快速傅里叶变换在导热逆问题中的应用

本文用通过快速傅里叶变换来进行逆拉氏变换的方法解决导热逆问题。众所周知,内点温度的测量误差往往导致导热逆问题计算的不稳定。作者用频谱分析的概念解决了这一困难。文中提出了测量温度时固体内点不同位置、内点温度的测量误差以及数值计算可采用的时间步长之间的关系。计算实例表明,本文所提供的方法对于瞬变现象的研究有很大的实用价值。     

一类非齐次抛物型方程确定系数反问题的唯一性

本文应用Gelfand—Levitan理论,根据已知观测值得到了非齐次方程未知函数a(x)的唯一性定理.     

导出极限序同态及逆系统的范畴性质

在文[1]的基础上,引入了LF拓扑空间的逆系统之间的映射以及导出极限序同态的概念,讨论了极限序同态的一些性质;利用LF拓扑空间的逆系统的极限刻划了范畴LFTZ中的投影极限;最后讨论了一些范畴的投影完备性.     

关于G-半群

这篇文章研究了(右、左)G-半群。文章中证明了有限集上全变换半群是右 G-半群;域上 n 阶方阵半群是 G-半群。文章中给出了右(左)G-半群的子群的刻划并且给出了 G-半群是逆半群的充要条件。     

部分势函数确定的逆Dirac问题

本文讨论了在一定的条件下,势函数的部分信息和有限的特征值可以唯一确定势函数。     

Hilbert空间中算子广义逆的共变性质

主要研究了Hilbert空间中算子的共变性质，给出了共变条件的充要条件；此外，考虑了EP算子的共变性质，并且证明了相同值域空间的EP算子具有相同的共变．     

一种虚拟维修动作生成的两阶段方法

虚拟维修仿真技术应用越来越广泛.在虚拟维修仿真中,虚拟维修人员的动作逼真性是较为重要的因素之一.对虚拟维修系统中维修动作的实时、连贯生成问题进行研究,提出一种两阶段方法,把虚拟维修动作生成分为目标接近阶段与目标到达阶段.在目标接近阶段应用快速的基于雅可比转置的逆向运动学算法求解;在目标到达阶段,应用线性插值和曲线拟合方法求解.最后在课题中应用该方法成功解决了由收敛性、动作特征等因素引起的动作不连贯,速度不一致问题.     

The inverse correlation between series resistance and parallel resistance of small molecule organic solar cells

Understanding the inversely correlated series resistance(Rs) and parallel resistance(Rp) remains a challenge. Here we report that the variation of Rs and Rp is inversely related through the morphology of the donor and acceptor interface in CuPc organic solar cells, when comparing the bilayer structure and bulk heterojunction structure. It was also found that the charge carrier concentration near the donor–acceptor interface plays an important role in the relationships of Rs and Rp under fixed interfacial morphology, which was verified by the change of Voc. The inversely correlated Rs and Rp contributes to the improvement of the fillfactor, and in turn the power conversion efficiency.     

多维随机变量的特征函数和概率函数的关系

主要推广了一维随机变量的特征函数的性质,讨论了二维随机变量的特征函数的性质以及特征函数与概率函数之间的关系,即二者能够互相唯一确定.     

Abduction, tomography, and other inverse problems

Charles S. Peirce introduced in the late 19^th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane functions from their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon’s theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.