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.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

针对连续变化法测定络合物稳定常数实验中可能出现的设计缺陷的讨论

连续变化法测定络合物组成和稳定常数是大学化学中的经典学生实验。但针对1：2和1：3的络合反应，实验教科书的设计中可能出现数据点过少也就是溶液配制过少的问题。如果按照要求配制溶液，由于没有完全反应的混合溶液，而其他混合溶液给出的数据又都呈良好的线性，就缺少了用来估算曲线的数据点，结果是，将没有足够的数据对稳定常数进行估算。对这种可能出现的数据点过少的实验设计的原因、结果和解决方法进行了探讨。     

Ultra high performance liquid chromatography-quadrupole-time of flight analysis for the identification and the determination of resveratrol and its metabolites in mouse plasma

Resveratrol is a polyphenol that has numerous interesting biological properties, but, per os, it is quickly metabolized. Some of its metabolites are more concentrated than resveratrol, may have greater biological activities, and may act as a kind of store for resveratrol. Thus, to understand the biological impact of resveratrol on a physiological system, it is crucial to simultaneously analyze resveratrol and its metabolites in plasma. This study presents an analytical method based on UHPLC-Q-TOF mass spectrometry for the quantification of resveratrol and of its most common hydrophilic metabolites. The use of ¹³C- and D-labeled standards specific to each molecule led to a linear calibration curve on a larger concentration range than described previously. The use of high resolution mass spectrometry in the full scan mode enabled simultaneous identification and quantification of some hydrophilic metabolites not previously described in mice. In addition, UHPLC separation, allowing run times lower than 10 min, can be used in studies that requiring analysis of many samples.     

锂离子电池正极材料LiNi0.5Mn1.5O4金属掺杂的第一性原理研究

近来尖晶石相LiNi0.5Mn1.5O4被认为是一种有前景的二次锂离子电池正极材料.但是其相对较差的循环性能和倍率性能限制了LiNi0.5Mn1.5O4的大规模应用.金属掺杂被认为是一种提高其电化学性能的有效方法.然而,还急需深层次地理解掺杂对材料结构和电化学性质的影响.采用第一性原理方法,系统地研究了金属掺杂的LiM0.125Ni0.375Mn1.5O4(M为Cr,Fe和Co)电极体系的结构与电子性质.计算结果显示,少量的过渡金属M取代LiNi0.5Mn1.5O4晶格中的Ni,能够有效抑制材料在电化学脱嵌锂过程中的体积变化(从锂化相到脱锂相,体积变化率约为4%,而未掺杂的情况为4.7%),提高材料循环性能.体系态密度表明金属掺杂能够减小体系的带隙,进而提高材料的电子传导.另外,通过Li离子的扩散计算,我们发现与未掺杂的LiNi0.5Mn1.5O4相比,Co掺杂使得Li在材料中两条不同扩散路径的扩散能垒分别降低了约90 meV和140 meV,表明Co掺杂有利于Li在材料中的快速扩散.     

Dimensional considerations on the mechanical properties of 3D printed polymer parts

Additive manufacturing offers a useful and accessible tool for prototyping and manufacturing small volume functional parts. Polylactic acid (PLA) and thermoplastic polyurethane (TPU) are amongst the most commonly used materials. Characterising 3D printed PLA and TPU is potentially important for both designing and finite element modelling of functional parts. This work explores the mechanical properties of additively manufactured PLA/TPU specimens with consideration to design parameters including size, and infill percentage. PLA/TPU specimens are 3D-printed in selected ISO standard geometries with 20%, 60%, 100% infill percentage. Tensile and compression test results suggest that traditional ISO testing standards might be insufficient in characterising 3D printed materials for finite element modelling or application purposes. Infill percentage in combination to design size, may significantly affect the mechanical performance of 3D printed parts. Dimensional variation may cause inhomogeneity in mechanical properties between large and small cross section areas of the same part. The effect was reduced in small cross section parts where reducing the nominal infill had less effect on the resulting specimens. The results suggest that for 3D printed functional parts with significant dimensional differences between sections, the material properties are not necessarily homogeneous. This consideration may be significant for designers using 3D printing for applications, which include mechanical loading.     

低压闪蒸液滴形态和温度变化的研究

将液滴在常压下突然置于低压环境中,液滴由最初的平衡状态变成过热状态,发生闪蒸.本文实验研究了低压闪蒸液滴内部形态和温度的变化,系统描述了液滴闪蒸过程中的各种形态变化,总结了稳态闪蒸和稳态结冰过程中环境压力和初始温度对温度变化的影响.实验结果表明液滴闪蒸分六种形态.稳态闪蒸中环境压力越低,液滴的最终温度也越低;液滴的初始温度越高,降到最低温度的时间越长.稳态结冰过程中,液滴初始温度增加,液滴结冰温度和结冰回升最高温度也随之增加;液滴的结冰温度和回升最高温度随环境压力的增高而减小.     

大角带宽高衍射效率体全息光栅的设计和制备

高性能体全息光栅是全息波导的重要耦合元件,角带宽小、平均衍射效率不高是制约体全息光栅性能的重要因素.以不对称倾斜记录为出发点,设计并制备了大角带宽高衍射效率的体全息光栅.首先讨论在横电模式光和横磁模式光下体全息光栅的记录参数与其衍射效率的关系,找到平均衍射效率较高的记录参数范围,随后进一步分析在此范围内的记录参数与体全...