一种求解半定规划的邻近外梯度算法

本文提出了一种求解半定规划的邻近外梯度算法.通过转化半定规划的最优性条件为变分不等式,在变分不等式满足单调性和Lipschitz连续的前提下,构造包含原投影区域的半空间,产生邻近点序列来逼近变分不等式的解,简化了投影的求解过程.将该算法应用到教育测评问题中,数值实验结果表明,该方法是解大规模半定规划问题的一种可行方法.     

斜投影-子空间夹角算法快速分析农药中阿维菌素

采用斜投影-子空间夹角算法快速分析农药中阿维菌素的含量。用斜投影算法从阿维菌素对照品中提取阿维菌素B_(1a)纯光谱数据,用子空间夹角判据计算农药中阿维菌素的含量。阿维菌素的质量浓度在4~14μg/mL范围内与用斜投影法提取的阿维菌素B_(1a)纯光谱吸光度呈良好的线性关系,相关系数r=0.9994。斜投影-子空间夹角算法加标回收率在98.80%~101.67%之间,测定结果的相对标准偏差小于2%(n=6)。用该方法与高效液相色谱法对同一样品进行测定,两种方法测定结果相接近,相对误差小于2.20%。该方法满足快速检测农药中阿维菌素含量的分析要求。     

Tunable Liquid Crystal Lens Based on Pretilt Angle Gradient Alignment

The new method of LC lenses fabrication based on innovative alignment material for pretilt angle gradient generation is developed. The alignment layer provides LC lens pretilt angle gradient via two-step treatment: uniform rubbing and gradient nonpolarized UV exposure. LC lens has uniform cell-gap, 2–10 V tunable voltage range. The fabrication method is scalable for lens arrays for two-dimensional/three-dimensional autostereoscopic and light-field displays.     

Heat kernel estimates for the Bessel differential operator in half‐line

In the paper we consider the Bessel differential operator in half‐line , , and its Dirichlet heat kernel . For , by combining analytical and probabilistic methods, we provide sharp two‐sided estimates of the heat kernel for the whole range of the space parameters and every , which complements the recent results given in 1 , where the case was considered.     

应用场光线传递方程计算鱼眼镜头像场像差

应用场光线传递方程,从鱼眼镜头的孔径光阑处,逆向追迹场光线传递方程,确定任意视场角场光线的初始位置,即光阑球差.正向追迹场光线计算鱼眼镜头系统物、像空间视场角之间的关系曲线;用多项式拟合求出关系曲线的解析表达式.通过反演运算,根据畸变图像复原物的图像分布,达到消除鱼眼镜头成像系统畸变的目的.最后,计算了一个160°鱼眼镜头光学系统的光阑球差和图像的畸变,并应用本文方法复原物的图像分布.计算结果表明:光阑球差的计算结果与真值的相对误差小于1%;复原的物方图像径向高度相对误差小于0.25%,说明本文计算鱼眼镜头像场像差的方法是可行的.     

部分相干光在大气湍流中的到达角起伏

研究了部分相干高斯谢尔光束在大气湍流中的到达角起伏.主要采用湍流内外尺度的修正Von Karmon谱模型及广义惠更斯-菲涅尔原理和交叉谱密度函数推导出了部分相干光在大气湍流中的到达角起伏表达式.对比分析了湍流内外尺度、湍流强度、传输距离、源相干参数以及波长等参数对部分相干光在大气湍流水平路径上传输时的到达角起伏的影响.结果表明:随着传输距离的增加,到达角起伏越来越小;随着大气湍流内外尺度和源相干参数的增加,到达角起伏也越来越大;与部分相干光相比,完全相干光的到达角起伏受湍流影响很小;随着波长和湍流强度的减小,到达角起伏越来越小.     

最小偏向角法测三棱镜折射率的相图探究

三棱镜折射率的测量是大学物理实验的重要组成部分,对培养学生的基本实验技能、加深对经典光学理论的理解具有重要作用。本文依据几何光学原理探究了最小偏向角法中在有出射光时最小偏向角与三棱镜顶角、折射率所对应的函数关系,建立了有出射光时入射角、折射率、顶角间以及最小偏向角时折射率、顶角、最小偏向角间的相图,阐明了两相图的物理意义。该研究拓展了三棱镜折射率实验的研究思路。     

基于倒立摆模型的四足机器人对角步态规划

为提高点着地四足机器人在匀速对角小跑过程中的动态稳定性,将对角小跑过程简化为一个倒立摆模型。针对四足机器人对角小跑过程中由于重心无法始终处于支撑对角线上所引起的翻转,在此模型中转换为由于重心引起的摆动角误差。采用虚位移原理对机器人摆动角的变化进行分析,确定不同重心运动变化对摆动角误差的影响并找到合适的重心起始位置,理论上能够使摆动角的误差为零。动态仿真实验验证了所提出的对角步态规划能够使四足机器人实现稳定的对角小跑的有效性。     

Review of non-reactive and reactive wetting of liquids on surfaces

Wettability is a tendency for a liquid to spread on a solid substrate and is generally measured in terms of the angle (contact angle) between the tangent drawn at the triple point between the three phases (solid, liquid and vapour) and the substrate surface. A liquid spreading on a substrate with no reaction/absorption of the liquid by substrate material is known as non-reactive or inert wetting whereas the wetting process influenced by reaction between the spreading liquid and substrate material is known as reactive wetting. Young's equation gives the equilibrium contact angle in terms of interfacial tensions existing at the three-phase interface. The derivation of Young's equation is made under the assumptions of spreading of non-reactive liquid on an ideal (physically and chemically inert, smooth, homogeneous and rigid) solid, a condition that is rarely met in practical situations. Nevertheless Young's equation is the most fundamental starting point for understanding of the complex field of wetting. Reliable and reproducible measurements of contact angle from the experiments are important in order to analyze the wetting behaviour. Various methods have been developed over the years to evaluate wettability of a solid by a liquid. Among these, sessile drop and wetting balance techniques are versatile, popular and provide reliable data. Wetting is affected by large number of factors including liquid properties, substrate properties and system conditions. The effect of these factors on wettability is discussed. Thermodynamic treatment of wetting in inert systems is simple and based on free energy minimization where as that in reactive systems is quite complex. Surface energetics has to be considered while determining the driving force for spreading. Similar is the case of spreading kinetics. Inert systems follow definite flow pattern and in most cases a single function is sufficient to describe the whole kinetics. Theoretical models successfully describe the spreading in inert systems. However, it is difficult to determine the exact mechanism that controls the kinetics since reactive wetting is affected by a number of factors like interfacial reactions, diffusion of constituents, dissolution of the substrate, etc. The quantification of the effect of these interrelated factors on wettability would be useful to build a predictive model of wetting kinetics for reactive systems.