Closed paths of light trapped in a closed Fermat curve

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the curve varies, including a generalization to non integer powers.     

Towards predicting the solubility of CO2 and N2 in different polymers using a quasi-SMILES based QSPR approach

The solubility of gases in various polymers plays an important role for the design of new polymeric materials. Quantitative structure–property relationship (QSPR) models were designed to predict the solubility of gases such as CO₂ and N₂ in polyethylene (PE), polypropylene (PP), polystyrene (PS), polyvinyl acetate (PVA) and poly (butylene succinate) (PBS) at different temperatures and pressures by using quasi-SMILES codes. The dataset of 315 systems was split randomly into training, calibration and validation sets; random split 1 led to 214 training (r² = 0.870 and RMSE = 0.019), 51 calibration (r² = 0.858 and RMSE = 0.020) and 50 validation (r² = 0.869 and RMSE = 0.017) sets. The suggested approach based on the quasi-SMILES, which are analogues of the traditional SMILES gives reasonable good predictions for solubility of CO₂ and N₂ in different polymers. The described methodology is universal for situations where the aim is to predict the response of an eclectic system upon a variety of physicochemical and/or biochemical conditions.     

13C NMR quantification of mono and diacylglycerols obtained through the solvent‐free lipase‐catalyzed esterification of saturated fatty acids

In the present investigation, we studied the enzymatic synthesis of monoacylglycerols (MAG) and diacylglycerols (DAG) via the esterification of saturated fatty acids (stearic, palmitic and an industrial residue containing 87% palmitic acid) and glycerol in a solvent‐free system. Three immobilized lipases (Lipozyme RM IM, Lipozyme TL IM and Novozym 435) and different reaction conditions were evaluated. Under the optimal reaction conditions, esterifications catalyzed by Lipozyme RM IM resulted in a mixture of MAG and DAG at high conversion rates for all of the substrates. In addition, except for the reaction of industrial residue at atmospheric pressure, all of these products met the World Health Organization and European Union directives for acylglycerol mixtures for use in food applications. The products were quantified by ¹³C NMR, with the aid of an external reference signal which was generated from a sealed coaxial tube filled with acetonitrile‐d3. After calibrating the area of this signal using the classical external reference method, the same coaxial tube was used repeatedly to quantify the reaction products. Copyright © 2012 John Wiley & Sons, Ltd.     

Toward a universal quantum QSPR operator

This article presents a discussion about the formalism, which might be associated to a general Quantum quantitative structure–properties relations operator, appearing in a Boltzmann‐like exponential form, which is based in turn on the definition of the concept of thermal voltage, applied to thermally scaled electronic density functions. Three practical numerical examples are presented, corresponding to the calculation of the polarization angle in assorted chiral molecules, the estimation of fish toxicity for perchlorobenzene within the set of chlorobenzenes and a typical quantum QSAR study on the popular Cramer steroid set.     

Simultaneous quantitation of 23 bioactive compounds in Tanreqing capsule by high‐performance liquid chromatography electrospray ionization tandem mass spectrometry

Tanreqing capsule (TRQC) is a formulation frequently used in traditional Chinese medicine to treat pyrexia, cough, expectoration and pharyngalgia. Since the pharmacological action of traditional Chinese medicines is closely related to their complex and diverse constituents, understanding the exact composition of TRQC is important to elucidate its clinical effectiveness and mechanism of action as well as to establish quality control methods and resolve safety issues. Herein, we employed high‐performance liquid chromatography coupled with electrospray ionization tandem mass spectrometry for the simultaneous quantitation of 23 bioactive compounds in five batches of TRQC; the analytes could be categorized into five types: organic acids (seven compounds), flavonoids (10 compounds), iridoids (two compounds), phenylethanoid glycosides (two compounds) and bile acids (two compounds). The calibration curves for all analytes showed good linearity (r > 0.9953), and the inter‐ and intra‐day precisions did not exceed 4.94 and 4.97%, respectively. The recoveries varied from 90.47% to 109.80%; the corresponding relative standard deviations (RSDs) did not exceed 4.94%; and the repeatability (RSD < 4.72%) and stability (RSD < 4.88%) were also within acceptable limits. Thus, this study can be viewed as a fundamental reference for setting comprehensive TRQC quality standards.     

Quantitative NMR (qNMR) for pharmaceutical analysis: The pioneering work of George Hanna at the US FDA

In the last two decades, quantitative NMR (qNMR) has become increasingly important for the analysis of pharmaceuticals, chemicals, and natural products including dietary supplements. For the purpose of quality control and chemical standardization of a large variety of pharmaceutical, chemical, and medicinal products, qNMR has proven to be a valuable orthogonal quantification method and a compelling alternative to chromatographic techniques. This work reviews a fundamental component of the early development of qNMR, reflected in the pioneering work of the late George M. Hanna during the years between 1984 and 2006 at the US Food and Drug Administration (FDA). Because Hanna performed the majority of his groundbreaking work on a 90‐MHz instrument, his legacy output connects with recent progress in low‐field benchtop NMR instrumentation. Hanna gradually established the utility of qNMR for the routine quality control analyses practiced in pharmaceutical and related operations well ahead of his peers. His work has the potential to inspire new developments in qNMR applied to small molecules of biomedical importance.     

Development of an HPLC‐DAD method for the determination of five alkaloids in Stephania yunnanensis Lo and in rat plasma after oral dose of Stephania yunnanensis Lo extracts

For the rational utilization and the quantitative quality control of the Stephania yunnanensis Lo, an HPLC‐DAD method was developed for the quantitative and simultaneous determination of five alkaloids in rat plasma (stepharine, sinomenine, palmatine, isocorydine and tetrahydropalmatine), which were the main active chemical constituents of this plant and belong to four kinds of isoquinoline‐type alkaloids (protoberberine, morphine, aporphine and protaporphine alkaloids). The contents of five alkaloids ranged from 0.09 to 2.32% (w/w). The method validation was tested for the linearity (r² > 0.9975), precision (intra‐day RSD < 4.8% and inter‐day RSD < 4.9%), extraction recovery (85.49 ± 2.29% to 99.21 ± 1.48%) and stability (98.5 ± 5.3% to 101.2 ± 3.4%). We developed an HPLC‐DAD method to simultaneously measure these alkaloids in rat plasma after oral administration of the extract of this plant to rats. The results supported the hypothesis that isoquinoline alkaloids were the compounds responsible for the main pharmacological activities for anti‐inflammatory and analgesic.     

Microwave‐assisted extraction in combination with HPLC‐UV for quantitative analysis of six bioactive oxoisoaporphine alkaloids in Menispermum dauricum DC

A novel and reliable method based on microwave‐assisted extraction (MAE) followed by HPLC‐UV was developed and validated for the simultaneous quantification of six pharmacologically important oxoisoaporphine alkaloids in the total plants of Menispermum dauricum DC. The optimal MAE extraction condition was performed at 60°C for 11 min with ethanol–water (70:30, v/v) as the extracting solvent, and the solvent to solid ratio was 20:1. Chromatographic separation was achieved on a reversed‐phase YMC C₁₈ column (250 × 4.6 mm, i.d., 5 µm) with a gradient mobile phase consisting of A (1% aqueous formic acid) and B (acetonitrile containing 1% formic acid) at a flow rate of 1.5 mL/min. The detection wavelength was set at 422 nm. Excellent linearity over the investigated concentration ranges was observed with values of r >0.999 for all analytes. The method developed was validated with acceptable sensitivity, intra‐ and inter‐day precision and extraction recoveries. It was successfully applied to the determination of six alkaloids in Menispermum dauricum DC from different sources and different parts of Menispermum dauricum DC. The results obtained indicated that the method is suitable for the quality control of Menispermum dauricum DC. Copyright © 2015 John Wiley & Sons, Ltd.     

Radioimmunologische Bestimmung von Pflanzenhormonen

In vorliegender Arbeit wird eine kurze Darstellung der Grundlagen, Erfordernisse, Vor- und Nachteile des Radioimmunoassay für Pflanzenhormone gegeben.

The purpose of this paper is to discuss briefly the basis, requirements, advantages, and disadvantages of radioimmunoassay with respect to plant hormones.     

A quantitative model of preferential evaporation and retention for atom probe tomography

It is well known that the apparent concentration of a solute element in metal, detected by atom probe tomography analysis, depends on the measurement condition such as specimen temperature, pulse fraction, and pulse frequency. The dependence was qualitatively interpreted to be caused by preferential evaporation and retention in field evaporation. A quantitative physical model accounting for the preferential evaporation and retention was proposed herein for the first time. The proposed model was applied to a ferritic iron–copper (Fe–Cu) alloy for preferential evaporation and a ferritic iron–silicon (Fe–Si) alloy for preferential retention. The model explained the temperature dependence on the apparent concentration of the solute element and the unwindowed background noise in each alloy well, whereas the dependence of pulse fraction and pulse frequency was not completely explained. The cause of the difference between the experimental and calculated results based on the model was discussed. Copyright © 2014 John Wiley & Sons, Ltd.