On the numerical solution of ill‐conditioned linear systems by regularization and iteration

We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning.     

Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000.     

增材制造金属反射镜的发展综述

随着光学测量与遥感领域的不断发展,折反式光学系统对重量、体积和环境适应性等需求不断提高。基于增材制造技术的金属反射镜以其便于实现优化设计、快速制造和加工工艺性好等优点,逐渐获得国内外学者的关注与研究。与传统金属反射镜相比,增材制造金属反射镜可以提高反射镜的结构刚度,同时可实现更高程度的轻量化。增材制造反射镜可以满足光学系统对环境适应性和快速性的需求。本文首先讨论了金属反射镜的评价指标;其次,综述了国内外在基于增材制造技术制备金属反射镜领域的发展现状和技术参数,从增材制造金属反射镜的基体设计与制备和基体的后处理2个方面展开论述;然后,通过分析,总结了增材制造金属反射镜的技术路线和关键技术;最后,对增材制造反射镜的应用前景提出了展望。     

基于模式跳变的井下便携式高精度CH_4浓度监测系统设计

为了在矿井中实现快速、便携式的甲烷浓度检测,同时系统还具备高灵敏度及长的工作周期,设计了基于半导体激光器模式跳变的差分光学光谱吸收法,建立了井下甲烷浓度无线检测系统。系统利用调制电流使半导体激光器的输出波长发生模式跳变,从而获得了两个相近波长的激光,其中一个在甲烷的特征吸收峰上,而另一个基本不被吸收。实验中将两束光分别照射被测气室时,两束光的光强之差代入比尔朗伯定律即可求解气室内的甲烷浓度。实验结果显示,调制电流从20.0 mA增大到60.0 mA过程中,输出波长在电流达到48.3 mA时发生跳变,由1 650.888 nm改变为1 651.020 m。通过HITRAN光谱数据库可知,波长1 650.888 nm位置可作特征吸收峰,而波长1 651.020 nm适合作参考波长。在此基础上,对密闭容器内标准浓度的甲烷气体进行测试,采用H-BD5GD410-HC型便携式甲烷检测仪的测试数据作对比。两种检测结果相近,但随着浓度不断地增高,该系统的检测误差相对平稳,略优于甲烷检测仪。系统的检测误差均低于0.050%,在不采用昂贵的锁相器、检相电路的条件下,实现了精度优于0.10%的井下甲烷浓度检测。     

Advances towards Cell-Specific Gene Transfection: A Small-Molecule Approach Allows Order-of-Magnitude Selectivity

A transfection vector that can home in on tumors is reported. Whereas previous vectors that allow moderately cell selective gene transfection used larger systems, this small-molecule approach paved the way for precise structure-activity relationship optimization. For this, biotin, which mediates cell selectivity, was combined with the potent DNA-binding motif tetralysine-guanidinocarbonypyrrol via a hydrophilic linker, thus enabling SAR-based optimization. The new vector mediated biotin receptor (BR)-selective transfection of cell lines with different BR expression levels. Computer-based analyses of microscopy images revealed a preference of one order of magnitude for the BR-positive cell lines over the BR-negative controls.     

A Flexible Framework for Cubic Regularization Algorithms for Nonconvex Optimization in Function Space

We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework.     

A coefficient identification problem for a mathematical model related to ductal carcinoma in situ

We consider a coefficient identification problem for a mathematical model with free boundary related to ductal carcinoma in situ (DCIS). This inverse problem aims to determine the nutrient consumption rate from additional measurement data at a boundary point. We first obtain a global‐in‐time uniqueness of our inverse problem. Then based on the optimization method, we present a regularization algorithm to recover the nutrient consumption rate. Finally, our numerical experiment shows the effectiveness of the proposed numerical method.     

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.