Micellar selectivity triangle for classification of chemical selectivity in electrokinetic chromatography

A novel micellar selectivity triangle (MST) is developed and used to characterize and classify the chemical selectivities of pseudo-phases in electrokinetic chromatography (EKC). The MST scheme is, in concept, similar to the widely known solvent selectivity triangle (SST) originally developed by Snyder. However, the MST is based on linear solvation energy relationships. Thus it incorporates the solvation characteristics of both the pseudo-phase and the bulk solvent; while the SST is basically for classification of pure solvents. The similarities and differences of these pseudo-phases are determined by the relative scales of hydrogen bond donating ability (X_b), hydrogen bond accepting ability (X_a) and dipolarity (X_s). The MST scheme is used for characterization and classification of a wide range of pseudo-phases such as micelles, polymers, vesicles, liposomes, as well as mixed systems such as mixed micelles, mixed polymer–surfactants, organically modified pseudo-phases, etc. Over seventy pseudo-phases were examined and four clusters of pseudo-phases with different selectivity patterns are recognized that include pseudo-phases with strong hydrogen bond acidities (e.g. fluorinated micelles or micelles modified with fluorinated alcohols), strong hydrogen bond acceptor pseudo-phases (such as bile salts, liposomes, microemulsions, as well as biphasic octanol–water system), strong dipolar phase of a class of polymeric pseudo-phase, and pseudo-phases with intermediate hydrogen bonding and dipolarity [like sodium dodecyl sulfate (SDS) and its analogs as well as organically modified SDS]. The MST scheme is also useful in identifying pseudo-phases that closely resemble the selectivities of octanol–water for determination of octanol–water partition coefficients by EKC.     

柴胡舒肝丸的毛细管电泳指纹图谱及其黄芩苷含量的测定

建立了柴胡舒肝丸(Chaihu Shugan Pill, CHSGP)的毛细管区带电泳指纹图谱(capillary electrophoresis fingerprint, CEFP),并采用内标法测定了黄芩苷的含量。以50 mmol/L硼砂-150 mmol/L磷酸二氢钠-50 mmol/L磷酸氢二钠(1:1:1, v/v/v)(含5 mmol/L庚烷磺酸钠)为背景电解质(BGE)溶液,采用未涂层石英毛细管(总长度75 cm,有效分离长度63 cm,内径75 μm),以色谱指纹图谱分离量指数(RF)为目标函数优化实验条件,在紫外检测波长265 nm、运行电压11 kV条件下,以黄芩苷峰为参照物峰,确定了22个共有指纹峰,建立了CHSGP的CEFP,通过对20批样品聚类分析确定用其中13批生成对照CEFP(RCEFP),以此RCEFP为标准用系统指纹定量法鉴别20批柴胡舒肝丸质量。结果其中的4批化学成分数量和分布比例不合格,4批含量明显偏低,其他12批完全合格。采用内标法测定黄芩苷的含量,在5～200 mg/L范围内线性良好(r=0.9999),平均回收率(n=9)为98.2%。该法具有较好的精密度和重现性,为柴胡舒肝丸的质量控制提供了一种新的参考。     

Divergent synthesis of the tetracyclic ethers of 6-X-7-6 ring systems

Ladder-shaped polyether natural products show diverse biological activities with extreme potency. As the initial phase of detailed SAR studies of bioactive polyethers, we set out to construct structurally simple mimics. This paper details the divergent synthesis of 6-X-7-6 tetracycles (X=7, 8, or 9) starting from a simple 6-membered ether. Key reactions in the synthesis include (i) the direct formation of an O,S-acetal by the coupling of an alcohol with an α-chlorosulfide, (ii) the construction of a 7-membered ring by radical cyclization, and (iii) cyclization to the 7, 8 or 9-membered ring via a ring-closing metathesis reaction. The neutral reaction conditions of our strategy enable the synthesis of a wide variety of substrates. The results of this study can be applied for the rapid construction of artificial polyether compounds with diversified molecular shapes and sizes.     

Fermilab top mass and modified Fritzsch mass matrices

Fritzsch like mass matrices with non-zero 22-elements both in U sector and D sector have been investigated in the context of latest data regardingm _t ^phys , |V _ub|, |V _cb|, |V _td| and |V _ts|. Unlike several other phenomenological models, the present model not only accommodates the value ofm _t ^phys in the range 150–240 GeV, encompassing the CDF and D0 values, but is also able to reproduce |V _cb| ≊0.040 and |V _ub/V_cb| = 0.08±0.02 and |V _td| is predicted to lie in the range 0.005–0.014. Further, the angles of the unitarity triangle, related to the CP-violating asymmetries, are calculated to be in the ranges −1.0⩽sin2α⩽−0.1, 0.6 ⩽sin2α⩽1.0 and 0.48⩽sin2β⩽0.56, which are in agreement with other recent calculations.     

A brief remark on van der Waerden spaces

We demonstrate that Martin's axiom for -centered notions of forcing implies the existence of a van der Waerden space that is not a Hindman space. Our proof is an adaptation of the one given by M. Kojman and S. Shelah that such a space exists if one assumes the continuum hypothesis to be true.

     

非线性不等式组的光滑近似方法及其收敛性

将非线性不等式组的求解转化成非线性最小二乘问题,利用引入的光滑辅助函数,构造新的极小化问题来逐次逼近最小二乘问题.在一定的条件下,文中所提出的光滑高斯-牛顿算法的全局收敛性得到保证.适当条件下,算法的局部二阶收敛性得到了证明.文后的数值试验表明本文算法有效.     

一个高精度收敛的变系数微分方程精确解析法*

文[1]给出精确解析法,可用于求解任意变系数微分方程,所得到的解具有二阶收敛精度.在此基础上,本文以变截面梁弯曲为例,给出一个高精度的算法.不增加工作量的情况下可达到四阶收敛精度.具有计算快,简单等特点,文末给出算例,仅用很少的单元即可获得高的收敛精度,表明了本文理论的正确性.     

Two‐step Newton‐type methods for solving inverse eigenvalue problems

In this paper, we apply the two‐step Newton method to solve inverse eigenvalue problems, including exact Newton, Newton‐like, and inexact Newton‐like versions. Our results show that both two‐step Newton and two‐step Newton‐like methods converge cubically, and the two‐step inexact Newton‐like method is super quadratically convergent. Numerical implementations demonstrate the effectiveness of new algorithms.     

Symplectic Shifted Tableaux and Deformations of Weyl's Denominator Formula for sp(2n)

A determinantal expansion due to Okada is used to derive both a deformation of Weyl's denominator formula for the Lie algebra sp(2n) of the symplectic group and a further generalisation involving a product of the deformed denominator with a deformation of flagged characters of sp(2n). In each case the relevant expansion is expressed in terms of certain shifted sp(2n)-standard tableaux. It is then re-expressed, first in terms of monotone patterns and then in terms of alternating sign matrices.