多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

砂岩方梁断裂过程区范围的实验确定方法

裂纹前端的断裂过程区是引起岩石非线性断裂及尺寸效应的主要原因。利用数字图像相关技术对砂岩开展了三点弯曲梁实验,获得观测区域高精度的全场位移和应变数据,根据断裂韧带区域水平位移和水平应变的分布特征,结合裂尖岩石颗粒变化的微观分析,提出采用裂纹尖端水平位移波动性和水平应变突变性所得到的波动系数和水平应变突变值,确定断裂过程区形状和临界尺寸的方法。结果表明:砂岩断裂过程区的形状为不规则的狭长带状区域,断裂过程区的临界长度为11~13mm,临界宽度为1.58~2.36mm。断裂过程区区域内形变在趋向裂尖时呈指数增加,但其单位区域内的形变增量呈波动状态。该方法能够更加准确判断岩石断裂过程区的范围,有助于分析岩石的非线性断裂特性。     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

S-O bond chemically constrained NiS2/rGO nanocomposite with enhanced Na-ion storage capacity

NiS₂ has become a research hotspot of anode materials for Na-ion batteries due to its high theoretical specific capacity. However, the volume effect, the dissolution of polysulfide intermediates and the low conductivity during the charge/discharge process lead to the low specific capacity and poor cycling stability. NiS₂/rGO nanocomposite was prepared by a facile two-step process: GO was prepared by modified Hummers method, and then NiS₂/rGO nanocomposite was synthesized by l-cys assisted hydrothermal method. NiS₂/rGO nanocomposite shows excellent cycle performance and rate performance, which could be attributed to the mesoporous structure on the graphene skeleton with high conductivity. Besides, the chemical constraint of a unique SO bond on NiS₂ could inhibit the dissolution of intermediates and the loss of irreversible capacity.     

用标准件对梯度磁场定标

就标准厚度卡片在霍尔传感器的定标方面的应用作了有益的探讨。在纵向测量微小长度时,霍尔片处于磁场边缘位置,其对磁场的梯度更大,即灵敏度更高,且靠中心位置的线性更好。     

Two-dimensional optical coherence tomography for real-time structural dynamical characterization

We present a two-dimensional optical coherence vibration tomography (2DOCVT) system with an ultra-precision displacement resolution of ~0.1 nm that is capable of in site real-time absolute displacement measurement of structural line vibrations. Experimental results of sinusoidal, sweep and impulse vibrations were reported. The key figures of merit such as the 2DOCVT system could obtain fast line vibration measurement without scanning and it also could be used to capture structural modal parameters in one single impulse excitation measurement without any vibration excitation input information, making it attractive for the application in low-frequency vibration measurement and response-only modal analysis.     

Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating

In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle. Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation. The singularity of stresses near the crack front is investigated, and the stress intensity factors (SIFs) as well as energy release rates (ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.     

Assessing G4-Binding Ligands In Vitro and in Cellulo Using Dimeric Carbocyanine Dye Displacement Assay

G-quadruplexes (G4) are the most actively studied non-canonical secondary structures formed by contiguous repeats of guanines in DNA or RNA strands. Small molecule mediated targeting of G-quadruplexes has emerged as an attractive tool for visualization and stabilization of these structures inside the cell. Limited number of DNA and RNA G4-selective assays have been reported for primary ligand screening. A combination of fluorescence spectroscopy, AFM, CD, PAGE, and confocal microscopy have been used to assess a dimeric carbocyanine dye B6,5 for screening G4-binding ligands in vitro and in cellulo. The dye B6,5 interacts with physiologically relevant DNA and RNA G4 structures, resulting in fluorescence enhancement of the molecule as an in vitro readout for G4 selectivity. Interaction of the dye with G4 is accompanied by quadruplex stabilization that extends its use in primary screening of G4 specific ligands. The molecule is cell permeable and enables visualization of quadruplex dominated cellular regions of nucleoli using confocal microscopy. The dye is displaced by quarfloxin in live cells. The dye B6,5 shows remarkable duplex to quadruplex selectivity in vitro along with ligand-like stabilization of DNA G4 structures. Cell permeability and response to RNA G4 structures project the dye with interesting theranostic potential. Our results validate that B6,5 can serve the dual purpose of visualization of DNA and RNA G4 structures and screening of G4 specific ligands, and adds to the limited number of probes with such potential.