Construction of conformal mappings by generalized polarization tensors

We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs

This paper addresses the solution of parabolic evolution equations simultaneously in space and time as may be of interest in, for example, optimal control problems constrained by such equations. As a model problem, we consider the heat equation posed on the unit cube in Euclidean space of moderately high dimension. An a priori stable minimal residual Petrov–Galerkin variational formulation of the heat equation in space–time results in a generalized least squares problem. This formulation admits a unique, quasi‐optimal solution in the natural space–time Hilbert space and serves as a basis for the development of space–time compressive solution algorithms. The solution of the heat equation is obtained by applying the conjugate gradient method to the normal equations of the generalized least squares problem. Starting from stable subspace splittings in space and in time, multilevel space–time preconditioners for the normal equations are derived. In order to reduce the complexity of the full space–time problem, all computations are performed in a compressed or sparse format called the hierarchical Tucker format, supposing that the input data are available in this format. In order to maintain sparsity, compression of the iterates within the hierarchical Tucker format is performed in each conjugate gradient iteration. Its application to vectors in the hierarchical Tucker format is detailed. Finally, numerical results in up to five spatial dimensions based on the recently developed htucker toolbox for MATLAB are presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal estimation of the diffusion coefficient from non-averaged and averaged noisy magnitude data

The magnitude operation changes the signal distribution in MRI images from Gaussian to Rician. This introduces a bias that must be taken into account when estimating the apparent diffusion coefficient. Several estimators are known in the literature. In the present paper, two novel schemes are proposed. Both are based on simple least squares fitting of the measured signal, either to the median (MD) or to the maximum probability (MP) value of the Probability Density Function (PDF). Fitting to the mean (MN) or a high signal-to-noise ratio approximation to the mean (HS) is also possible. Special attention is paid to the case of averaged magnitude images. The PDF, which cannot be expressed in closed form, is analyzed numerically. A scheme for performing maximum likelihood (ML) estimation from averaged magnitude images is proposed. The performance of several estimators is evaluated by Monte Carlo (MC) simulations. We focus on typical clinical situations, where the number of acquisitions is limited. For non-averaged data the optimal choice is found to be MP or HS, whereas uncorrected schemes and the power image (PI) method should be avoided. For averaged data MD and ML perform equally well, whereas uncorrected schemes and HS are inadequate. MD provides easier implementation and higher computational efficiency than ML. Unbiased estimation of the diffusion coefficient allows high resolution diffusion tensor imaging (DTI) and may therefore help solving the problem of crossing fibers encountered in white matter tractography.     

An explanation of the unusual strength of the hydrogen bond in small water clusters

We seek to explain why the hydrogen bond possesses unusual strength in small water clusters that account for many of the complex behaviors of water. We have investigated and visualized the donation of covalent character from covalent (sigma) to hydrogen bonds by calculating the eigenvector coupling properties of quantum theory of atoms in molecules (QTAIM), stress tensor σ ( r ), and Ehrenfest Force F ( r ) on the F ( r ) molecular graph. The next-generation three-dimensional (3-D) bond-path framework sets are presented, and only the F ( r ) bond-path framework sets reproduce the earlier finding on the coupling between covalent (sigma) and hydrogen bonds that possess a degree of covalent character. Exploration of the bond-path between the covalent (sigma) and hydrogen bond's critical points provides an explanation for the previously obtained coupling results. The directional character of the covalent (sigma) and hydrogen bonds' 3-D bond-path framework sets for the F ( r ) explains differences found in the earlier results from QTAIM and the stress tensor σ ( r ).     

PBL节点初始平动刚度计算及设计参数优化

为研究钢桁腹混凝土组合箱梁中PBL(Perfobond Leiste)节点的初始平动刚度及其影响因素,首先基于组件法,运用卡氏第二定理推导出考虑了开孔钢板与混凝土间的界面剪切力和混凝土榫贡献的PBL节点的初始平动刚度表达式,其次以某工程实例为背景,结合有限元模型验证所推公式的合理性;在此基础上分析了混凝土强度、腹杆直径、腹杆壁厚、开孔钢板开孔孔径和开孔钢板厚度等构造参数对初始平动刚度的影响,并利用正交分析法对以上5个参数进行优化组合。研究结果表明,本文方法计算的PBL节点初始平动刚度结果与有限元计算结果间的误差在8.0%以内;相较运用解三角形计算腹杆平动位移的方法,采用卡氏第二定理不仅可以简化计算,还可以减小解三角形过程中因多次计算变形带来的误差累积;腹杆刚度对PBL节点整体平动刚度的贡献最大,可达到82.5%;保持原设中的混凝土强度不变,将腹杆直径增加20 mm,将钢腹杆壁厚增加4 mm,将开孔钢板开孔孔径增加4 mm,将开孔钢板厚度增加4 mm,可以将PBL节点理论初始平动刚度提高约25.7%。     

一般矩阵函数的变差

设Sn是n次对称群,G为Sn的子群,χ是G的次数为1的特征标.如果A是一个n阶复变矩阵,定义一般矩阵函数dχG为dχG(A)=∑σ∈Gχ(σ)∏ni=1aiσ(i).本文用lp-算子范数(1≤p≤∞)的性质证明了一般矩阵函数变差的两个不等式.     

脑胶质瘤磁共振弥散张量成像定量参数与VEGF、MMP-9表达的相关性

本研究旨在分析脑胶质瘤患者的磁共振弥散张量成像(DTI)参数与病变组织血管内皮生长因子(VEGF)和基质金属蛋白酶-9(MMP-9)表达的相关性,以及DTI参数对脑胶质瘤进行分级诊断的价值.根据病理分级将102例脑胶质瘤患者分为低级别组(47例)和高级别组(55例),均行MRI和DTI检查,定量测定表观弥散系数(ADC...     

基于高斯曲率极值点的桥梁结构损伤识别方法

目前中小桥梁日常安全巡检存在对检查人员依赖性高、缺乏可量化的科学依据等不足.针对这些问题,本文提出了一种利用高斯曲率极值点对结构进行损伤识别的方法.将桥面视为受弯弹性薄板,根据弹性薄板的弯曲理论得到了在荷载作用下结构刚度变化与桥面弯曲程度(高斯曲率)的理论关系,并由此推导了高斯曲率对结构刚度损伤的敏感程度公式.通过有限...     

任意高差的多档输电线动刚度理论建模

针对目前多档输电线动力特性研究中存在的不足,将任意一档导线视为子结构并基于现有的索振动理论获得了其动张力;利用相邻两档导线的动张力建立了悬垂绝缘子串绕其悬挂点摆动的动力学方程;综合每一档导线的振动方程以及悬垂绝缘子串的摆动方程建立了两档及三档输电线的动力学方程,求解得到由端部位移激励产生的动刚度;通过对动刚度进行分析得到了多档输电线的固有频率以及模态的理论表达形式;建立了小高差的两档及三档导线的有限元模型,理论分析结果与有限元结果一致,验证了理论公式的正确性。本文提出的动刚度理论对于研究多档输电线的动态响应具有重要的应用价值。     

四原子分子中Majorana算子矩阵元的新计算公式

李代数方法在研究双原子分子、三原子分子振－转光谱及相关问题等方面已被证明是一种有效方法[‘－0,并被成功推广到多原子分子[’－门．构造代数哈密顿量是此方法的关键,这就要求选择合适的