稠密k-子图问题的双非负松弛

稠密k-子图问题是组合优化里面一类经典的优化问题,其在通常情况下是非凸且NP-难的。本文给出了求解该问题的一个新凸松弛方法-双非负松弛方法,并建立了问题的相应双非负松弛模型,而且证明了其在一定的条件下等价于一个新的半定松弛模型。最后,我们使用一些随机例子对这些模型进行了数值测试,测试的结果表明双非负松弛的计算效果要优于等价的半定松弛。     

基于发射率模型约束的多光谱辐射真温反演法

温度测量是工业生产或科学实验中保证产品质量、降低生产成本和确保实验安全的重要因素之一。目前非接触的测温方法以辐射测温法为主,二次测量法是多光谱辐射测温中一种常用的方法。但是,二次测量法不适用于实时数据处理。针对此问题,基于多光谱亮度温度数学模型引入了发射率模型约束条件,提出了一种多光谱辐射真温快速反演法。对于非黑体,根据不同波长下的亮度温度的关系,得出当亮度温度在一个区间内是增函数或者常数函数时,发射率在该区间内是增函数;当亮度温度在一个区间内是减函数时,则发射率在该区间内满足一个关于发射率和波长的不等式。该发射率模型约束条件根据亮度温度的信息,将发射率假设值的构建由多类减少到一类,避免了不必要的发射率的构建。实验分别采用实际发射率随波长单调下降、单调上升、先下降再上升、先上升再下降和随机变化的具有代表性的五个被测目标,针对两个被测温度点进行了仿真对比分析。结果表明,与二次测量法相比,对于同一个被测目标,在相同的温度初值和相同的发射率搜索范围下,新算法在保证精度的情况下,不仅所得结果相同,而且处理速度提升了19.16%～43.45%。     

稀土单分子磁体

单分子磁体因其磁性双稳态和慢弛豫机制而在超高密度存储材料、自旋电子器件等领域具有潜在的应用. 稀土单分子磁体因为具有较大的磁矩和磁各向异性而成为近年来研究的热点话题. 目前有关稀土单分子磁体的综述都主要集中在它们的合成、结构及磁性能, 而在其它性质方面缺少深入而系统的研究. 因此, 本论文结合现有的研究成果, 围绕稀土单分子磁体的高翻转能垒、复杂的多弛豫机制、可调控的磁性以及多功能材料的四个特点进行了综述, 旨在更好的理解稀土单分子磁体的物理、化学本质, 为稀土单分子磁体的设计与调控提供思路.     

乙二醇的分子间氢键结构动力学的飞秒非线性红外光谱

利用稳态线性红外光谱和飞秒泵浦-探测红外光谱技术, 研究了在乙腈(MeCN)、丙酮(AC)、四氢呋喃(THF)和二甲基亚砜(DMSO)溶剂中乙二醇(EG)的结构和羟基(―OH)伸缩振动动力学. 结果表明, 乙二醇的―OH伸缩振动的频率位置、峰宽以及振动弛豫动力学都表现出强烈的溶剂依赖性. 乙二醇溶液中至少存在两种形式的分子间氢键, 一种是溶质-溶剂团簇的分子间氢键, 另一种是溶质-溶质团簇的分子间氢键. 量子化学计算预测的―OH伸缩振动频率的溶剂依赖性与我们的红外光谱实验观测结果一致. 进一步, 我们发现在乙腈中参与形成溶质-溶剂团簇氢键的乙二醇―OH伸缩振动具有最慢的弛豫动力学, 丙酮和四氢呋喃次之, 而最快的弛豫动力学过程发生在二甲基亚砜中. 在每一溶剂条件下, 乙二醇/乙二醇溶质团簇中―OH伸缩振动弛豫都更快一些. 本文结果有助于认识在溶质-溶质、溶质-溶剂分子团簇共存的体系中不同分子间氢键的结构动力学特性.     

Reflection and transmission of plane waves from fluid-piezothermoelastic solid interface

The reflection and transmission of plane waves from a fluid-piezothermoelastic solid interface are studied. The expressions for amplitude ratios and energy ratios corresponding to reflected waves and transmitted waves are derived analytically. The piezo-thermoelastic solid half-space is assumed to have 6mm type symmetry and assumed to be loaded with water. The effects of angle of the incidence, the frequency, the specific heat, the relaxation time, and the thermal conductivity on the reflected and transmitted energy ratios are studied numerically for a particular model of cadmium selenide (CdSe) and water. Some special cases are also studied.     

甲基紫分子拉曼激发虚态的研究

从拉曼峰强入手,求得了甲基紫分子的“时间分辨键极化率”,并与第一原理计算的基态电子密度做对比,讨论了该分子的激发拉曼虚态的性质.研究结果表明,该分子的拉曼激发虚态中电子向分子外围以及两环之间的键流动,并且拉曼弛豫后的键极化率分布与基态电子的密度分布相似.通过研究键极化率的弛豫过程,发现连接两环的键上的键极化率弛豫时间较其他键大.这些结果说明了甲基紫这类双环分子拉曼激发虚态的性质,这对于研究拉曼散射的中间态具有一定意义. 关键词： 拉曼峰强 时间分辨键极化率 弛豫特征时间     

Retrospective correction for T1-weighting bias in T2 values obtained with various spectroscopic spin-echo acquisition schemes

Localized tissue transverse relaxation time (T₂) is obtained by fitting a decaying exponential to the signals from several spin-echo experiments at different echo times (TE). Unfortunately, time constraints in magnetic resonance spectroscopy (MRS) often mandate in vivo acquisition schemes at short repetition times (TR), that is, comparable with the longitudinal relaxation constant (T₁). This leads to different T₁-weighting of the signals at each TE. Unaccounted for, this varying weighting causes systematic underestimation of the T₂'s, sometimes by as mush as 30%. In this article, we (i) analyze the phenomenon for common MRS spin-echo T₂ acquisition schemes; (ii) propose a general post hoc T₁-bias correction for any (TR, TE) combination; (iii) show that approximate knowledge of T₁ is sufficient, since a 20% uncertainty in T₁ leads to under 3% bias in T₂; and consequently, (iv) efficient, precision-optimized short TR spin-echo T₂ measurement protocols can be designed and used without risk of accuracy loss. Tables of correction for single-refocusing (conventional) spin-echo and double refocusing, such as, PRESS acquisitions, are provided.     

Reproducibility of myelin water fraction analysis: a comparison of region of interest and voxel-based analysis methods

This study compared region of interest (ROI) and voxel-based analysis (VBA) methods to determine the optimal method of myelin water fraction (MWF) analysis. Twenty healthy controls were scanned twice using a multi-echo T₂ relaxation sequence and ROIs were drawn in white and grey matter. MWF was defined as the fractional signal from 15 to 40 ms in the T₂ distribution. For ROI analysis, the mean intensity of voxels within an ROI was fit using non-negative least squares. For VBA, MWF was obtained for each voxel and the mean and median values within an ROI were calculated. There was a slightly higher correlation between Scan 1 and 2 for the VBA method (R²=0.98) relative to the ROI method (R²=0.95), and the VBA mean square difference between scans was 300% lower, indicating VBA was the most consistent between scans. For the VBA method, mean MWF was found to be more reproducible than median MWF. As the VBA method is more reproducible and gives more options for visualization and analysis of MWF, it is recommended over the ROI method of MWF analysis.     

Effects of time delay on the statistical fluctuations for a bistable system driven by cross-correlated noises

We study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T _c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T _c and C(s) are obtained. Based on numerical computations, it is found that the delay time τ slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (∈ > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (∈ < 0). The effects of the delay time τ on the T _c and C(s) are entirely opposite for ∈ 〉 0 and ∈ < 0.