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.     

Four-Step Spin Crossover in a New Cyano-Bridged Iron-Silver Coordination Polymer

Spin-crossover complexes with multistep transitions attract much attention due to their potential applications as multi-switches and for data storage. A four-step spin crossover is observed in the new iron(II)-based cyanometallic guest-free framework compound Fe(2-ethoxypyrazine)₂{Ag(CN)₂}₂ during the transition from the low-spin to the high-spin state. A reverse process occurs in three steps. Crystallographic studies reveal an associated stepwise evolution of the crystal structures. Multiple transitions in the reported complex originate from distinct Fe^II sites which exist due to the packing of the ligand with a bulky substituent.     

Linear independence of a finite set of time-frequency shifts

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L² function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.     

Shape optimisation problem for stability of Navier–Stokes flow field

ABSTRACT

This paper presents the numerical results of a shape optimisation problem with regard to delaying the transition of a Navier–Stokes flow field from laminar to turbulent by using the theory developed by Nakazawa and Azegami. The theory was reviewed within the framework of functional analysis and updated with another expression of the shape derivative with respect to the objective function. A computer program was developed with the FreeFEM++. Numerical analyses were performed for two types of problems: a two-dimensional Poiseuille flow field with a sudden expansion and a two-dimensional uniform flow field around an isolated body. From the first example, two local minimum points of symmetric and asymmetric flow fields were determined, and the asymmetric flow field was found to be more stable. With regard to the second example, we reached the local minimum point of an elliptical shape, and infrequently determined a solution converging to an elliptical shape with the bluff in the leeward direction. By comparison, the superiority of the elliptical shape was obvious.     

基于不确定理论的铁路货运需求预测

合理预测铁路货运需求是铁路管理部门建设、运营等决策基础。为应对铁路货运需求的复杂变化,基于Pearson相关性分析方法筛选出铁路货运需求的七个具有关键影响的因素,并结合不确定理论建立不确定多元线性回归模型,相应的铁路货运预测结果由传统单一值变成可能的需求区间范围,更加符合处于不确定环境下的铁路货运需求实际情况。选取国家统计局2004~2016年相关数据进实证研究,并与回归模型以及BP模型的预测结果对比分析,实验表明不确定多元线性回归的预测结果更加精确。