On packing 3‐vertex paths in a graph

Let G be a connected graph and let eb(G) and λ(G) denote the number of end‐blocks and the maximum number of disjoint 3‐vertex paths Λ in G. We prove the following theorems on claw‐free graphs: (t1) if G is claw‐free and eb(G) ≤ 2 (and in particular, G is 2‐connected) then λ(G) = ⌊| V(G)|/3⌋; (t2) if G is claw‐free and eb(G) ≥ 2 then λ(G) ≥ ⌊(| V(G) | − eb(G) + 2)/3 ⌋; and (t3) if G is claw‐free and Δ^*‐free then λ(G) = ⌊| V(G) |/3⌋ (here Δ^* is a graph obtained from a triangle Δ by attaching to each vertex a new dangling edge). We also give the following sufficient condition for a graph to have a Λ‐factor: Let n and p be integers, 1 ≤ p ≤ n − 2, G a 2‐connected graph, and |V(G)| = 3n. Suppose that G − S has a Λ‐factor for every S ⊆ V(G) such that |S| = 3p and both V(G) − S and S induce connected subgraphs in G. Then G has a Λ‐factor. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 175–197, 2001     

Statistical Analysis of Simulated Random Packings of Spheres

This paper describes two algorithms for the generation of random packings of spheres with arbitrary diameter distribution. The first algorithm is the force‐biased algorithm of Mościński and Bargieł. It produces isotropic packings of very high density. The second algorithm is the Jodrey‐Tory sedimentation algorithm, which simulates successive packing of a container with spheres following gravitation. It yields packings of a lower density and of weak anisotropy. The results obtained with these algorithms for the cases of log‐normal and two‐point sphere diameter distributions are analysed statistically, i. e. standard characteristics of spatial statistics such as porosity (or volume fraction), pair correlation function of the system of sphere centres and spherical contact distribution function of the set‐theoretical union of all spheres are determined. Furthermore, the mean coordination numbers are analysed. These results are compared for both algorithms and with data from the literature based on other numerical simulations or from experiments with real spheres.     

Method development for the determination of 24S‐hydroxycholesterol in human plasma without derivatization by high‐performance liquid chromatography with tandem mass spectrometry in atmospheric pressure chemical ionization mode

We developed a highly sensitive and specific high‐performance liquid chromatography with tandem mass spectrometry method with an atmospheric pressure chemical ionization interface to determine 24S‐hydroxycholesterol, a major metabolite of cholesterol formed by cytochrome P450 family 46A1, in human plasma without any derivatization step. Phosphate buffered saline including 1% Tween 80 was used as the surrogate matrix for preparation of calibration curves and quality control samples. The saponification process to convert esterified 24S‐hydroxycholesterol to free sterols was optimized, followed by liquid–liquid extraction using hexane. Chromatographic separation of 24S‐hydroxycholesterol from other isobaric endogenous oxysterols was successfully achieved with gradient mobile phase comprised of 0.1% propionic acid and acetonitrile using L‐column2 ODS (2 μm, 2.1 mm id × 150 mm). This assay was capable of determining 24S‐hydroxycholesterol in human plasma (200 μL) ranging from 1 to 100 ng/mL with acceptable intra‐ and inter‐day precision and accuracy. The potential risk of in vitro formation of 24S‐hydroxycholesterol by oxidation from endogenous cholesterol in human plasma was found to be negligible. The stability of 24S‐hydroxycholesterol in relevant solvents and human plasma was confirmed. This method was successfully applied to quantify the plasma concentrations of 24S‐hydroxycholesterol in male and female volunteers.     

On-Line Coupling of Separation Techniques to NMR

The hyphenation of chromatographic separation techniques with NMR spectroscopy is one of the most powerful and time-saving methods for the separation and structural elucidation of unknown compounds and molecular compositions of mixtures. Most of the routinely used NMR flow-cells have detection volumes between 40–180 μL for conventional separations with analytical columns, and the newest designs employ detection volumes in the order of 200 nL for capillary separations. The low flow rates used in capillary chromatography permit the use of deuterated solvents. Unequivocal structural assignment of unknown chromatographic peaks is possible by two-dimensional stopped-flow capillary HPLC-NMR experiments.     

Characterization of Ascentis RP-Amide column: Lipophilicity measurement and linear solvation energy relationships

This study investigates lipophilicity determination by chromatographic measurements using the polar embedded Ascentis RP-Amide stationary phase. As a new generation of amide-functionalized silica stationary phase, the Ascentis RP-Amide column is evaluated as a possible substitution to the n  -octanol/water partitioning system for lipophilicity measurements. For this evaluation, extrapolated retention factors, log k^′_w$\text{log}{k^{\prime }}_w$, of a set of diverse compounds were determined using different methanol contents in the mobile phase. The use of n-octanol enriched mobile phase enhances the relationship between the slope (S  ) of the extrapolation lines and the extrapolated log k^′_w$\text{log}{k^{\prime }}_w$ (the intercept of the extrapolation), as well as the correlation between log P   values and the extrapolated log k^′_w$\text{log}{k^{\prime }}_w$ (1:1 correlation, r² = 0.966). In addition, the use of isocratic retention factors, at 40% methanol in the mobile phase, provides a rapid tool for lipophilicity determination. The intermolecular interactions that contribute to the retention process in the Ascentis RP-Amide phase are characterized using the solvation parameter model of Abraham. The LSER system constants for the column are very similar to the LSER constants of the n-octanol/water extraction system. Tanaka radar plots are used for quick visual comparison of the system constants of the Ascentis RP-Amide column and the n-octanol/water extraction system. The results all indicate that the Ascentis RP-Amide stationary phase can provide reliable lipophilic data.     

分离生物大分子的液相色谱固定相

本文介绍了各类用于生物大分子分离的液相色谱填料,并对它们在生物大分子分离及制备中的性能、基本特征作了评述。     

基于MATLAB的色谱分析初级专家系统的设计

MATLAB是 Mathworks公司推出的适用于科学和工程计算的数学软件系统 ,可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题 ,且具有可视化图形处理、使用方便、开放式多功能于一体的新一代计算机语言。文中讨论了利用 MATLAB开放式可扩充体系结构 ,开发出色谱分析综合性计算机初级专家系统的构想和设计思想。     

Intermolecular interactions and structural dichotomy in 1,3,2,4-benzodithiadiazine crystals

The intermolecular interactions and structural dichotomy in 1,3,2,4-benzodithiadiazine crystals (1) (the heterocycle is planar for one derivative, but bent for another) were studied in terms of topological analysis of electron density (ED) using QTAIM theory and crystal packing modeling in an OPiX approximation. The intermolecular interactions in crystals 1 can be detected and quantified by means of the critical points (CPs) of ED with (3, ?1). The total value of ED at all CPs of a molecule can be correlated with the torsion angle that defines the bending of its heterocycle; the larger the total ED at intermolecular CPs, the smaller the bending of the heterocycle. Thus, under the conditions of weak intermolecular interactions in crystal, molecules 1 preserve the bent conformations typical of the gas phase; strong intermolecular interactions lead to planar conformations.     

Advantages of a small-volume counter-current chromatography column

Counter-current chromatography (CCC) works with a support-free liquid stationary phase. This allows for preparative separations and purifications. However, there are serious technical constraints because of the need to keep a liquid stationary phase in a column. Centrifugal fields are used. A new commercial hydrodynamic 18 mL column made with a narrow-bore 0.8 mm Teflon tubing was evaluated by comparing it with older hydrodynamic CCC columns and a similar 19 mL column but made with 1.6 mm Teflon tubing. A small-volume CCC column allows for reliable and fast solute partition coefficient determination. When resolution is required, both high efficiency and liquid stationary phase retention are needed. Unfortunately, these two requirements bear technical contradictions. A column coiled with a narrow tubing bore will provide a high chromatographic efficiency while a column containing wider tubing bore will achieve higher stationary phase retention. In all cases, increasing the magnitude of the centrifugal field also increases the stationary phase retention. The solution is to build centrifuges able to produce high fields that will provide acceptable liquid phase retention with narrow-bore tubes. The new 18 mL 0.8 mm tubing bore column is able to rotate as fast as 2100 rpm generating a 240 × g field. The two older CCC columns cannot compete with the new one. However, the small 19 mL column with 1.6 mm bore tubing can be useful when fast results are desired without top resolution.