矩阵论中的图论匹配法

G.Birkhoff用代数的方法证明了如果一个矩阵是双随机矩阵,则它能表示成置换矩阵的凸线性组合.设G是具有两分类(X,Y)的二部图,则G中含有饱和X中的所有顶点的匹配M的充分必要条件为:对∀S⊆X,有d_G(S)≥|S|.文章借助上述二部图的匹配思想,给出这一结论的图论证明.     

An algorithm for fast 3D inversion of surface electrical resistivity tomography data: application on imaging buried antiquities

In this work a new algorithm for the fast and efficient 3D inversion of conventional 2D surface electrical resistivity tomography lines is presented. The proposed approach lies on the assumption that for every surface measurement there is a large number of 3D parameters with very small absolute Jacobian matrix values, which can be excluded in advance from the Jacobian matrix calculation, as they do not contribute significant information in the inversion procedure. A sensitivity analysis for both homogeneous and inhomogeneous earth models showed that each measurement has a specific region of influence, which can be limited to parameters in a critical rectangular prism volume. Application of the proposed algorithm accelerated almost three times the Jacobian (sensitivity) matrix calculation for the data sets tested in this work. Moreover, application of the least squares regression iterative inversion technique, resulted in a new 3D resistivity inversion algorithm more than 2.7 times faster and with computer memory requirements less than half compared to the original algorithm. The efficiency and accuracy of the algorithm was verified using synthetic models representing typical archaeological structures, as well as field data collected from two archaeological sites in Greece, employing different electrode configurations. The applicability of the presented approach is demonstrated for archaeological investigations and the basic idea of the proposed algorithm can be easily extended for the inversion of other geophysical data.     

A simplified nonlinear analysis method for piled raft foundation in layered soils under vertical loading

This paper presents a simplified nonlinear solution for piled raft foundations in layered soils under vertical loading. Based on the elastic–plastic analysis of a single pile in a layered soil, the shielding effect between a receiver pile and the soil is taken into account to modify the conventional interaction factor between two piles. An approximate approach with the concept of the interaction factor is employed to study the nonlinear behavior of pile groups with a rigid cap. Considering the variation of soil properties, the solution to multilayered elastic materials is used to calculate the settlement of the soil. The interactions between pile–soil–raft are taken into account to determine the stiffness matrix of the piled raft. By solving the stiffness matrix equations, the settlement and the load shared by the piles and raft could be obtained. Compared with results of the available published literatures, the proposed solution provides reasonable results.     

地震层析成像中LSQR算法的快速求解

针对传统LSQR反演算法计算时间长、占用内存大的不足,这里提出了一种LSQR的快速算法,通过线性三元组存储稀疏矩阵,实现相应的矩阵运算,使LSQR算法的运算速度及内存占用都有较大地改善。     

基于两种颗粒体模型的巷道围岩应力应变分析

本文将岩石视为颗粒体材料,采用两种模型对巷道围岩的应力、应变及破坏区的分布规律进行了数值模拟。第一种模型是连续介质模型,其中考虑了颗粒、界面及基体。第二种模型是将第一种模型中的基体去掉。研究结果表明:当基体强度参数降低较少时,巷道围岩中的环向和径向应力在传统结果附近波动;当基体强度参数降低较多时,两种应力的波动幅度提高,而且,基体位置的应力向其周围的颗粒或界面转移。第二种模型结果的波动幅度更大。随着基体强度参数的降低,巷道围岩中的应变集中区向深部转移,形成相互交织的滑移线网,滑移线网的位置主要位于基体和界面中,这与第二种模型的结果有明显的差异(多个环向的应变集中区)。     

后赤潮过程中现场水样的三维荧光光谱特征分析

对发生在青岛近岸水域的后赤潮过程中赤潮藻密度、藻种进行鉴别的同时,对现场水样的三维荧光光谱进行了测量,获得了一套三维特征荧光数据。分析结果表明,1）当海水中生物密度达到或接近赤潮密度时,Ex最高峰值波长位于245nm,Em最高峰值波长在445nm,激发转折波长在260nm,荧光转折波长在245nm;2）在非赤潮区,Ex...     

浮基多体系统在波浪中展开的数值模拟

浮基多体系统在波浪中展开过程的顺序与快慢对系统的运动响应和连接处的力矩有较大影响。介绍了建立在齐次矩阵方法基础上的浮基多体系统时域运动求解,并对一具体浮基系统进行了建模和数值模拟,分析了上部机构以一定规律快速展开和慢速展开时系统的运动响应。结果表明,把齐次矩阵方法引入浮基多体系统的求解领域,其符号推导方便,运动学和动力学方程表达式变得相当简洁,而且编制程序也相对简便快捷。在相同波浪周期的情况下,多体系统的最大横摇角响应与波高正相关;在相同波高情况下,长周期的最大横摇响应要比短周期小;相对于波周期,波高对系统横摇响应的影响要大的多。     

Developing an algorithm for reconstruction of blocky systems in discontinuous media: two-dimensional analysis

Block detection is one of the most important steps in all discontinuous methods of analysis like Discontinuous Deformation Analysis (DDA) and Discrete Element Method (DEM). This is in fact a pre-processing step for those methods. In this study, a comprehensive computational algorithm, for tracing rock block created by discontinuities, has been developed. Using square matrices with integer elements and performing edge regularization step, reduce the size of the matrices due to elimination of unnecessary edges and vertices. Therefore speed and accuracy of block tracing operation will be increased. This algorithm is able to trace and identify all kind of blocks including convex and concave blocks formed by limited or unlimited fractures. The algorithm was programmed in C#.Net by over 3400 code lines and some cases were modeled by the code as example.     

非负矩阵分解和Curvelet在遥感图像融合中的应用

非负矩阵分解是一种提取图像原始信息局部特征的新方法,第二代Curvelet变换是一种效果较好的多尺度变换分析方法。结合两者特征提出一种基于NMF和Curvelet的遥感图像的融合方法,首先对已配准的多光谱图像和全色图像进行Curevelet分解,得到各层系数（Coarse、Detail和Fine尺度层）。然后对Coarse尺度层（低频系数）进行NMF分解,提取出包含特征基的低频系数;对Detail和Fine尺度层（高频系数）采用方差为测度参数进行邻域融合。最后进行Curevelet逆变换得到融合图像。实验结果表明,该方法的融合图像能较好地保留光谱信息,并在空间细节信息上得到改善,优于小波方法、Curvelet等方法。     

Site effect on vulnerability of high-rise shear wall buildings under near and far field earthquakes

Worldwide experience repeatedly shows that damages in structures caused by earthquakes are highly dependent on site condition and epicentral distance. In this paper, a 21-storey shear wall-structure built in the 1960s in Hong Kong is selected as an example to investigate these two effects. Under various design earthquake intensities and for various site conditions, the fragility curves or damage probability matrix of such building is quantified in terms of the ductility factor, which is estimated from the ratio of storey yield shear to the inter-storey seismic shear. For high-rise buildings, a higher probability of damage is obtained for a softer site condition, and damage is more severe for far field earthquakes than for near field earthquakes. For earthquake intensity of VIII, the probability of complete collapse (P) increases from 1 to 24% for near field earthquakes and from 1 to 41% for far field earthquakes if the building is moved form a rock site to a site consisting a 80 m thick soft clay. For intensity IX, P increases from 6 to 69% for near field earthquake and from 14 to 79% for far field earthquake if the building is again moved form rock site to soft soil site. Therefore, site effect is very important and not to be neglected. Similar site and epicentral effects should also be expected for other types of high-rise structures.