高增益负反馈的幅度稳定系统

 从控制理论的角度对幅度稳定系统进行了研究,提出用黑箱办法,结合实验分析控制对象,确定其数学模型,并依此来设计控制器,以达到在保证环路稳定的基础上提高回路增益的目的。     

A Global Linear and Local Quadratic Continuation Smoothing Method for Variational Inequalities with Box Constraints

In this paper, we propose a continuation method for box constrained variational inequality problems. The continuation method is based on the class of Gabriel-Moré smooth functions and has the following attractive features: It can start from any point; It has a simple and natural neighborhood definition; It solves only one approximate Newton equation at each iteration; It converges globally linearly and locally quadratically under nondegeneracy assumption at the solution point and other suitable assumptions. A hybrid method is also presented, which is shown to preserve the above convergence properties without the nondegeneracy assumption at the solution point. In particular, the hybrid method converges finitely for affine problems.     

On NCP-Functions

In this paper we reformulate several NCP-functions for the nonlinear complementarity problem (NCP) from their merit function forms and study some important properties of these NCP-functions. We point out that some of these NCP-functions have all the nice properties investigated by Chen, Chen and Kanzow [2] for a modified Fischer-Burmeister function, while some other NCP-functions may lose one or several of these properties. We also provide a modified normal map and a smoothing technique to overcome the limitation of these NCP-functions. A numerical comparison for the behaviour of various NCP-functions is provided.     

投影映射的一种光滑函数

在只增加一维松弛变量的情况下,利用熵函数给出了投影映射ΠX(x)的一种新的可计算的光滑逼近函数y(ε,x),并证明了y(ε,x)的单调性、导数对称半正定性和一致收敛性.     

基于束间动态干涉的快速匀滑新方法

针对高功率激光装置中靶面辐照均匀性的高要求,提出了一种利用束间动态干涉改善辐照均匀性的快速匀滑方法.基本原理是利用共轭相位板阵列对存在一定波长差的多束激光附加相位调制,从而使各子束在远场两两相干叠加以产生动态的干涉图样,进而引起焦斑内部散斑的动态扫动,在ps时间内抹平不均匀性.以典型惯性约束聚变装置中的激光集束为例,通过建立基于束间动态干涉的快速匀滑物理模型,定量分析了相位板类型、相位调制幅度和束间波长差等因素对焦斑动态干涉图样的影响及规律,进而对其束匀滑特性进行了讨论.结果表明,基于束间动态干涉的快速匀滑方法可以有效地实现多方向、多维度的焦斑内部散斑快速扫动,且通过与传统束匀滑技术的联用,可以在更短的时间内达到更好的焦斑均匀性.     

基于激光诱导荧光的油类污染物检测系统研究

油类污染物具有破坏海洋生态系统和间接污染大气及土壤的危害,快速、准确地检测污染物的成分及其浓度具有重要意义。由于油类污染物光谱重叠严重,因此难以通过传统荧光分析准确加以区分。本文基于激光诱导荧光技术,以氙灯作为激发光设计荧光光谱检测系统,并对0#柴油、92#汽油和煤油进行扫描和检测,从而获得激发/发射光谱以及最佳激发/发射波长。并对该系统的软件算法部分进行改进,运用Savitzky-Golay卷积平滑直接获得更加精确的激发/发射光谱,更能全面、准确地反映油类物质的荧光特性信息。并与传统的荧光光谱仪得到的光谱图进行对比,经实验验证激光诱导荧光技术的荧光光谱检测系统的有效性,对油类污染物的荧光光谱信号的检测具有更高的灵敏度。     

求解浅水方程的光滑粒子流体动力学法

文章将光滑粒子流体动力学(SPH)法应用于浅水方程,针对传统SPH法中存在的边界缺陷问题,引入了一种处理边界条件的方法,即虚粒子法,对一维溃坝问题进行模拟,并将所得结果与用有限差分法等数值方法得到的结果相比较,结果表明SPH法能够捕捉到水坝崩溃后的激波现象,并且所得图像较为平滑,在间断处也较为锐利。     

Local smoothing of uniformly smooth maps

We solve the problem on the uniform approximation of uniformly continuous (smooth) maps by maps having the maximum possible local and uniform smoothness. In particular, we prove that each uniformly continuous map of the Hilbert space l ₂ into itself can be approximated by locally infinitely differentiable maps having a Lipschitz derivative.     

Mollification formulas and implicit smoothing

This paper develops some mollification formulas involving convolutions between popular radial basis function (RBF) basic functions Φ, and suitable mollifiers. Polyharmonic splines, scaled Bessel kernels (Matern functions) and compactly supported basic functions are considered. A typical result is that in ℛ^d the convolution of |{•}|^β and (•²+c ²)^−(β+2d)/2 is the generalized multiquadric (•²+c ²)^β/2 up to a multiplicative constant. The constant depends on c>0, β, where ℜ(β)>−d, and d. An application which motivated the development of the formulas is a technique called implicit smoothing. This computationally efficient technique smooths a previously obtained RBF fit by replacing the basic function Φ with a smoother version Ψ during evaluation.     

An analytical solution for electromagnetic wave scattering by multiple wedges

In this work an analytical solution to the problem of electromagnetic wave diffraction by multiple coplanar wedges is found by means of an infinite-order discrete superposition of non-integer cylindrical waves, i.e. products of a non-integer order Bessel function times an exponential factor. The evaluation of the expansion coefficients is accomplished by imposing the boundary conditions on every side of the geometry; the corresponding equations are solved in a ‘weak form’, i.e. by representing the dependence of the boundary fields with respect to the radial abscissa in terms of an expansion over a set of Laguerre orthogonal polynomials. A detailed study is carried out for estimating accuracy performances relevant to the finite-order numerical implementation of the method.