共轭线性对称性及其对PT-对称量子理论的应用

传统量子系统的哈密顿是自伴算子,哈密顿的自伴性不仅保证系统遵循酉演化和保持概率守恒,而且也保证了它自身具有实的能量本征值,这类系统称为自伴量子系统.然而,确实存在一些物理系统(如PT-对称量子系统),其哈密顿不是自伴的,这类系统称为非自伴量子系统.为了深入研究PT-对称量子系统,并考虑到算子PT的共轭线性性,首先讨论了共轭线性算子的一些性质,包括它们的矩阵表示和谱结构等;其次,分别研究了具有共轭线性对称性和完整共轭线性对称性的线性算子,通过它们的矩阵表示,给出了共轭线性对称性和完整共轭线性对称性的等价刻画;作为应用,得到了关于PT-对称及完整PT-对称算子的一些有趣性质,并通过一些具体例子,说明了完整PT-对称性对张量积运算不具有封闭性,同时说明了完整PT-对称性既不是哈密顿算子在某个正定内积下自伴的充分条件,也不是必要条件.     

Photochemical synthesis: Using light to build C–C bonds under mild conditions

A review of recent advancements in metal-free arylations via photogenerated triplet aryl cations and decatungstate anion ([W₁₀O₃₂]⁴⁻) photocatalyzed C–C bond formation is reported herein. These approaches are two examples of the great potentialities of photons as green activants in organic synthesis, allowing the functionalization of different chemical substrates under mild conditions (room temperature, aqueous solvents, absence of aggressive and unstable reactants and of expensive transition metal-based catalysts, and chance to use solar light as the energy source).     

Development of a competitive ELISA for the quantification of F5 conjugate in HER2-targeted STEALTH immunoliposome doxorubicin in plasma samples

HER2 (human epidermal growth factor receptor 2, erbB2, or neu) is overexpressed by a large number of tumor types and has been identified as an important target for cancer therapy. F5 is a single-chain human antibody fragment that recognizes HER2 receptor and is covalently conjugated to PEGylated lipid to form F5 conjugate (F5CG) in the product HER2 targeted STEALTH immunoliposome doxorubicin. Here we described the method development of a competitive enzyme-linked immunosorbent assay (ELISA) for the determination of total concentration of F5 conjugate in plasma samples. The method involved the biotinylation of F5CG, detergent treatment of plasma sample to solubilize F5CG into monomeric form, and competitive ELISA for solubilized F5CG competitively binding to anti-F5CG antibody with biotinylated F5CG for the determination of total F5CG in plasma. The detection range of this method was from 0.2 ng/mL to 125 ng/mL for F5CG in plasma. The lower limit of quantification (LLOQ) was 0.2 ng/mL. This method was established and used for the measurement of F5CG concentration to provide information about F5CG circulation after the administration of immunoliposome in preclinical studies.      

Modulation of Multifunctional N,O,P Ligands for Enantioselective Copper‐Catalyzed Conjugate Addition of Diethylzinc and Trapping of the Zinc Enolate

In this work, we have successfully synthesized a new family of chiral Schiff base–phosphine ligands derived from chiral binaphthol (BINOL) and chiral primary amine. The controllable synthesis of a novel hexadentate and tetradentate N,O,P ligand that contains both axial and sp³‐central chirality from axial BINOL and sp³‐central primary amine led to the establishment of an efficient multifunctional N,O,P ligand for copper‐catalyzed conjugate addition of an organozinc reagent. In the asymmetric conjugate reaction of organozinc reagents to enones, the polymer‐like bimetallic multinuclear Cu? Zn complex constructed in situ was found to be substrate‐selective and a highly excellent catalyst for diethylzinc reagents in terms of enantioselectivity (up to >99 % ee). More importantly, the chirality matching between different chiral sources, C₂‐axial binaphthol and sp³‐central chiral phosphine, was crucial to the enantioselective induction in this reaction. The experimental results indicated that our chiral ligand (R,S,S)‐ L1 ‐ and (R,S)‐ L4 ‐based bimetallic complex catalyst system exhibited the highest catalytic performance to date in terms of enantioselectivity and conversion even in the presence of 0.005 mol % of catalyst (S/C=20 000, turnover number (TON)=17 600). We also studied the tandem silylation or acylation of enantiomerically enriched zinc enolates that formed in situ from copper‐ L4 ‐complex‐catalyzed conjugate addition, which resulted in the high‐yield synthesis of chiral silyl enol ethers and enoacetates, respectively. Furthermore, the specialized structure of the present multifunctional N,O,P ligand L1 or L4 , and the corresponding mechanistic study of the copper catalyst system were investigated by ³¹P NMR spectroscopy, circular dichroism (CD), and UV/Vis absorption.     

3β-羟基-16α,17α,21－三甲基孕甾-5-烯-20-酮的合成

皮质激素;;甲基化;共轭加成;瑞美松龙;3β-羟基-16α;17α;21－三甲基孕甾-5-烯-20-酮的合成     

3-维不定空间中晶体群的分类

设V是3-维不定空间,W是V中某个不可约根系的无限Weyl群,本文在仿射群A(V)中共轭的意义下,给出了点群为W的晶体群的分类。     

一类非线性矩阵方程对称解的双迭代算法

利用逆矩阵的Neumann级数形式,将在Schur插值问题中遇到的含未知矩阵二次项之逆的非线性矩阵方程转化为高次多项式矩阵方程,然后采用牛顿算法求高次多项式矩阵方程的对称解,并采用修正共轭梯度法求由牛顿算法每一步迭代计算导出的线性矩阵方程的对称解或者对称最小二乘解,建立求非线性矩阵方程的对称解的双迭代算法.双迭代算法仅要求非线性矩阵方程有对称解,不要求它的对称解唯一,也不对它的系数矩阵做附加限定.数值算例表明,双迭代算法是有效的.     

非即变相位共轭反馈对半导体激光器动态特性的影响

从四波混频产生相位共轭的物理原因出发,定义了相位共轭镜（PCM）的响应时间．建立起非即变相位共轭反馈条件下半导体激光器的外腔模型。以响应时间及频率失调为参变量,对其分岔及噪声等动态行为进行数值分析。结果表明,不考虑噪声影响时,增加相位共轭镜响应时间会使混沌带出现的次数和范围得到较大的抑制,当响应时间增大到1．5ns时,混沌带消失,半导体激光器保持稳定的单周期状态;考虑噪声影响后,随若响应时间的相对强度噪声（RIN）可减小几dB甚至十几dB,产生突变需要的反馈量也增大一个数量级以上,且其频谱的峰值向高频方向移动;另外,由于共轭反馈引起的频率失调低于半导体激光器激射频率3个数量级以上．它只对分岔特性有影响．对相对强度噪声的影响几乎为零。     

一类新共轭梯度法的全局收敛性

共轭梯度法是求解无约束最优化问题的有效方法.本文在βkDY的基础上对βk引入参数,提出了一类新共轭梯度法,并证明其在强Wolfe线性搜索条件下具有充分下降性和全局收敛性.     

On block preconditioners for saddle point problems with singular or indefinite (1, 1) block

We discuss a class of preconditioning methods for the iterative solution of symmetric algebraic saddle point problems, where the (1, 1) block matrix may be indefinite or singular. Such problems may arise, e.g. from discrete approximations of certain partial differential equations, such as the Maxwell time harmonic equations. We prove that, under mild assumptions on the underlying problem, a class of block preconditioners (including block diagonal, triangular and symmetric indefinite preconditioners) can be chosen in a way which guarantees that the convergence rate of the preconditioned conjugate residuals method is independent of the discretization mesh parameter. We provide examples of such preconditioners that do not require additional scaling. Copyright © 2010 John Wiley & Sons, Ltd.