求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

Pitch-Based Laminated Carbon Formed by Pressure Driving at Low Temperature as High-Capacity Anodes for Lithium Energy Storage Systems

Pitch has been used to prepare electrodes by high-temperature heat treatments for supercapacitors, lithium-ion batteries, on account of its rich aromatic ring structure. Here, the toluene-soluble component of pitch is used to prepare a kind of laminated carbon. This was realized by a template-free synthesis at low temperature with the addition of pressure. The toluene-soluble component has a small molecular weight, which makes the thermal deformation ability stronger and then enhances the orientation of the carbon layer with the help of pressure. The prepared anode exhibits a splendid electrochemical performance compared with the traditional graphite anode. A high stable capacity of approximately 550 mAh g⁻¹ at 50 mA g⁻¹, which is much higher than graphite (372 mAh g⁻¹), is obtained. Also, when the current density is up to 2 A g⁻¹, the capacity is about 150 mAh g⁻¹. Surprisingly, it also delivers a superior cycling performance. And when used as the anode/cathode electrode for lithium-ion capacitors, a high energy density can be obtained. The present work offers an opportunity to utilize the pitch source in lithium energy storage with promising cycle life, high energy/power density, and low cost.     

Alkaloid and Glycoside Compounds from the Fruits of Berberis atrocarpa and Their Anticomplementary Activities

Chemistry of Natural Compounds -     

Enhanced antifungal activities of four Zn(II) complexes based on uniconazole

Four Zn(II) complexes, [Zn L ₂(SO₄)]_n ( 1 ), [Zn L ₄(H₂O)₂]?2(NO₃)?4EtOH ( 2 ), [Zn L ₂Cl₂]? L ( 3 ), and [Zn L ₂Br₂]? L ( 4 ) ( L  = uniconazole), were synthesized using a hydrothermal method and characterized by elemental analysis, FT‐IR spectroscopy, and single‐crystal XRD. Complex 1 formed a one‐dimensional polymer chain. However, complexes 2 ‐ 4 were obtained as zero‐dimensional mononuclear coordination compounds. The antifungal activities of these complexes were then evaluated against four selected fungi using the mycelial growth rate method. The resulting data indicate that all complexes show better antifungal activities than their ligands and mixtures. In addition, the interactions between the metal salts of complexes 1 ‐ 4 and uniconazole seem to be synergistic. Furthermore, the polymer chain structure of complex 1 significantly enhanced the bioactivity, especially against Botryosphaeria ribis ( I ). Density functional theory (DFT) calculations were carried out to help explain the enhanced bioactivity after the formation of Zn(II) complexes. The resulting data show that the HOMO–LUMO energy gaps of complexes 1 ‐ 4 (0.0578, 0.0946, 0.1053, and 0.1245 eV) are smaller than that of the free ligand (0.1247 eV) and correlate with the antifungal activity of the zinc complexes.     

Highly selective propylene dimerization catalyzed by C1‐symmetric zirconocene complexes

A series of ethylene‐bridged C₁‐symmetric ansa‐(3‐R‐indenyl)(fluorenyl) zirconocene complexes ( 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ) incorporating a pendant arene substituent on the 3‐position of indenyl ring have been synthesized. The structure of complex 4 was further confirmed by X‐ray diffraction analysis. When activated with methylaluminoxane, four sterically less encumbered complexes 1 , 2 , 4 and 5 could catalyze the dimerization of propylene in toluene at 100°C to afford 2‐methyl‐1‐pentene with high selectivities up to 95.7–98.4% and moderate activities of 2.00 × 10⁴ to 7.89 × 10⁴ g (mol‐Zr?h)^?1. Copyright © 2014 John Wiley & Sons, Ltd.     

Quantum Fisher information and chaos in the Dicke model

We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in position and momentum variables, during a tunable time span. We study two cases: the reconstruction of the wavefunctions of pure states and the direct measurement of the density matrix of mixed states. We show that our method can be applied to several physical systems where high quantum control can be experimentally achieved.     

Enantioselective Self‐Assembly of Triangular Dy3 Clusters with Single‐Molecule Magnet Behavior

Three pairs of enantiopure chiral triangular Ln₃ clusters, [Ln₃L_{RRRRRR/SSSSSS}(μ₃‐OH)₂(H₂O)₂(SCN)₄]?xCH₃OH?yH₂O ( R ‐Dy₃ , Ln=Dy, x=6, y=0; S ‐Dy₃ , Ln=Dy, x=6, y=1; R ‐Ho₃ , Ln=Ho, x=6, y=1; S ‐Ho₃ , Ln=Ho, x=6, y=1; R ‐Er₃ , Ln=Er, x=6, y=0; S ‐Er₃ , Ln=Er, x=6, y=1), have been successfully synthesized by a rational enantioselective synthetic strategy. The core of triangular Ln₃ is bound in the central N₆O₃ of the macrocyclic ligand, and the coordination spheres of Ln ions are completed by four SCN^? anions and two H₂O molecules in axial positions of the macrocycle. The circular dichroism (CD) and vibrational circular dichroism (VCD) spectra of the enantiomers demonstrate that the chirality is successfully transferred from the ligands to the resulting Ln₃ clusters. Ac susceptibility measurements reveal that single‐molecule magnet behavior occurs for both enantiopure clusters of R ‐Dy₃ and S ‐Dy₃ . This work is one of the few examples of the successful design of a pair of triangular Dy₃ clusters showing simultaneously slow magnetic relaxation and optical activity, and this might open up new opportunities to develop novel multifunctional materials.     

Enantioselective Synthesis of a Chiral Coordination Polymer with Circularly Polarized Visible Laser

Circular dichroism is known to be the feature of a chiral agent which has inspired scientist to study the interesting phenomena of circularly polarized light (CPL) modulated molecular chirality. Although several organic molecules or assemblies have been found to be CPL‐responsive, the influence of CPL on the assembly of chiral coordination compounds remains unknown. Herein, a chiral coordination polymer, which is constructed from achiral agents, was used to study the CPL‐induced enantioselective synthesis. By irradiation with either left‐handed or right‐handed CPL during the reaction and crystallization, enantiomeric excesses of the crystalline product were obtained. Left‐handed CPL resulted in crystals with a left‐handed helical structure, and right‐handed CPL led to crystals with a right‐handed helical structure. It is exciting that the absolute asymmetric synthesis of a chiral coordination polymer could be enantioselective when using CPL, and provides a strategy for the control of the chirality of chiral coordination polymers.