是CdTe量子点的1.1倍,其双光子吸收系数随量子点尺寸的减小而增大,这是由于CdTe:Mn量子点非线性吸收属于反饱和吸收,掺杂了Mn元素,减小了表面缺陷浓度,表明掺杂量子点具有很好的双光子吸收现象。     

随机介质的相干背散射与局域化研究

研究了不同尺度参数和粒子浓度下的ZnO随机介质相干背散射强度的分布规律,采用时域有限差分法分析了不同浓度随机介质的光场能量空间分布,预测了随机激光器阈值的高低。结果表明:同一折射率的介质随着介质尺寸的增大,相干背散射的带宽变窄,局域化参量kl值相应增大,使得局域化程度呈较大幅度减弱趋势;并且随着介质浓度的增加,相干背散射的带宽变宽,局域化程度增强,阈值降低。相干背散射有着光子局域化的先期特征,现在已成为研究光子局域化出现与否的基本判断依据,对研究光子局域化以及随机激光器具有重要意义。     

Probing Structural Compositions of Porous Media with Two-dimensional Nuclear Magnetic Resonance

Combination of two-dimensional nuclear magnetic resonance (2-D NMR) correlation maps and a simple three-component model are proposed here to identify the structural composition of porous media. Homogeneous magnetic field and field with constant gradient of a novel Halbach sensor are employed for respective relaxation and diffusion measurements. NMR results are compared and confirmed with independent measurements on a scanning electron microscope and by energy dispersive spectrometer methods.     

模拟颗粒凝并过程的快速Monte Carlo方法

对常规异权值Monte Carlo(MC)方法进行改进,基于强核函数思想,通过颗粒群单重遍历即可求得强核函数最大值,采用接受-拒绝法随机搜寻凝并对,并利用搜寻过程中拒绝和接受的所有凝并对的信息来估计凝并事件的等待时间(时间步长),从而避免颗粒群的双重遍历,以提高MC的效率.对典型工况的模拟结果显示该快速方法计算代价仅为O(N_s),能够显著提高计算效率,同时保持足够的计算精度,较好地协调计算代价与计算精度之间的矛盾.     

纳米晶ZrO2:Er3+-Yb3+的制备及其室温上转换发射

用化学共沉淀法制备了ZrO₂:Er³⁺-Yb³⁺纳米晶粉体，所制备的纳米晶粉体具有较强的室温上转换发射和红外发射.研究了样品的晶体结构和上转换发光性质随着Yb³⁺掺杂浓度和煅烧温度的变化关系.通过X射线衍射谱分析发现，经800℃煅烧2h后得到的ZrO₂:Er³⁺-Yb³⁺纳米晶是四方相和单斜相的混合结构，经950℃煅烧2h后得到的样品以单斜相为主，随着Y