The geometric mean of two matrices from a computational viewpoint

The geometric mean of two matrices is considered from a computational viewpoint. Several numerical algorithms based on different properties and representations of the geometric mean are discussed and analyzed. It is shown that most of the algorithms can be classified in terms of the rational approximations of the inverse square root function. A review of relevant applications is given. Copyright © 2015 John Wiley & Sons, Ltd.     

MATLAB GUI设计在几何作图中的应用

本文考虑MATLAB软件在几何作图中的应用.以在教学中遇到的两个几何作图为例,介绍了相应GUI设计界面的制作和演示过程.通过演示,得到了两个常微分方程的解的几何形状及其形成过程,从而对所得结论有更加直观和形象的认识,也加深了学生对问题本身的理解,进一步提高了教学效果.     

Lipschitz continuity of an approximate solution mapping for parametric set-valued vector equilibrium problems

The purpose of this paper is to generalize and improve some topological properties of solutions set to the set-valued vector equilibrium problems by using the scalar characterization method. Moreover, the Lipschitz continuity of an approximate solution mapping for the parametric set-valued vector equilibrium problems is studied.     

非线性自回归模型的几何非常返性

本文研究了非线性自回归模型的随机稳定性.通过建立恰当的Foster-Lyapunov条件,得到了非线性自回归模型几何非常返的充分条件.     

Integrated multidimensional and comprehensive 2D GC analysis of fatty acid methyl esters

Fatty acid methyl ester (FAME) profiling in complex fish oil and milk fat samples was studied using integrated comprehensive 2D GC (GC × GC) and multidimensional GC (MDGC). Using GC × GC, FAME compounds – cis‐ and trans‐isomers, and essential fatty acid isomers – ranging from C18 to C22 in fish oil and C18 in milk fat were clearly displayed in contour plot format according to structural properties and patterns, further identified based on authentic standards. Incompletely resolved regions were subjected to MDGC, with Cn (n = 18, 20) zones transferred to a ²D column. Elution behavior of C18 FAME on various ²D column phases (ionic liquids IL111, IL100, IL76, and modified PEG) was evaluated. Individual isolated Cn zones demonstrated about four‐fold increased peak capacities. The IL100 provided superior separation, good peak shape, and utilization of elution space. For milk fat‐derived FAME, the ²D chromatogram revealed at least three peaks corresponding to C18:1, more than six peaks for cis/trans‐C18:2 isomers, and two peaks for C18:3. More than 17 peaks were obtained for the C20 region of fish oil‐derived FAMEs using MDGC, compared with ten peaks using GC × GC. The MDGC strategy is useful for improved FAME isomer separation and confirmation.     

Equicontinuity and Sensitivity of Group Actions*

Let(X, G) be a dynamical system(G-system for short), that is, X is a topological space and G is an infinite topological group continuously acting on X. In the paper,the authors introduce the concepts of Hausdorff sensitivity, Hausdorff equicontinuity and topological equicontinuity for G-systems and prove that a minimal G-system(X, G) is either topologically equicontinuous or Hausdorff sensitive under the assumption that X is a T₃-space and they provide a classification of transitive d...     

一种新的求解拟单调变分不等式的压缩投影算法

2020年Liu和Yang提出了求解Hilbert空间中拟单调且Lipschitz连续的变分不等式问题的投影算法,简称LYA。本文在欧氏空间中提出了一种新的求解拟单调变分不等式的压缩投影算法,简称NPCA。新算法削弱了LYA中映射的Lipschitz连续性。在映射连续、拟单调且对偶变分不等式解集非空的条件下得到了NPCA所生成点列的聚点是解的结论。当变分不等式的解集还满足一定条件时,得到了NPCA的全局收敛性。数值实验结果表明NPCA所需的迭代步数少于LYA的迭代步数,NPCA在高维拟单调例子中所需的计算机耗时也更少。     

State-Independent Geometric Quantum Gates via Nonadiabatic and Noncyclic Evolution

Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not been fully explored in previous investigations. Here,a scheme is proposed for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. In the scheme, only geometric phase can be accumulated in a fast way, and thus it not only fully utilizes the local noise resistant property of geometric phase but also reduces the difficulty in experimental realization. Numerical results show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. Furthermore, it proposes to construct universal quantum gate on superconducting circuits, with the fidelities of single-qubit gate and nontrivial two-qubit gate can achieve 99.97% and 99.87%, respectively. Therefore, these high-fidelity quantum gates are promising for large-scale fault-tolerant quantum computation.