Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Densitometry and indirect normal‐phase HPTLC–ESI–MS for separation and quantitation of drugs and their glucuronide metabolites from plasma

The present work describes novel methods using densitometry and indirect or off‐line high performance thin‐layer chromatography–mass spectrometry (HPTLC–MS) for the simultaneous detection and quantification of asenapine, propranolol and telmisartan and their phase II glucuronide metabolites. After chromatographic separation of the drugs and their metabolites the analytes were scraped, extracted in methanol and concentrated prior to mass spectrometric analysis. Different combinations of toluene and methanol–ethanol–n‐butanol–iso‐propanol were tested for analyte separation and the best results were obtained using toluene–methanol–ammonia (6.9:3.0:0.1, v/v/v) as the elution solvent. All of the drug–metabolite pairs were separated with a homologous retardation factor difference of ≥22. The conventional densitometric approach was also studied and the method performances were compared. Both of the approaches were validated following the International Conference on Harmonization guidelines, and applied to spiked human plasma samples. The major advantage of the TLC–MS approach is that it can provide much lower limits of detection (1.98–5.83 pg/band) and limit of quantitation (5.97–17.63 pg/band) with good precision (?3.0% coefficient of variation) compared with TLC–densitometry. The proposed indirect HPTLC–MS method is simple yet effective and has tremendous potential in the separation and quantitation of drugs and their metabolites from biological samples, especially for clinical studies.     

100kV直流高温超导电缆终端应力锥设计

本文提出了一种新的单直线应力锥设计方法,根据PPLP材料的绝缘特性,结合超导电缆的本体尺寸和设计电压,给出了增饶绝缘厚度和应力锥轴向长度的设计数据,其中增饶绝缘厚度为3.5 mm,应力锥轴向长度为38.5 mm,并对单直线应力锥进行电场数值分析,结果表明,所设计的单直线应力锥满足100 kV直流高温超导电缆运行要求。     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

A review of mobility metrics for next generation vehicle mobility models

In the United States, the NATO Reference Mobility Model (NRMM) has been used for evaluating military ground vehicle mobility and the Vehicle Cone Index (VCI) has been selected as a mobility metric. VCI represents the minimum soil strength required for a vehicle to consistently make a specific number of passes, usually one or fifty passes. In the United Kingdom, the Mean Maximum Pressure (MMP) has been adopted as a metric for assessing military vehicle cross-country mobility. MMP is the mean value of the maxima occurring under all the wheel stations of a vehicle. Both VCI and MMP are empirically based. This paper presents a review of the basis upon which VCI and MMP were developed, as well as their applications to evaluating vehicle mobility in practice. With the progress in terramechanics and in modelling and simulation techniques in recent years, there is a growing desire to develop physics-based mobility metrics for next generation vehicle mobility models. Based on the review, criteria for selecting physics-based mobility metrics are proposed. Following these criteria, metrics for characterizing military vehicle traction limits and traversability on a given operating area are recommended.     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

Goos-Hänchen and Imbert-Fedorov shifts in tilted Weyl semimetals

We establish the beam models of Goos-Hänchen (GH) and Imbert-Fedorov (IF) effects in tilted Weyl semimetals (WSMs), and systematically study the influences of Weyl cone tilting and chemical potential on the GH and IF shifts at a certain photon energy 1.96 eV. It is found that the GH and IF shifts in tilted type-I and type-Ⅱ WSMs are both almost symmetric about the Weyl cone tilting. Meanwhile, the GH and IF shifts in type-I WSMs almost do not change with the tilt degree of Weyl cones, while those in type-Ⅱ WSMs are extremely dependent on tilt degree. These trends are mainly due to the nearly symmetric distribution of WSMs conductivities, where the conductivities keep stable in type-I WSMs and gradually decrease with tilt degree in type-Ⅱ WSMs. By adjusting the chemical potential, the boundary between type-I and type-Ⅱ WSMs widens, and the dependence of the beam shifts on the tilt degree can be manipulated. Furthermore, by extending the relevant discussions to a wider frequency band, the peak fluctuation of GH shifts and the decrease of IF shifts occur gradually as the frequency increases, and the performance of beam shifts at photon energy 1.96 eV is equally suitable for other photon frequencies. The above findings provide a new reference for revisiting the beam shifts in tilted WSMs and determining the types of WSMs.     

师范类专业认证下地方高校化学专业人才培养模式研究*

专业认证是保障高等教育质量和持续发展的重要手段。基于师范专业认证标准,化学专业人才培养过程中存在培养目标不清晰、课程设置不合理及教学评价不规范等问题。结合OBE教育理念,通过构建“模块化”的课程体系,建立“三层次、四阶段、多环节”的教学质量保障体系和“三位一体”协同育人机制,探索了适应地方高校化学专业的人才培养模式,以提高人才培养质量。     

The PyPES library of high quality semi‐global potential energy surfaces

In this article, we present a Python‐based library of high quality semi‐global potential energy surfaces for 50 polyatomic molecules with up to six atoms. We anticipate that these surfaces will find widespread application in the testing of new potential energy surface construction algorithms and nuclear ro‐vibrational structure theories. To this end, we provide the ability to generate the energy derivatives required for Taylor series expansions to sixth order about any point on the potential energy surface in a range of common coordinate systems, including curvilinear internal, Cartesian, and normal mode coordinates. The PyPES package, along with FORTRAN, C, MATLAB and Mathematica wrappers, is available at http://sourceforge.net/projects/pypes-lib . © 2015 Wiley Periodicals, Inc.     

师范专业认证背景下无机化学课程教学改革探索*

以北京师范大学化学专业的无机化学课程改革为例,从教学内容、教学方法、课程考核等方面探讨无机化学课程优化和改革。明确教学目标,提升教学质量,达成化学(师范)专业的毕业要求,全面提升学生的思想政治素养、专业知识技能和教育情怀。