半无限规划与方向导数

本文对半无限凸规划提出一个用方向导数表述的对偶问题，其对偶间隙为零．     

n维广义函数的集值导数

本文将文献［9］中给出的一维广义函数的集值导数的某些结果，推广到n维情形，并给出一些与优化有关的其他结果．     

Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes

Let {X_t} be a Gaussian ARMA process with spectral density f_θ(λ), where θ is an unknown parameter. The problem considered is that of testing a simple hypothesis H:θ = θ₀ against the alternative A:θ ≠ θ₀. For this problem we propose a class of tests , which contains the likelihood ratio (LR), Wald (W), modified Wald (MW) and Rao (R) tests as special cases. Then we derive the χ² type asymptotic expansion of the distribution of T up to order n⁻¹, where n is the sample size. Also we derive the χ² type asymptotic expansion of the distribution of T under the sequence of alternatives A_n: θ = θ₀ + /√n, ε > 0. Then we compare the local powers of the LR, W, MW, and R tests on the basis of their asymptotic expansions.     

温度对涂有溶胶-凝胶多层干涉膜的卤钨灯光谱的影响

本文叙述了两个问题.首先,采用溶胶-凝胶浸渍水解法在H4汽车灯上制备了多层干涉膜.该膜层温度升高使这种灯透过膜层的光谱有所移动,于是引起灯发射光谱的变化.其次,我们研究了温度对膜材料光学性质的影响.     

基于智能手机和Matlab的居家悬滴法表面张力测量实验

本文基于智能手机和Matlab软件设计了一种居家环境下可实现的悬滴法水滴表面张力测量实验.借助智能手机拍照功能获得水滴图像,利用Matlab进行边缘检测及计算,从而得出表面张力系数.对于不同清晰度的情况提出了对应的分析和处理方法,实验结果表明该方法稳定可靠.为后疫情时代开展居家大学物理实验教学提供了一个典型案例.     

矩形截面多量子阱脊形波导模式特性

本文根据多量子阱双折射率的性质,运用有效折射率法分析了矩形截面多量子阱脊形波导E_mn^x模和模E_mn^y的模式特性。     

两水平无重复因析试验散度效应的估计

本文对两水平无重复因析试验给出了散度效应的一种新的估计,称为AMH估计,改进了文献中散度效应的较好的MH估计的一个缺陷,给出并证明了AMH估计的无偏条件,证明了AMH估计比MH估计有更小的方差下界.最后通过模拟试验比较了AMH和MH估计的偏度,方差和均方误差.     

A nonmonotone adaptive trust region method for unconstrained optimization based on conic model

In this paper, we present a nonmonotone adaptive trust region method for unconstrained optimization based on conic model. The new method combines nonmonotone technique and a new way to determine trust region radius at each iteration. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments show that our algorithm is effective.     

一阶微分方程数值解的一种误差估计方法

针对于微分方程数值解,介绍了一种新的误差估计方法.方法证实了伪谱方法具有精度高速度快的优点,进而引出了修正的伪谱方法.     

A reliable algorithm to solve 3D frictional multi-contact problems: Application to granular media

We present in this paper an improved non-smooth Discrete Element Method (DEM) in 3D based on the Non-Smooth Contact Dynamics (NSCD) method. We consider a three-dimensional collection of rigid particles (spheres) during the motion of which contacts can occur or break. The dry friction is modeled by Coulomb’s law which is typically non-associated. The non-associativity of the constitutive law poses numerical challenges. By adopting the use of the bi-potential concept in the framework of the NSCD DEM, a faster and more robust time stepping algorithm with only one predictor-corrector step where the contact and the friction are coupled can be devised. This contrasts with the classical method where contact and friction are treated separately leading to a time stepping algorithm that involves two predictor-corrector steps. The algorithm has been introduced in a 3D version of the NSCD DEM software MULTICOR. Numerical applications will show the robustness of the algorithm and the possibilities of the MULTICOR software for solving three-dimensional problems.