商榷

第32届IMO试题如图 1,P为ΔABC内任意一点,求证：∠1,∠2,∠3中至少有一个不大于30°．     

T1—2212超导薄膜的制备

以铝酸镧晶体为基片，采用两步法制备T1-2212超导薄膜，包括在低温(150℃)下利用激光脉冲沉积(PLD)工艺沉淀Ba2CaCu2Ox非晶前驱体薄膜和在高温(740～830℃)下前驱体薄膜的铊化结晶、取向生长过程，实验结果表明所制得的膜的相组成为T1-2212，表面存在大量均匀分布的成分为T12Ba2CaCu2Ox的亚微米颗粒，其零电阻温度为101K，薄膜与基片之间界面清晰，没有过渡层，薄膜具有良好的c取向外延条纹。     

基于变压红外光谱研究离子液体[MPIM][I]与石墨烯氧化物之间的相互作用

本研究利用红外光谱研究不同压力下离子液体1-Methy1-3-propylimidazolium iodide([MPIM][I])与石墨烯及其氧化物的相互作用.结果表明,[MPIM][I]对压力的变化具有高敏感度,咪唑环与烷基链在0.4 GPa时产生相变化,可明显观察到吸收峰的裂解,且连续加压会导致咪唑环与烷基链的振动频率蓝移.[MPIM][I]与石墨烯作用时加压至2.5 GPa也未观测到相变化的产生,且咪唑环与烷基链的振动频率蓝移趋势也不明显;[MPIM][I]与石墨烯氧化物作用时咪唑环与烷基链的结果与添加石墨烯时几乎相同.石墨烯氧化物具有羟基、羧基、环氧基等共价键结在其表面,这些羟基会扰动[MPIM][I]中的咪唑环与烷基链,导致在常压下振动频率发生蓝移,进而表明石墨烯表面的官能基团会与离子液体产生相互作用.     

巧换元两法证一题

中学生数学2010年1月上给出的一道“巧证不等式”题：已知a,b∈R＋,且a＋b=1,求证：an＋bn≥（1/2）n-1（n∈N＋）.     

Annealing effect on magnetic anisotropy in ultrathin（Ga,Mn）As

We investigated the effect of low temperature annealing on magnetic anisotropy in 7-nm ultrathin Ga0.94Mn0.06As devices by measuring the angle-dependent planar Hall resistance(PHR).Obvious hysteresis loops were observed during the magnetization reversal through the clockwise and counterclockwise rotations under low magnetic fields(below 1000 Gs,1 Gs = 10-4 T),which can be explained by competition between Zeeman energy and magnetic anisotropic energy.It is found that the uniaxial anisotropy is dominant in the whole measured ferromagnetic range for both the as-grown ultrathin Ga0.94Mn0.06As and the annealed one.The cubic anisotropy changes more than the uniaxial anisotropy in the measured temperature ranges after annealing.This gives a useful way to tune the magnetic anisotropy of ultrathin(Ga,Mn)As devices.     

An Estimation for the Power-Law Distribution Parameter Based on Entropy

A new estimation based on the Shannon entropy for the power-law distribution parameter is presented, The maximum likelihood estimation （MLE） of the parameter is discussed and the relation between the MLE and the moment estimation of the parameter is given out. It is shown that the minimum Shannon entropy estimation is equivalent to the MLE giving the log expectation.     

A waveguide polarizer based on Si-coated Ti:LiNbO_3 planar structure

A novel design of a transverse magnetic (TM)-pass waveguide polarizer based on Si on an X-cut, Y-propagatiou Ti:LiNbO3 planar waveguide is presented. The eigenvalue functions of such structure have been obtained by using Wenzel-Kramers-Brillouin (WKB) method with modified Airy functions. The intervals of the silicon thickness have been found which result in transverse electric (TE) light suffering strong attenuation while TM wave propagating with fairly low loss. A planar waveguide polarizer is fabricated and its polarization-dependent measurements lead to the best polarization extinction ratio ~ 34 dB and the insertion loss < 0.4 dB.     

利用DISLab改进机械能守恒的实验

1问题提出一般探究机械能守恒定律的实验是使用轨道小车.将轨道的一端垫高,平衡摩擦力使小车从轨道上下滑拖动纸带,用打点计时器记录运动的情况.再计算出相应的物理量,探究机械能守恒定律.但这样的设计中摩擦力的平衡不好把握,计算量也比较大,导致课堂效率低下.如果用气垫导轨代替轨道小车,     

便携式X射线荧光光谱仪快速监测重金属土壤环境质量

便携式X射线荧光光谱仪(PXRF)作为一种新型快速测试手段具有突出的应用前景,但也存在检测范围和检测限的局限,为此本文研究PXRF仪器在快速监测土壤环境质量中Cr,Ni,Cu,Zn,Pb,Cd,As和Hg等8种重金属元素的适用性,筛选仪器可检测元素,评价检测结果准确度。具体方法是使用仪器测试重金属污染土壤样品,测试结果与电感耦合等离子体质谱分析方法(ICP-MS)测试值进行对比,评判检测结果精密度,建立PXRF仪器测试值与ICP-MS仪器测试值的线性回归关系。结果表明：(1)在监测重金属土壤环境质量时,PXRF仪器可用于检测土壤中Pb,Zn,Cr和Cu含量,但不适于检测Ni,Cd,As和Hg含量。(2)Pb和Zn测试值稍低于ICP-MS测试值,Cu偏高,而Cr过高;PXRF仪器测试值需要参照标准分析方法进行线性校正。研究结论为：便携式X射线荧光光谱仪适用于Pb,Zn,Cr和Cu等4种重金属的土壤环境质量监测,是一种简单快速、准确可靠的低成本土壤重金属分析手段。该研究的创新之处是合理规避PXRF仪器的缺点,将仪器应用于土壤环境质量监测,提高了测试结果应用价值。