On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

磁场下有原子自旋轨道耦合的各向异性量子点的精确解析传播子

量子力学中很少有系统能够精确地计算传播子, 特别是在考虑了自旋轨道耦合效应的情况下. 利用相空间的群论方法, 首先导出了有原子自旋轨道耦合的各向异性量子点传播子的精确解析表达式. 随后利用传播子来计算自旋高斯波包的演化与相应的概率密度, 并研究了原子自旋轨道耦合效应和磁场强度对距离期望值的影响.     

80.5 MeV/u碳离子诱发铜靶的放射性剩余产物测量

高能重带电粒子能直接穿透靶原子核外电子层,与原子核发生直接碰撞,发生散裂反应,产生一系列具有放射性的剩余产物核.重带电粒子诱发靶材放射性剩余核与辐射防护和人员安全有着密切联系,当前,大部分剩余核产额主要依靠蒙特卡罗粒子输运程序进行模拟计算,其准确程度亟需通过实验测量进行准确评估.本文利用能量为80.5 MeV/u的(12)^C⁶⁺粒子对薄铜靶开展了辐照实验与伽玛射线测量,结合伽玛谱学分析方法,得出了辐照产生的18种放射性剩余产物的初始活度和产生截面值,并与PHITS模拟结果进行对比.结果表明,PHITS模拟程序对放射性剩余核种类的估计具有较高可靠性,在其绝对产额方面,与实验测量仍具有较大偏差.     

An efficient edge based data structure for the compressible Reynolds-averaged Navier–Stokes equations on hybrid unstructured meshes

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.     

改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

Linear independence of a finite set of time-frequency shifts

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L² function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.     

基于2,5-二溴对苯二甲酸配体的锌/钴配合物合成、晶体结构及性质

将有机物2,5-二溴对苯二甲酸(H₂L₁)和2,2′-联吡啶(L₂)作为双配体,使用溶剂热法和七水合硫酸锌(ZnSO₄·7H₂O)、六水合硝酸钴(Co(NO₃)₂·6H₂O)分别反应,得到配合物[Zn(L₁)(L₂)(H₂O)]_n(1)和配合物[Co(L₁)(L₂)(H₂O)]_n(2)。采用单晶X射线衍射、元素分析、红外光谱、紫外光谱、荧光光谱、热重分析等测试方法对这两种物质进行分析研究。单晶测试结果表明配合物1是单斜晶系,以Zn²⁺配位连接L^2-₁与L₂形成一维链状结构,各条链在分子间氢键和π…π共轭作用下有规律地堆叠形成三维网络结构。配合物2是三斜晶系,Co1离子和Co1ⁱ离子由H₂L₁上的羧酸氧原子O4和O4ⁱ连接,形成双齿螯合的配位结构单元,以Co²⁺配位连接 L^2-₁和L₂形成二维网格结构,各层在O—H…O分子间氢键和范德瓦耳斯力作用下有规律的堆叠形成三维网络结构。配合物1和2均含有芳香杂环、羧基杂环和氮杂环,具有良好的荧光性质和热稳定性,最大发射波长分别为345 nm和333 nm。