On the convergence of <Emphasis Type="Italic">s</Emphasis>-dependent GFR conjugate gradient method for unconstrained optimization

In this paper, the authors present an s-dependent conjugate gradient method for unconstrained optimization problem and make two different kinds of estimations of upper bounds of β _k with respect to \(\beta_{k}^{\mathrm{FR}}\) which are called dependent ratio. The global convergence of s-dependent GFR conjugate gradient method using several step-size rules is obtained.     

基于简单二次函数模型的带线搜索的信赖域算法

基于简单二次函数模型, 结合非精确大步长Armijo线搜索技术, 建立了一个新的求解无约束最优化问题的组合信赖域与线搜索算法, 证明了算法的全局收敛性. 数值例子表明算法是有效的, 适合求解大规模问题.       

Skin Thickness and β-Crystals Development in Injection-Molded iPP Along the Flow Direction

In this study, iPP was injection molded at 180°C, 200°C, and 220°C. According to polarization optical microscopy (POM) results, for a given part, the skin thickness steadily decreases along the flow direction. However, at the same distance from the gate, the skin thickness of the parts molded at lower melt temperature is larger than that molded at higher melt temperature. It is found that flow time (here, the time taken for melt to pass the specific position along the flow direction) and melt temperature are two significant factors leading to this phenomenon, while the gate size is another one.

The DSC and WAXD results show that the relative fraction of β-form crystals, for a specific part, decreases along the flow direction, which is mainly determined by flow time. However, for the parts molded at different molding temperatures, the fraction of the β-form crystals is mainly determined by the molding temperature, though this influence is very complex.     

基于无人机探测大柴旦地区近地层气溶胶特征

通过改装多旋翼无人机（UAV）和搭载各类载荷以及联合地基观测设备对大柴旦地区大气、环境以及气溶胶参数进行测量。利用获得的数据资料，对该地区近地层气溶胶粒子数浓度（即单位体积空气中气溶胶粒子的数目）、消光系数以及气象要素等特征进行了分析。结果表明，在大柴旦地区，近地层气溶胶粒子数浓度日变化显著，呈现双峰形态，气溶胶粒子数浓度的变化范围为75～220 cm^-3,消光系数的变化范围为0.004～0.038 km^-1;当风速小于6 m/s时，气溶胶粒子数浓度与风速呈负相关关系；当风速大于6 m/s时，二者呈正相关关系；相对湿度对气溶胶粒子的影响较小，这可能是由于该地区以沙尘型气溶胶为主，吸湿性较弱。本研究基于多旋翼无人机探测平台，可以有效地获得近地层精细化大气、环境结构，有助于研究人员了解该地区气溶胶的结构、变化特征以及建立气溶胶模式，同时也为气溶胶及大气环境参数探测方法提供了技术支撑及思路拓展。     

Rigidity of compact manifolds with boundary and nonnegative Ricci curvature

Let be an ()-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary . Assume that the principal curvatures of are bounded from below by a positive constant . In this paper, we prove that the first nonzero eigenvalue of the Laplacian of acting on functions on satisfies with equality holding if and only if is isometric to an -dimensional Euclidean ball of radius . Some related rigidity theorems for are also proved.

     

半结晶聚合物注射成型中结晶动力学的数值模拟

对半结晶聚合物注射成型过程及其结晶过程进行偶合模拟,分析了二者的相互影响.具体是在注射成型数值模拟中考虑结晶动力学效应,分别在本构方程、能量方程及材料物性参数方程中引入反映结晶效应的参数;同时在结晶动力学计算中考虑流动诱导效应,从能量的角度提出并使用修正的动力学模型,用材料流动过程的耗散能表征流动对结晶的影响.通过对等规聚丙烯(iPP)和聚对苯二甲酸乙二醇酯(PET)两种半结晶聚合物注射过程模拟结果的分析比较,证实成型过程具有加速结晶的作用.同时,材料的结晶也对注射成型加工过程,尤其是保压与冷却过程的温度场分布有较大的影响.     

半无限规划问题的一个有效解法

1．引言在计算机辅助设计和工程设计中,经常遇到下面的两类优化问题1,2］．1．无约束半无限极大极小问题．其中外x）二——x。。Im。x。。。Yi夕（x;N）这里J二（】,2,·,｝对任何7E八岁：R－xR”。＋R是连续可微的函数,X是R”。中的一个紧子集,且VYj）一O,这里问h）表示X体积．2．约束半无限代化问题．其中I一（1,2,·．小记L二《0｝UI对任何jCL冲’（x）一max。。。Yi夕（x,yi）·这里拉：PX＊n＋R是连续可微函数,X是”。中的一个紧子集,且NU）一0·注．设Y（Z,一二切EyW一叫卜4．今后对本文用到的紧子集地做…     

Saddle Points Theory of Two Classes of Augmented Lagrangians and Its Applications to Generalized Semi-infinite Programming

In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle points is that we do not need the uniqueness of the optimal solution. Furthermore, we show that the existence of global saddle points is a necessary and sufficient condition for the exact penalty representation in the framework of augmented Lagrangians. Based on these, we convert a class of generalized semi-infinite programming problems into standard semi-infinite programming problems via augmented Lagrangians. Some new first-order optimality conditions are also discussed. This research was supported by the National Natural Science Foundation of P.R. China (Grant No. 10571106 and No. 10701047).     

由Bezier曲线构造的聚合物熔体剪切黏度模型

为提高聚合物熔体剪切黏度模型的描述精度,提出了一个基于二次Bezier 曲线的黏度模型. 模型采用分段函数描述,在对数坐标系中,低剪切速率时的牛顿区和高剪切速率时的幂律区采用线性函数,介于二者之间的过渡区采用二次Bezier 曲线. 通过牛顿区和幂律区的直线延长线构造Bezier 曲线的控制多边形,从而保证三段曲线的光滑过渡. 模型可以明确给出任意温度下低剪切速率时牛顿区的结束点,以及高剪切速率时幂律区的开始点. 拟合算例表明,所提出模型的拟合精度明显高于Cross-Arrhenius 黏度模型.