Optimizing gradient conditions in online comprehensive two‐dimensional reversed‐phase liquid chromatography by use of the linear solvent strength model

The linear solvent strength model was used to predict coverage in online comprehensive two‐dimensional reversed‐phase liquid chromatography. The prediction model uses a parallelogram to describe the separation space covered with peaks in a system with limited orthogonality. The corners of the parallelogram are assumed to behave like chromatographic peaks and the position of these pseudo‐compounds was predicted. A mix of 25 polycyclic aromatic compounds were used as a test. The precision of the prediction, span 0–25, was tested by varying input parameters, and was found to be acceptable with root mean square errors of 3. The accuracy of the prediction was assessed by comparing with the experimental coverages. Less than half of experimental coverages were outside prediction ± 1 × root mean square error and none outside prediction ± 2 × root mean square error. Accuracy was lower when retention factors were low, or when gradient conditions affected parameters not included in the model, e.g. second dimension gradient time affects the second dimension equilibration time. The concept shows promise as a tool for gradient optimization in online comprehensive two‐dimensional liquid chromatography, as it mitigates the tedious registration and modeling of all sample constituents, a circumstance that is particularly appealing when dealing with complex samples.     

Optimization of multiwalled carbon nanotubes reinforced hollow‐fiber solid–liquid‐phase microextraction for the determination of polycyclic aromatic hydrocarbons in environmental water samples using experimental design

A novel design of hollow‐fiber liquid‐phase microextraction containing multiwalled carbon nanotubes as a solid sorbent, which is immobilized in the pore and lumen of hollow fiber by the sol–gel technique, was developed for the pre‐concentration and determination of polycyclic aromatic hydrocarbons in environmental water samples. The proposed method utilized both solid‐ and liquid‐phase microextraction media. Parameters that affect the extraction of polycyclic aromatic hydrocarbons were optimized in two successive steps as follows. Firstly, a methodology based on a quarter factorial design was used to choose the significant variables. Then, these significant factors were optimized utilizing central composite design. Under the optimized condition (extraction time = 25 min, amount of multiwalled carbon nanotubes = 78 mg, sample volume = 8 mL, and desorption time = 5 min), the calibration curves showed high linearity (R ² = 0.99) in the range of 0.01–500 ng/mL and the limits of detection were in the range of 0.007–1.47 ng/mL. The obtained extraction recoveries for 10 ng/mL of polycyclic aromatic hydrocarbons standard solution were in the range of 85–92%. Replicating the experiment under these conditions five times gave relative standard deviations lower than 6%. Finally, the method was successfully applied for pre‐concentration and determination of polycyclic aromatic hydrocarbons in environmental water samples.     

Simultaneous determination of eight short‐chain aliphatic amines in drug substances by HPLC with diode array detection after derivatization with halonitrobenzenes

Short‐chain aliphatic amines are a class of hazardous impurities in drug substances. A simple method, involving derivatization followed by high‐performance liquid chromatography with diode array detection, has been developed for residue determination of eight aliphatic amines simultaneously in drug substances. Different halonitrobenzenes derivatization reagents were systematically compared. As a result, 1‐fluoro‐2‐nitro‐4‐(trifluoromethyl)benzene was selected since the derivatization effectively shifted the absorption wavelength to the visible region (400–450 nm), where most drug substances, impurities and even the derivatization reagent absorb very weakly. Due to the redshift effect, interference was minimized and adequately low limits of quantitation were reached (0.24–0.80 nmol/mL). Moreover, the derivatization reaction was readily carried out in dimethyl sulfoxide at room temperature for 1 h using N ,N‐diisopropylethylamine as catalyst to achieve the highest yield. Without any pre‐treatment, the derivatives were analyzed by high‐performance liquid chromatography with diode array detection. The high stability of the derivatives within 24 h at room temperature (RSD<1.04%) further facilitated the simultaneous preparation and consecutive analysis of quantities of samples. Finally, the proposed method was successfully applied for residue determination of eight aliphatic amines simultaneously in eight drug substance samples. This study could be helpful for the routine analysis and residue control of aliphatic amines in drug substances.     

Sulfonated poly(styrene‐divinylbenzene) modified with amines and the application for pipette‐tip solid‐phase extraction of carbendazim in apples

Sulfonated poly(styrene‐divinylbenzene) modified with five kinds of amine functional groups was applied to the determination of carbendazim in apple samples with a pipette‐tip solid‐phase extraction method. The structures of the polymers were characterized by scanning electron microscopy, Fourier transform infrared spectroscopy, and thermogravimetric analysis. Five different modifications of the solid‐phase extraction sorbent based on sulfonated poly(styrene‐divinylbenzene) were tested under static and pipette‐tip solid‐phase extraction conditions. The polymer modified with p‐methoxyaniline showed the best recognition capacity and adsorption amount for carbendazim. Under the optimum conditions, 3.00 mg of the adsorbent, 1.00 mL of ethyl acetate as washing solvent, and 1.00 mL of ammonia/acetonitrile (5:95, v/v) as elution solvent were used in the pretreatment procedure of apple samples. The calibration graphs of carbendazim in methanol were linear over 5.00–200.00 μg/mL, and the limits of detection and quantification were 0.01 and 0.03 μg/mL, respectively. The method recoveries of carbendazim were in the range of 91.31–98.13% with associated intraday relative standard deviations of 0.76–2.13% and interday relative standard deviations of 1.10–1.85%. Sulfonated poly(styrene‐divinylbenzene) modified with p‐methoxyaniline showed satisfactory results (recovery: 97.96%) and potential for the rapid purification of carbendazim in apple samples combined with the pipette‐tip solid‐phase extraction.     

Lanthanide(III)‐Based Multicolor Luminescent Hybrid Gel for Amine Sensing

Bridged polysilsesquioxanes (BPs) show great potential in the development of lanthanide‐based luminescent materials, owing to their capacity to loading lanthanide complexes with high concentration and their flexible processability. A novel BP precursor, consisting of a C ₃‐symmetrical benzene central core moiety, capable of sensitizing the luminescence of Eu³⁺ and Tb³⁺ is reported. Tunable, full‐color luminescent gels were facilely prepared by mixing the as‐synthesized precursor and Ln³⁺ ions in appropriate solvents. By either changing the Eu³⁺/Tb³⁺ molar ratio or altering the excitation wavelength, the emission colors of the final gels can be finely tuned. Additionally, the yellow‐colored emissive gel with a molar ratio of Eu³⁺ to Tb³⁺ of 0.5 can be used as an effective ratiometric luminescent sensor for distinguishing amines with lower pK _a (<5) from those with higher pK _a (>9).     

C0-estimates and smoothness of solutions to the parabolic equation defined by Kimura operators

Kimura diffusions serve as a stochastic model for the evolution of gene frequencies in population genetics. Their infinitesimal generator is an elliptic differential operator whose second-order coefficients matrix degenerates on the boundary of the domain. In this article, we consider the inhomogeneous initial-value problem defined by generators of Kimura diffusions, and we establish $C^0$-estimates, which allows us to prove that solutions to the inhomogeneous initial-value problem are smooth up to the boundary of the domain where the operator degenerates, even when the initial data is only assumed to be continuous.     

Integral geometry of translation invariant functionals,II: The case of general convex bodies

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures.     

Gabor systems and almost periodic functions

Inspired by results of Kim and Ron, given a Gabor frame in $L^2(\mathbb{R})$, we determine a non-countable generalized frame for the non-separable space ${\mathit{AP}}_2(\mathbb{R})$ of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of ${\mathit{AP}}_2(\mathbb{R})$ are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.