数学之神——阿基米德

近代数学史家倍尔说,任何一张列出有史以来三个最伟大的数学家的名单中,必定会包括阿基米德,另外两位通常是牛顿和高斯.其实,早在公元1世纪就有人称阿基米德为“数学之神”.阿基米德到底是怎样的一尊“神”呢? 阿基米德,公元前287年生于意大利半岛南端西西里岛的叙拉古城,他有一位当天文学家的父亲,他从小就受到了良好的家庭教育.后来,阿基米德的亲戚当上了叙拉古国王,又使他有机会飘洋过海,到号称“智慧之都”的亚历山大城学习.在那里,阿基米德受到了良好的数学教育,结交了不少著名学者.返回叙拉古后,阿基米德毕生从事研究工作.     

Generation of near transform-limited ultrashort laser pulses in kilohertz chirped-pulse amplification system by compensating high order phase distortions

The effects of gain narrowing and high order dispersions on the pulse duration in our kilohertz chirped-pulse amplification system have been compensated experimentally. Using an acousto-optic programmable dispersive filter (AOPDF), the spectral full-width at half-maximum (FWHM) is expanded from 30 to 50 nm. Stable laser pulses with the duration of 30 fs (FWHM), which is 1.07 times Fourier-transform-limitation, have been acquired by pre-compensating the high order phase distortions using the phase measured by spectral phase interferometry for direct electric-field reconstruction (SPIDER).     

关于等比数列定义的探讨

本文将讨论有关等比数列的几个关系式的等价性,从而深入地探讨等比数列的种种定义,同时兼论一些数学书籍和资料中关于等比数列问题解答上的失误。(一) 在不少数学书籍、刊物和资料中,常见到有这样的结论:     

NETS IN MULTISYSTEMS OF n 3 AND n 4 PHASES

From the free energy surfaces in G-p-T space a series of basic characteristics have beensummarized. For the reactions of most systems with phases of constant composition, eachof the surfaces should be approximate to a plane. After they meet, the points, curves andsurfaces possess distinct stability levels. Across the intersecting curves and points, the freeenergy surfaces and curves will change their stability levels. Linking invariant points ofdistinct stability levels, we can get various univariant curves differing in structure. Theangular extent between two univariant curves around the invariant points is less than 180°.The surfaces meeting in space and projecting onto the p-T section will give rise to partiallyclosed or open, rather than completely closed nets. Finally, based upon the basic characteristicsand criteria, we have derived the partially closed nets of n 3 and n 4 phases with maxi-mum closure by using geometrical and analytical methods. From the free energy surfaces in G-p-T space a series of basic characteristics have beensummarized. For the reactions of most systems with phases of constant composition, eachof the surfaces should be approximate to a plane. After they meet, the points, curves andsurfaces possess distinct stability levels. Across the intersecting curves and points, the freeenergy surfaces and curves will change their stability levels. Linking invariant points ofdistinct stability levels, we can get various univariant curves differing in structure. Theangular extent between two univariant curves around the invariant points is less than 180°.The surfaces meeting in space and projecting onto the p-T section will give rise to partiallyclosed or open, rather than completely closed nets. Finally, based upon the basic characteristicsand criteria, we have derived the partially closed nets of n 3 and n 4 phases with maxi-mum closure by using geometrical and analytical methods.     

北京谱仪Ⅱ顶点探测器的径迹重建

描述了采用模式识别方法的北京谱仪Ⅱ顶点探测器径迹重建软件系统─—VCJULI.经过蒙特卡罗和真实数据的运行检查,证明该程序能对顶点探测器的径迹给出较好的空间分辨和径迹寻找效率.     

sin nx+cos mx周期的求法

1956年第12期《数学通报》上曾发表过阿意今斯他和別罗郭夫斯卡娅写的“求三角函数的周期”一文(由张鉴卿譯自苏联“中学数学”),該文提出了求f_1(x)=cos(3/2)x-sin(x/3),f_2(x)=cos 2x-tgx的周期的問題。本文打算就这些問題加以推广,进而求sin nx+cos mx的周期(其中m,n为实数)。分析:若該函数存在周期b(b>0),則根据周期函数的周期的定义,f(x+b)=sin n(x+b)+cos m(x+b) =sin(nx+nb)+cos(mx+mb) =sin nx+cos mx=f(x). 現在的任务是判断b是否存在;如果存在,如何把它求出来。根据三角函数的性貭知道,对sin nx来說,要使sin(nx+nb)=sin nx对一切x的值都成立,則     

横向补给系统高架索的稳定性与分岔研究

考虑集中质量对系统动力学行为的影响,建立了横向补给系统高架索振动的理论模型.利用Galerkin方法和多尺度方法对动力学方程进行渐近分析.通过对系统Jacobi矩阵特征值的讨论,分析了系统的稳定性.根据系统渐近解的消除永年项条件,得到了系统的振幅分岔方程.借助Mathematica软件,对系统的局部分岔行为进行研究,得到了系统的转迁集以及相应的局部分岔图,研究表明横向补给系统高架索的振动中存在的多种分岔现象.     

空地激光通信跟踪精度主要外界影响因素研究

为了分析空地激光通信外界因素对跟踪精度的影响情况,将平台振动、大气湍流和背景光三个主要影响因素归结到对跟踪精度影响的统一框架下进行了研究。使用实际测量得到的平台振动数据,建立空地激光通信跟踪仿真系统,分析了不同条件下,三种外界因素对跟踪精度的综合影响情况。在文中假设基础上,分析可知:粗跟踪单元可以较好的抑制地面运动平台的振动,保证激光能够进入精跟踪视场;中强度的湍流使精跟踪残差标准差增大4倍左右,如果试验地点选择在高海拔地区,大气湍流使精跟踪残差标准差增大2倍左右。     

张玉霞：规范是企业的生命线

拥有7500亿元资产、50万职工、6000万从业人员、每年给国家创造1/10财政收入的中国烟草业,绝对称得上是世界级的＂超级国企＂。     

量子密钥分发私密放大的实现

在量子密钥分发系统中,私密放大是合法通信双方提取共享安全密钥的一个必不可少的环节.本文主要介绍了实现私密放大的两种加速算法,采用将两种加速算法进行有效组合的方法,既可以保证私密放大的安全性,同时又有效地减少了运算的操作次数.在连续变量量子密钥分发实验系统中,采用上述组合加速算法,实现了安全密钥的提取.