I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(Ⅰ)

设随机变量Ｘ１,Ｘ２,…ｉｉｄ;称Ｕｎ＝１≤ｉ＜ｊ≤ｎＸｉＸｊ,为两两乘积之和,本文意在给出 Ｕｎ／ｎ~２→０即文中（０．３）式成立的充分必要条件．我们在这部分工作中虽未能彻底解决这个问题,但却揭示出这类条件与Ｓｎ／ｎ→０（Ｓｎ＝ｎｉ＝１Ｘｉ）之条件间的本质上的不同之处,就是说,这是一类不能完全用Ｘ１的矩来刻划的条件,它们要更为深层次地依赖于Ｘ１的尾分布性质．     

A class of solvable coupled nonlinear oscillators with amplitude independent frequencies

Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically.     

Probabilistic approaches to compute uncertainty intervals and sensitivity factors of ultrasonic simulations of a weld inspection

For comprehension purpose, numerical computations are more and more used to simulate the propagation phenomena observed during experimental inspections. However, the good agreement between experimental and simulated data necessitates the use of accurate input data and thus a good characterization of the inspected material. Generally the input data are provided by experimental measurements and are consequently tainted with uncertainties. Thus, it becomes necessary to evaluate the impact of these uncertainties on the outputs of the numerical model. The aim of this study is to perform a probabilistic analysis of an ultrasonic inspection of an austenitic weld containing a manufactured defect based on advanced techniques such as polynomial chaos expansions and computation of sensitivity factors (Sobol, DGSM). The simulation of this configuration with the finite element code ATHENA2D was performed 6000 times with variations of the input parameters (the columnar grain orientation and the elastic constants of the material). The 6000 sets of input parameters were obtained from adapted statistical laws. The output parameters (the amplitude and the position of the defect echo) distributions were then analyzed and the 95% confidence intervals were determined.     

隐性字迹的快速光谱显现与高光谱分类技术研究

擦除、密写、掩盖等隐性字迹的快速、无损显现与检验是法庭科学文件检验领域的研究难点。当前多采用切换多波段光源与滤光片的方法对隐性字迹进行显现,但对隐性字迹显现的光谱学机理分析较少,因此隐性字迹的显现效率与检验成功率均不高。为提高擦除、密写、掩盖三类隐性字迹的显现效率与检验精度,通过测量字迹的激发与荧光光谱、反射与透过光谱、微观形貌,对其显现机理与快速显现方法进行深入研究。并且基于液晶可调谐滤光器（LCTF）的高光谱成像技术与支持向量机（SVM）分类算法,提出一种对隐性字迹同时显现与分类的快速检验方法。晨光与百乐可擦笔字、荧光密写笔、柠檬汁均可在365 nm长波紫外光激发下发出较强荧光,其中可擦笔和柠檬汁的荧光波长为716 nm左右,荧光密写笔荧光波长为447 nm。此外,采用254或365 nm波长对柠檬汁隐性字迹进行紫外反射成像也可有效显现柠檬汁字迹。掩盖字迹的研究中发现,在700～2 500 nm红外波段,走珠笔、记号笔、可擦笔字迹透过率在60%以上,而中性笔字迹透过率在20%以下。因此,采用近红外波段850 nm成像有效显现了百乐走珠笔所覆盖的晨光中性笔字迹。同时,采用LCTF高光谱相机对三类隐性字迹在400～720 nm范围进行步长为5 nm的高光谱成像,并通过SVM分类算法对图像中不同笔迹成分进行同时显现和分类,分类总精度达99.284 4%,Kappa系数达0.959 1。以365 nm波长光源作为激发光进行光致发光成像可有效显现擦除与密写字迹。由于不同墨迹在近红外波段反射率差异较大,近红外成像可以有效显现掩盖字迹。基于LCTF高光谱成像的SVM分类技术可实现不同类别隐性字迹的同时显现与分类,并且有较高的显现效率与分类精度。     

一种完备完全分配格上矩阵方程的求解方法

模糊理论已经在决策、模式识别、故障诊断、过程控制等许多方面得到了广泛应用，在这些应用问题求解中往往要遇到求解模糊关系方程。本文从完备完全分配格的角度给出了一种求解模糊关系方程极小解的完备解法，并用计算机实现了提出的算法，为实际问题求解计算机化打下了基础。     

THE COMPLETE LANGLANDS PARAMETERS CORRESPONDING TO THE REPRESENTATIONS OF THE CLASSICAL GROUPS WITH INTEGRAL REGULAR INFINITESIMAL CHARACTERS

1.CompleteLanglandsParametersandL-PacketsInthissectionwereviewsomebasicfactsfrom[1].Wedenotethesetsofrealnumbers,complexnumbersandintegersbyR,CandZ,respectively.SupposethatGisaconnectedcomplexreductivealgebraicgroup.WehaveanextendedgrouPGrforG,andvGrisanE-groupforGr.WedenotethesetofLanglandsparametersandthesetofgeometricparametersforvGrbYp(vG')andX(VG'),respectively.ThereisanaturalmapfromP(VG')toX(vG').ItinducesabijectionfromequivalenceclassesofLanglandsparameterstogeometricparamet…     

管式炉中半导体激光器巴条Au80Sn20焊料封装研究

为了提高半导体激光器的封装质量和效率,引入管式炉利用夹具进行批量封装。由于封装质量的好坏直接影响半导体激光器的输出特性和使用寿命,利用MOCVD生长808 nm芯片,重点分析了管式炉温度和封装时间对半导体激光器巴条双面金锡封装质量的影响。利用X射线检测、结电压、光电特性参数和smile效应测试手段,确定了管式炉封装半导体激光器巴条的最优封装条件,为以后的产业化提供了指导意义。     

双参数变形玻色湮没算符高次幂的本征态及其量子统计性质

本文构造了双参数变形玻色湮没算符高次幂a^'k(k≥3)的k个正交归一木征态的数学结构,发现它们能构成一个完备的Hilbert空间,并且讨论了它们的量子统计性质.     

基于液面旋转平移法的绝对检验技术研究

绝对检验作为一种光学元件高精度检测方法,其中的两平晶绝对检验无法精确测量平移过程中的倾斜误差,导致恢复的面形中二次项出现偏差.液面在位置变化前后能够保持水平,在旋转平移过程中不会产生倾斜误差.推导了平移过程中倾斜误差和恢复面形中离焦项的关系,并通过仿真分析加以验证,当不存在倾斜误差时,残差面PV值小于1nm.在300m...