一道高中数学预赛题的多向推广

众所周知,等差数列存在一些美妙的性质,列出如下. 性质1 等差数列{an｝的前n项之和An=an2+bn. 性质2 若等差数列{an｝与等差数列{bn｝前n项之和分别为An,Bn,则An/Bn=an+b/cn+d. 证明:设{an｝,{bn｝的公差分别为d1,d2,由An=na1+n(n-1)d1,Bn=nb1+n(n-1)d2,得An/Bn=d1/2n+(a1-d1/2)/d2/2n+(b1-d2/2)=an+b/cn+d,其中a=d1/2,b=a1-d1/2,c=d2/2,d=b1-d2/2.     

X射线辐射输运分解实验研究

在“星光Ⅱ”激光装置上进行了X射线辐射输运分解实验研究.实验中利用高时空分辨的MCP选通X射线皮秒分幅相机和软X射线条纹相机从缝口观测腔内壁X射线辐射时空分布,得到X射线在腔中的输运速率、X射线持续发射时间和轴向强度衰减量;利用X射线CCD针孔透射光栅谱仪观测到腔内X射线辐射光谱随空间位置的变化,得到X射线在输运过程中被多次吸收和发射后谱的变化特征;用X射线二极管和亚千X射线能谱仪分别得到源和输运末端X射线辐射总量和辐射温度.介绍了实验中采用的诊断技术和实验方法,并给出了获得的典型结果. 关键词：     

527nm激光辐照盘靶背向散射能量测量

在星光Ⅱ激光装置上,测量了脉宽1ns、能量40-110J的527nm激光在不同条件下辐照Au盘靶、Al盘靶的背向散射能量。结果表明:激光辐照Au盘靶时．在聚焦条件下背向散射能量约占打靶激光能量的7．8％;在束匀滑条件下背向散射能量份额下降到6.2％左右,证明了束匀滑可有效抑制背向散射。对比Au盘靶、Al盘靶背反能量与打靶激光能量关系曲线,可以看出背向散射能量与打靶激光能量基本上成线性关系。 Au and Al disk target were irradiated with -1 ns, 40-110 J, 527 nm laser at Xingguang-Ⅱ facility. The backscattered lights by laser-produced plasma were studied experimentally. The results are in troduced in this paper. Backscattered light energy is 7.8% of laser energy when laser is focused on Au disk target; when laser beam is smoothed, it is 6.2%. The comparison shows that laser smoothing can restrain backscattered light efficiency. The experimental results :also show that there is a linear relation between backscattered light energy and the laser energy.