Opinion dynamics in networks with heterogeneous confidence and influence

We propose a discrete-time model of opinion dynamics. The neighborhood relationship is decided by confidence radius and influence radius of each agent. We investigate the influence of heterogeneity in confidence/influence distribution on the behavior of the network. The simulations suggest that the heterogeneity of single confidence or influence networks can promote the opinions to achieve consensus. It is shown that the heterogeneous influence radius systems converge in fewer time steps and more often in finite time than the heterogeneous confidence radius systems. We find that heterogeneity does not always promote consensus, and there is an optimal heterogeneity so that the relative size of the largest consensus cluster reaches maximum in heterogeneous confidence and influence networks.     

On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues

For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s^{\text{th}}$ (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs.     

The effect of cation size (H+, Li+, Na+, and K+) on McLafferty-type rearrangement of even-electron ions in mass spectrometry

Protonation and alkali-metal cation adduction are the most important ionization processes in soft-ionization mass spectrometry.Studies on the fragmentation mechanism of protonated and alkali-metal-cationized compounds in tandem mass spectrometry are essential and helpful for structural analysis.In some cases,it was often observed that a compound attached by different alkali-metal cations(or proton)exhibits similar fragmentation patterns but the relative abundances of product ions are different.This difference was considered to derive from the different electrostatic interactions of alkali-metal cations(or the bonded effect of proton)with the analyte.The alkali-metal cation with a smaller ionic radius shows stronger electrostatic interaction with the molecule because of its higher charge density.In addition,the bonded effect of the proton is stronger than the electrostatic interaction of the alkali-metal cation.In the present study,which used McLafferty-type rearrangements of even-electron ions([M+Cat]+,Cat=H,Li,Na,K)as model reactions,the effect of cation size in mass spectrometric fragmentation reactions is highlighted.These considerations were also successfully applied to interpret the similar but distinct fragmentation behavior of proton and alkali-metal cation adducts of a synthetic compound(2-(acetamido(phenyl)methyl)-3-oxobutanoate)and a drug(entecavir).     

Extremal graph characterization from the bounds of the spectral radius of weighted graphs

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained.     

Estimates for eigenvalues of stochastic matrices

It is well-known that the eigenvalues of stochastic matrices lie in the unit circle and at least one of them has the value one. Let {1, r 2 , ··· , r N } be the eigenvalues of stochastic matrix X of size N × N . We will present in this paper a simple necessary and sufficient condition for X such that |r j | < 1, j = 2, ··· , N . Moreover, such condition can be very quickly examined by using some search algorithms from graph theory.     

Defocus and binocular vision based stereo particle pairing method for 3D particle tracking velocimetry

We propose a new method, based on the depth-from-defocus technique and binocular vision, for solving the stereo particle pairing problem in 3D particle tracking velocimetry (PTV). Firstly, the apparent particle depth is measured with a single camera, using the depth-from-defocus technique. Secondly, a strict mathematical model of the particle-to-particle correspondence relationship between the left and right images, taking into account the refractions at the interfaces in the optical path, is presented, with the assumption that the apparent particle depth is measured. Thirdly, based on the apparent particle depth and particle-to-particle correspondence relationship, the epipoplar line is truncated into a short line segment by cutting off, where the apparent particle depth extends beyond its estimated range. For the first time, the range of the blur circle radius is employed as an additional stereo particle pairing constraint. Finally, the optimal pairing particle is selected by applying the epipolar line segment and blur circle radius constraints. The experimental results show that the rate of correct pairing is significantly improved compared with the epipolar line nearest neighbor analysis, especially when the particle density is increasing.     

一种精确测量光学球面曲率半径的方法

在简要总结各种检测光学球面曲率半径方法优缺点的基础上,提出了利用激光跟踪仪和激光干涉仪测量光学球面曲率半径的新方法。首先,通过激光跟踪仪精确定位测量干涉仪出射球面波前的焦点和待测球面镜的曲率中心点坐标,再调整待测球面镜与干涉仪的相对位置,使待测球面镜达到零条纹干涉状态,用激光跟踪仪测定此时待测球面镜上多点的位置坐标,通过计算分析即可得到待测球面镜的曲率半径。研究和分析了这种测量光学球面曲率半径方法的基本原理,并提出了针对凸球面镜曲率半径的多区域测定平均综合优化的方法。结合实例对一口径为400mm的球面透镜进行了曲率半径的测量,测量得到其两面曲率半径分别为1022.283mm(凸面)和4069.568mm(凹面),并将该透镜进行了轮廓法测量对比,其相对误差都小于0.05%。     

Experimental research of effects of different rotation radii on the growth rate of potassium dihydrogen phosphate crystals

Comparing with the traditional concentric rotation method (rotation radius is 0 cm), the effects of different rotation radii on the growth rate of KDP crystals were studied by experimental methods. It was found that with the increase of rotation radius from 0 cm, the growth rate of each direction of crystals first increased and then decreased in a size‐unchanged vessel. The smaller the distance between the crystal and vessel wall, the less the growth rate. This phenomenon was named the “wall collision effect”. Also, the value of growth rate reached a maximum when the rotation radius was about half of its allowable largest value in the size‐unchanged vessel. In addition, an increase of the rotation radius could improve the crystal growth rate under the same linear velocity of crystal movement. Finally, the uniformity of crystal growth has also been analyzed compared with the concentric rotation radius. It was found that the uniformity of crystal growth was best when the rotation radius was half of its allowable maximum value, and it was more conducive to the actual application of KDP crystals.     

一般矩阵函数的不等式

本文研究一般矩阵函数不等式.运用一般矩阵函数的两个公式和lp-范数的性质,结出了两个矩阵运算的一般矩阵函数不等式.