截断分层B样条基的Lp稳定性

The truncated hierarchical B-spline basis has been proposed for adaptive data fitting and has already drawn a lot of attention in theory and applications.However the stability with respect to the L_p-norm,1≤p∞,is not clear.In this paper,we consider the L_p stability of the truncated hierarchical B-spline basis,since the L_p stability is useful for curve and surface fitting,especially for least squares fitting.We prove that this basis is weakly L_p stable.This means that the associated constants to be considered in the stability analysis are at most of polynomial growth in the number of the hierarchy depth.     

Zone fluidics for measurement of octanol–water partition coefficient of drugs

A novel zone fluidics (ZF) system for the determination of the octanol–water partition coefficient (P_ow) of drugs was developed. The ZF system consisted of a syringe pump with a selection valve, a holding column, a silica capillary flow-cell and an in-line spectrophotometer. Exact microliter volumes of solvents (octanol and phosphate buffer saline) and a solution of the drug, sandwiched between air segments, were sequentially loaded into the vertically aligned holding column. Distribution of the drug between the aqueous and octanol phases occurred by the oscillation movement of the syringe pump piston. Phase separation occurred due to the difference in densities. The liquid zones were then pushed into the detection flow cell. In this method, absorbance measurements in only one of the phase (octanol or aqueous) were employed, which together with the volumes of the solvents and pure drug sample, allowed the calculation of the P_ow. The developed system was applied to the determination of the P_ow of some common drugs. The log (P_ow) values agreed well with a batch method (R² = 0.999) and literature (R² = 0.997). Standard deviations for intra- and inter-day analyses were both less than 0.1log unit. This ZF system provides a robust and automated method for screening of P_ow values in the drug discovery process.     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS(Ⅰ)

ＮＯＴＥＳＯＮＡＳＴＵＤＹＯＦＶＥＣＴＯＲＢＵＮＤＬＥＤＹＮＡＭＩＣＡＬＳＹＳＴＥＭＳ（Ⅰ）ＬｉａｏＳｈａｎｔａｏ（廖山涛）（ＭａｔｈｅｍａｔｉｃｓＤｅｐａｒｔｍｅｎｔａｎｄＭａｔｈｅｍａｔｉｃｓＩｎｓｔｉｔｕｔｅ，ＰｅｋｉｎｇＵｎｉｒｅｒｓｉｔｙ，...     

Solid‐phase microextraction with gas chromatography and mass spectrometry determination of benzo(a)pyrene in microcrystalline waxes used as food additives

Microcrystalline waxes are mixtures of solid, saturated hydrocarbons mainly branched and characterized by a carbon number over C₆₀. They are used as food additives for the surface treatment of confectionery and some fruit varieties, in chewing gum base, protective coatings, defoaming agents, and surface finishing agents. Commission Regulation No 231/2012 established physical and chemical specifications for microcrystalline waxes to use in food, and posed a limit of 50 μg/kg for benzo(a)pyrene. Due to the low solubility of microcrystalline waxes in organic solvents and matrix interferences, analytical determination of benzo(a)pyrene represents a difficult task. The official method for indirect determination of total polycyclic aromatic hydrocarbons uses unspecific spectrophotometric detection and a quite laborious, time‐ and solvent‐consuming extraction method. A liquid–liquid partition method followed by solid‐phase microextraction was developed to isolate benzo(a)pyrene from the bulk of saturated hydrocarbons in microcrystalline waxes, with the aim to have a simple and effective method to verify compliance with the legal limit. The final determination was carried out by gas chromatography coupled to mass spectrometry. Good linearity was obtained, along with a recovery of about 80% from the liquid–liquid partitions. The repeatability of the entire method was <6% and accuracy was <3%.     

Fundamental studies on the feasibility of deep eutectic solvents for the selective partition of glaucarubinone present in the roots of Simarouba glauca

Several deep eutectic solvents prepared by the complexation of choline chloride as the hydrogen bond acceptor and hydrogen bond donors such as urea, thiourea, ethylene glycol, and glycerol were employed to partition glaucarubinone, an antimalarial compound present in roots of the plant, Simarouba glauca. Among all the solvents, the deep eutectic solvent consisting of the mixture of choline chloride and urea the most suitable to partition the antimalarial compound from the extract selectively. Analytical tools such as high‐performance liquid chromatography and electrospray ionization mass spectrometry were used for characterizations, and glaucarubinone extracted from the roots of the plant by conventional solvent extraction method was used as a reference for comparison. The hydrogen and noncovalent bonds formed between glaucarubinone and the deep eutectic solvents could be responsible for the selective partition of the drug molecule.     

一类六边形网格上拉普拉斯4点差分格式及其预条件子

本文提出平面上拉普拉斯算子在一类平行六边形网格上的成对4点差分格式.这种差分格式虽然只有一阶的局部截断误差,但实际具有二阶的收敛性.基于平行六边形网格可以被分解为两套三向三角形网格,我们给出成对4点格式的二阶收敛性的证明,并且提出相应的预条件子快速解法.文末给出的数值算例符合我们的结论.     

利用气相色谱相对比保留体积估算芳烃的正辛醇/水分配系数

采用气相色谱法在９种常见的固定液上分别测定了１３种芳烃的相对比保留体积,同时对经典的摇瓶法测定了相同化合物的正辛醇／水分配系数,并以此建立了（Ｖｇ〈Ｒ〉－Ｋｖｗ回归方程。利用所建立的回归方程和１３种芳烃化合物的Ｖｇ〈Ｒ〉值对其Ｋｖｗ进行估算的结果表明,选用９种固定液中的任何一种,其Ｋｖｗ估算值的相对误差均在允许的范围内,其中以选用固定液ＤＣ－２００,ＳＥ－３０和ＰＥＧ－２０Ｍ误差较小。     

Temperature dependence of the calibration factor of radon and radium determination in water samples by SSNTD

The sensitivity of a ²²⁶Ra determination method of water samples by SSNTD was measured as a function of storage temperature during exposure. The method is based on an etched track type radon monitor, which is closed into a gas permeable foil and is immersed in the water sample. The sample is sealed in a glass vessel and stored for an exposure time of 10–30 days. The sensitivity increased more than a factor of two when the storage temperature was raised from 2 °C to 30 °C. Temperature dependence of the partition coefficient of radon between water and air provides explanation for this dependence. For practical radio-analytical application the temperature dependence of the calibration factor is given by fitting the sensitivity data obtained by measuring ²²⁶Ra standard solutions (in the activity concentration range of 0.1–48.5 kBq m⁻³) at different storage temperatures.     

胆固醇基键合相-反相高效液相色谱法测定正辛醇/水分配系数

通过反相高效液相色谱法系统地考察了中性和弱酸性化合物在新型胆固醇基键合相色谱柱（Cholester柱）上的保留行为。以甲醇和乙腈为有机调节剂,建立了保留因子（k）与有机调节剂比例（φ）间的关系,并外推获取100%水相为流动相时的log k_w;同时进一步建立并验证了不同流动相下正辛醇/水分配系数的对数（log K_ow）和log k_φ（log k_w）间的模型,并预测了部分化合物的log K_ow。结果表明,使用Cholester柱测定log K_ow时,甲醇比乙腈更适合作为有机调节剂;对中性化合物和中性状态的酸性化合物,可以用任意甲醇比例下获取的log k_φ预测log K_ow;对存在离解的酸性化合物,依然用外推方式获取的log k_w预测log K_ow。将采用Cholester柱与文献中采用C₁₈柱、C₈柱建立的log K_ow-log k_φ模型进行对比,结果表明化合物与胆固醇基键合相存在特别的作用。     

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.