Propagation properties of Gaussian beams through cat eye optical lens with center shelter

Based on the method of matrix decomposition and expanding the aperture function into a sum of finite complex Gaussian functions, the analytical propagation equations of Gaussian beams through cat eye optical lens with center shelter are derived. Through numerical calculation, the laws governing the variation of the intensity distribution of the cat eye reflected light with the center shelter ratio and the diameter of the detector at the focal plane are given. The results show that the diffraction series and the intensity of the cat eye reflected light depend strongly on the center shelter ratio. As a further extension, it is found that the eye optical lens can be interpreted as a spatial filter, and different filter effect can be obtained by changing the pinhole size.     

一类非凸区域的拟法锥构造方法及其在非凸规划求解中的应用

本文给出基于球形的一类满足拟法锥条件区域的拟法锥构造方法,基于该可行域的拟法锥,建立求解在该类非凸区域上的规划问题的K-K-T点的部分凝聚同伦组合方程,并证明了该同伦内点法的整体收敛性,给出实现同伦内点法的具体数值跟踪算法步骤,并通过数值例子证明算法是可行的和有效的．     

一种关于汽车整车不确定需求的组合预测模型

提出了一种针对汽车生产企业整车不确定需求的组合预测模型,即利用神经网络拟合数据基本变化趋势,然后对企业产品的市场占有率进行评价,以调节需求变化趋势.应用实例,对模型进行了验证,说明该模型能够较好地诠释企业产品需求信息,具有较好的预测能力.     

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??How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

Conservative finite-difference scheme for the problem of a femtosecond laser pulse with an axially symmetric profile propagating in a medium with cubic nonlinearity

Conservative finite-difference schemes are constructed for the problem of a femtosecond laser pulse propagating in a cubically nonlinear medium in the axially symmetric case with allowance for temporal dispersion of the nonlinear response of the medium. The process is governed by the nonlinear Schrödinger equation involving the time derivative of the nonlinear term. The invariants of the differential problem are presented. It is shown that the difference analogues of these invariants hold for the solution to the finite-difference schemes proposed for the problem. As an example, the numerical results obtained for the self-focusing of a femtosecond light beam are presented.     

一种新型的飞行视觉系统设计

针对电子制造设备中元件拾放的定位对准需求,提出了一种基于半透半反镜的飞行视觉系统设计方案。该方案仅需使用一部摄像机,可分别或同时完成对元件及其安装位的视觉图像采集、对准,并且图像采集、对准过程可与元件拾放过程并行执行,附加的飞行视觉机构不会对拾放操作产生干涉。该系统可有效地提升电子制造装备的工作效率和设备的工作稳定性,且具有结构简单、便于工程实现等优点。     

修整保费——一个新的定价模型

在期望原理保费与个体风险的风险调整保费定价模型的基础上,引入修整系数β,得到了一个组合风险的定价模型—修整保费,从而解决了在大量个体风险并存的保险业务和多项投资中,如何合理地对组合风险进行定价的问题.