一类非线性常微分方程振荡解的渐近表示

在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示．在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程．当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简．     

理论研究电流注入对垂直腔面发射激光器多横模行为的影响

从包含时空变量的速率方程出发,针对弱折射率导引垂直腔面发射激光器(VCSELs),利用空间积分法分析了典型电注入参数对VCSELs多横模行为的影响,在不降低模型准确性的前提下提高了仿真效率。仿真结果表明,注入盘孔径和注入环越小、注入强度越低以及电流扩散越弱时,VCSELs更易实现单横模工作;反之,VCSELs高阶横模开始出现并呈现较强的模式竞争,引发了载流子空间烧孔效应,并导致基模强度降低。进一步得出,在环形注入方式下,高阶模式更容易出现且彼此间的竞争较盘形注入时强。     

一类Marangoni对流边界层方程的近似解析解

利用Adomain解析拆分和Padé逼近方法对由Marangoni对流诱发的层流边界层问题进行了研究, 提供了一种求解边界层方程的解析分析方法. 得到了问题的近似解析解并对相应的流动及传热特性进行了探讨. 本文所提出的思想方法可以用于解决其他科学和工程技术问题. 关键词： Marangoni对流 非线性 Adomain拆分法 近似解析解     

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

On a nonlinear multigrid algorithm with primal relaxation for the image total variation minimisation

Digital image restoration has drawn much attention in the recent years and a lot of research has been done on effective variational partial differential equation models and their theoretical studies. However there remains an urgent need to develop fast and robust iterative solvers, as the underlying problem sizes are large. This paper proposes a fast multigrid method using primal relaxations. The basic primal relaxation is known to get stuck at a ‘local’ non-stationary minimum of the solution, which is usually believed to be ‘non-smooth’. Our idea is to utilize coarse level corrections, overcoming the deadlock of a basic primal relaxation scheme. A further refinement is to allow non-regular coarse levels to correct the solution, which helps to improve the multilevel method. Numerical experiments on both 1D and 2D images are presented.     

多元线性回归应用于近代物理实验

本文介绍非线性方程转化直线性方程和多元线性回归法来分析近代物理实验中塞曼效应分裂干涉圆环多处选点测量的处理过程。     

厚胶光刻非线性畸变的校正

利用厚胶光刻技术制作大深度微结构元件是一种有效的途径,但厚胶光刻过程中的非线性畸变对光刻面形质量的严重影响限制了该技术的应用,基于此,提出了一种对掩模透射率函数进行校正的方法。分析空间像形成及其在光刻胶内传递、曝光、显影等过程中非线性因素的影响,利用模拟退火算法对掩模透射率函数进行校正,以提高光刻面形质量,并以凹面柱透镜为例,给出了校正前后的显影轮廓模拟结果,其校正后浮雕面形的体积偏差仅为2.63%。该方法在有效改善面形质量的同时,并没有引起掩模的设计、制作难度及费用增加,这对于设计、制作高质量的微结构元件有重要意义。     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

脑细胞激活素药物的化学成分分析

采用日本岛津LC-60A型高压液相色谱仪和美国P-E3030型原子吸收分光光度计，对该药进行了氨基酸、维生素和化学元素的含量测定。结果表明，该药含有18种氨基酸，不少于3种维生素和20几种化学元素，为进一步改进该药物的合理配制方法和临床应用提供了参考数据。     

在CPM非稳腔Nd:YAG激光器中用被—被动锁模方法选单脉冲的探讨

在CPM Nd:YAG非稳腔激光器中,我们使用透过率较大的可饱和吸收体使单脉冲序列中的脉冲个数减少到3—5个,在输出的单序列中再使用非线性介质进行处理,可以得到比较接近的单脉冲输出。