A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook

Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s ₁ψ₁ summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares. Dedicated to Richard Askey on the occasion of his 70th birthday. 2000 Mathematics Subject Classification Primary—33D15 B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency. A. J. Yee: Research partially supported by a grant from The Number Theory Foundation.     

光纤光栅反射谱对非均匀应变的展宽响应

光纤布拉格光栅在非均匀应力场作用下，其纤芯折射率及光栅栅距都将产生非均匀变化，本文给出了光纤光栅与非均匀应变场的相互作用模型，建立了反射谱对非均匀应变的响应关系。并给出了线性应力场的实验结果。     

一种全场三维共焦检测的新方法

提出了一种利用微光学阵更合成器件实现全场三维面形并行检测、记录的共焦方法。此方法的关键是，在共焦系统中引入一一微光学耻列合成器件来产生一点光源阵列，实现了对同一一剖面同时并行检测，并首次采用了ＣＣＤ面阵像元取代上孔光阑直接截取三维信息光强。本文讨论了该方法的三信息检测原理，响应关系，给出了初步的实验结果和三维重构图。     

钽酸锂、蓝宝石在高压下的光学性质从头算研究

采用量子力学从头算和赝势平面波基组以及非局域广义梯度近似(PP-GGA)方法对两种光学窗口材料(单晶LiTaO3和蓝宝石α-Al2O3)在0~250 GPa静水压力范围内的光学透明性进行了研究.结果表明,随着压力的增加蓝宝石和钽酸锂的最大吸收峰位置均向低波长区移动(蓝移).蓝宝石在0~250 GPa压力下,可见光范围内一直保持其透明性,而LiTaO3则在高压下时就变得不透明了,其原因是钽酸锂的前沿能带闭合而导致其吸收带宽随外界压力的增大变宽所致.     

三维裂纹体应力强度因子的计算

本文采用塌缩三棱柱形奇异单元的位移计算应力强度因子，给出了一个新的全三维外推公式，它是Ｃｈｅｎ和Ｋｕａｎｇ公式〔１３〕的全三维推广，特例证明，它的精度比Ｉｎ－ｇｒａｆｆｅａ和Ｍａｎｕ的公式〔８〕高一阶。数值计算表明，结果稳定和对单元尺寸改变不敏感     

The Onset of Convection in an Inclined Anisotropic Porous Layer with Oblique Principle Axes

We consider the onset of convection in an inclined anisotropic porous layer heated from below. To date the principle axes of the permeability and diffusivity tensors have been assumed to be aligned with the coordinate directions. Therefore particular emphasis is laid upon how the basic flow and criteria for the onset of convection are altered by the presence of oblique principle axes. When these axes are not aligned with the coordinate directions and when the ratios of the principle permeabilities or diffusivities are not too large or too small, we find that there is always a smooth transition in the orientation of the most dangerous mode of instability as the inclination increases from the horizontal. In more extreme cases there may be sudden changes in the orientation, Darcy–Rayleigh number and wavenumber.     

三轴运动模拟转台的结构对称性与动力学计算

本文给出了三轴运动模拟转台动力学相互作用的计算公式，并讨论了它的结构对称性问题。     

三轴模拟台的交叉耦合及其控制方法的研究

本文主要从三轴转台的模型出发，研究了采用状态反馈的最优控制及状态观测器来提高控制系统的自适应能力，以解决三轴台特有的不确定非线性耦合问题和变结构解耦控制。     

等达因图象的自动采集与识别

文中提出了一种机机械扫描系统．小功率激光器、图象板、相移元件、微机和程序软件组成的等达因图象自动采集与处理系统，用灰度值比较的思想实现了等达因图象的跟踪采集。提出了四幅图象相移法实现等达因图象的自动识别。系统能快速、实时、精确和全自动地实现等达因图象的记录和分析。给出与物体内各点应力状态一一对应的位相图。并用来研究了其他实验方法困难的局部三维效应问题。     

A STRESS VECTOR-BASED CONSTITUTIVE MODEL FOR COHESIONLESS SOIL (Ⅱ)-APPLICATION

The stress vector-based constitutive model for cohesionless soil, proposed by SHI Hong-yan et al., was applied to analyze the deformation behaviors of materials subjected to various stress paths. The result of analysis shows that the constitutive model can capture well the main deformation behavior of cohesionless soil, such as stress-strain nonlinearity, hardening property, dilatancy, stress path dependency, non-coaxiality between the principal stress and the principal strain increment directions, and the coupling of mean effective and deviatoric stress with deformation. In addition, the model can also take into account the rotation of principal stress axes and the influence of intermediate principal stress on deformation and strength of soil simultaneously. The excellent agreement between the predicted and measured behavior indicates the comprehensive applicability of the model. Biography: SHI Hong-yan (1962-), Associate Professor, Doctor