关于迭代Tikhonov正则化的最优正则参数选取

本文讨论了算子和右端都近似给定的第一类算子方程的迭代Ｔｉｋｈｏｎｏｖ正则化，给出了不依赖于准确解的任何信息但能得到最优收敛阶的正则参数选取法。     

原子分子工程的设计基础—计算机及其程序设计

阐述了计算机科学对原子分子学科研究的重要作用，针对原子与分子领域中一些典型的问题，介绍了计算方法及程序设计，并对有关课题编出了计算程序。从而表明：借助于计算机可使原子与分子研究工作规范化、工程化，计算机及其程序设计是原子分子工程的设计基础     

Mössbauer studies of interstitial intermetallics

After an introduction to interstitial incorporation of 2p elements in iron-based alloys, the main physical effects of these interstitials on the intrinsic properties of rare-earth intermetallics are outlined. Then follows a survey of the results obtained using the⁵⁷Fe and several rare-earth resonances for rare-earth intermetallics with the Th₂Zn₁₇, Th₂Ni₁₇, ThMn₁₂ and BaCd₁₁ structures in which nitrogen or carbon has been interstitially incorporated. The results of Mössbauer studies in this area are discussed, and future prospects are assessed.     

119Sn Mössbauer spectra of RMnSn2 intermetallics (R = La,Ce, Pr,Nd, Sm)

The ternary stannide series of RMnSn₂ compounds crystallize in the defect orthorhombic CeNiSi₂-type structure. They order magnetically close to room temperature. Isomer shifts are approximately 1.9 and 2.8 mm/s at the two tin sites, and there are transferred hyperfine fields of 3–6 T at 15 K, which depend on the rare-earth partner, especially at Sn₂ sites. The magnitude of the transferred hyperfine field per manganese neighbour is 4T.     

Solving nonlinear inverse problems by evolution equations based on Gauss–Newton methods

In this article, we solve nonlinear inverse problems by an evolution equation method which can be viewed as the continuous analogue of the Gauss–Newton method. Under certain conditions we prove the convergence and derive the rate of convergence when the discrepancy principle is coupled.     

On a regularized Levenberg–Marquardt method for solving nonlinear inverse problems

We consider a regularized Levenberg–Marquardt method for solving nonlinear ill-posed inverse problems. We use the discrepancy principle to terminate the iteration. Under certain conditions, we prove the convergence of the method and obtain the order optimal convergence rates when the exact solution satisfies suitable source-wise representations.     

在超音速F-F2-IF与NH3气流中产生IF(B3Π0+)的研究

研究了在超音速F-F_2-IF气流与NH_3气流中通过化学反应与碰撞传能产生IF(B~(3Π_0~+))的过程。用光学多通道分析仪在450-750 nm范围内记录到IF(B~(3Π_0~+)→X~(1∑~+))辐射的33条光谱线。提出了产生IF(B~(3Π_0~+))的机制。     

On the iteratively regularized Gauss–Newton method in Banach spaces with applications to parameter identification problems

In this paper we propose an extension of the iteratively regularized Gauss–Newton method to the Banach space setting by defining the iterates via convex optimization problems. We consider some a posteriori stopping rules to terminate the iteration and present the detailed convergence analysis. The remarkable point is that in each convex optimization problem we allow non-smooth penalty terms including $L^1$ and total variation like penalty functionals. This enables us to reconstruct special features of solutions such as sparsity and discontinuities in practical applications. Some numerical experiments on parameter identification in partial differential equations are reported to test the performance of our method.     

On the order optimality of the regularization via inexact Newton iterations

Inexact Newton regularization methods have been proposed by Hanke and Rieder for solving nonlinear ill-posed inverse problems. Every such a method consists of two components: an outer Newton iteration and an inner scheme providing increments by regularizing local linearized equations. The method is terminated by a discrepancy principle. In this paper we consider the inexact Newton regularization methods with the inner scheme defined by Landweber iteration, the implicit iteration, the asymptotic regularization and Tikhonov regularization. Under certain conditions we obtain the order optimal convergence rate result which improves the suboptimal one of Rieder. We in fact obtain a more general order optimality result by considering these inexact Newton methods in Hilbert scales.     

On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems

We consider the computation of stable approximations to the exact solution of nonlinear ill-posed inverse problems F(x) = y with nonlinear operators F : X → Y between two Hilbert spaces X and Y by the Newton type methods