Determination of the Catalytic Sites for Ziegler‐Natta Homo‐Polymerization from GPC Data

Deconvolution of the MWD of a polymer produced by multi‐site catalysts into independent Flory modes is the first step in modeling the polymerization process. A new deconvolution procedure for GPC data is developed that does not require an a priori assumption concerning the nature of the discrete distribution and can be used with a continuous distribution. The MWD measured via GPC is a linear function of the individual catalytic sites, but it is numerically ill‐conditioned, preventing direct inversion of the GPC data. Tikhonov regularization has been developed to uniquely invert the MWD. Applying the regularizing method to a polyethylene produced via a Ziegler‐Natta catalyst, seven discrete sites were found, and the kinetic constant ratios were determined for each of these sites.

     

A combined BDF‐semismooth Newton approach for time‐dependent Bingham flow

This article is devoted to the numerical simulation of time‐dependent convective Bingham flow in cavities. Motivated by a primal‐dual regularization of the stationary model, a family of regularized time‐dependent problems is introduced. Well posedness of the regularized problems is proved, and convergence of the regularized solutions to a solution of the original multiplier system is verified. For the numerical solution of each regularized multiplier system, a fully discrete approach is studied. A stable finite element approximation in space together with a second‐order backward differentiation formula for the time discretization are proposed. The discretization scheme yields a system of Newton differentiable nonlinear equations in each time step, for which a semismooth Newton algorithm is used. We present two numerical experiments to verify the main properties of the proposed approach. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

A log-exponential smoothing method for mathematical programs with complementarity constraints

In this paper a log-exponential smoothing method for mathematical programs with complementarity constraints (MPCC) is analyzed, with some new interesting properties and convergence results provided. It is shown that the stationary points of the resulting smoothed problem converge to the strongly stationary point of MPCC, under the linear independence constraint qualification (LICQ), the weak second-order necessary condition (WSONC), and some reasonable assumption. Moreover, the limit point satisfies the weak second-order necessary condition for MPCC. A notable fact is that the proposed convergence results do not restrict the complementarity constraint functions approach to zero at the same order of magnitude.     

L1正则化Logistic回归在财务预警中的应用

线性模型和广义线性模型已广泛地用于社会经济、生产实践和科学研究中的数据分析和数据挖掘等领域,如公司财务预警,引入L1范数惩罚技术的模型在估计模型系数的同时能实现变量选择的功能,本文将L1范数正则化Logistic回归模型用于上市公司财务危机预报,结合沪深股市制造业ST公司和正常公司的T-2年财务数据开展实证研究,舛比Logistic回归和L2正则化Logistic回归模型进行对比分析.实验结果表明L1正则化Logistic回归模型的有效性,其在保证模型预测精度的同时提高模型的解释性.     

正则化回归算法的快速学习率

本文讨论了再生核Hilbert 空间上一类广泛的正则化回归算法的学习率问题. 在分析算法的样本误差时, 我们利用了一种复加权的经验过程, 保证了方差与惩罚泛函同时被阈值控制, 从而避免了繁琐的迭代过程. 本文得到了比之前文献结果更为快速的学习率.     

Nuclear norm-regularized SENSE reconstruction

SENSitivity Encoding (SENSE) is a mathematically optimal parallel magnetic resonance (MRI) imaging technique when the coil sensitivities are known. In recent times, compressed sensing (CS)-based techniques are incorporated within the SENSE reconstruction framework to recover the underlying MR image. CS-based techniques exploit the fact that the MR images are sparse in a transform domain (e.g., wavelets). Mathematically, this leads to an l(1)-norm-regularized SENSE reconstruction. In this work, we show that instead of reconstructing the image by exploiting its transform domain sparsity, we can exploit its rank deficiency to reconstruct it. This leads to a nuclear norm-regularized SENSE problem. The reconstruction accuracy from our proposed method is the same as the l(1)-norm-regularized SENSE, but the advantage of our method is that it is about an order of magnitude faster.     

零像散宽波段平场全息凹面光栅的优化设计

平场全息凹面光栅的理想像面应为一平面,此时子午焦线与弧矢焦线均位于像面内且彼此重合,形成接近理想像点的光谱像。但子午焦线总是存在弯曲,只有弧矢焦线在满足一定条件的情况下可以成为直线。鉴于此,提出一种满足平场弧矢焦线条件的平场全息凹面光栅设计方法。利用光学设计软件ZEMAX研究了运用此方法设计的零像散光栅的成像特性,并与原有设计方法得到的结果进行比较。模拟结果显示,满足平场弧矢焦线条件的光栅能够达到与原有方法所设计光栅相当的光谱分辨率,而其全波段零像散特性使其拥有更加出色的弧矢方向聚焦性能,显著提高平场光谱仪的信噪比。     

小型宽波段凹面全息光栅单色仪的优化设计

随着户外物性分析实验的日渐增多,开发轻小型、便携式,且响应波段范围宽的光谱仪器的需求越来越迫切。根据凹面全息光栅均方根优化理论,设计了一款轻小型宽波段单色仪。该单色仪主要由三块IV型凹面全息光栅和上下两层可旋转的平台组成,三块光栅对称地固定于上层平台上,由一台步进电机带动上层平台旋转实现光栅之间的切换,另一台步进电机带动下层平台旋转实现单块光栅的扫描。三块光栅的响应波长范围分别为400～1000,1000～1700和1700～2500nm,其理论分辨极限分别优于2.5,2.8和4.0nm。并对三块光栅的制作误差和双层平台结构误差进行了分析,结果表明,在能够保证的误差范围内,该单色仪的光谱质量可以较好地满足户外光谱分析的要求。     

大气廓线参数反演中基于大气可反演指数的正 则化参数选择方法

以大气可反演指数为指标, 采用Nelder-Mead单纯形法求解方法, 提出了一种卫星遥感资料反演大气廓线算法中动态的正则化参数选择方案. 同时针对四条典型区域廓线, 进行了选择试验. 从选择结果看, 不同廓线所对应的最优正则化参数变化幅度非常小, 因此在实际反演过程中, 为提高计算效率, 可近似取正则化参数为固定值. 这为利用卫星遥感资料进行大气廓线反演问题中正则化参数的选择提供了一种可借鉴的方法.     

Inversion algorithm based on the generalized objective functional for compressed sensing

Owing to providing a novel insight for signal and image processing, compressed sensing (CS) has attracted increasing attention. The accuracy of the reconstruction algorithms plays an important role in real applications of the CS theory. In this paper, a generalized reconstruction model that simultaneously considers the inaccuracies on the measurement matrix and the measurement data is proposed for CS reconstruction. A generalized objective functional, which integrates the advantages of the least squares (LSs) estimation and the combinational M-estimation, is proposed. An iterative scheme that integrates the merits of the homotopy method and the artificial physics optimization (APO) algorithm is developed for solving the proposed objective functional. Numerical simulations are implemented to evaluate the feasibility and effectiveness of the proposed algorithm. For the cases simulated in this paper, the reconstruction accuracy is improved, which indicates that the proposed algorithm is successful in solving CS inverse problems.