Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Rapid simulation procedure for fretting wear on the basis of the method of dimensionality reduction

We suggest a numerical procedure for rapid simulation of fretting wear in a contact of two bodies subjected to tangential oscillations with a small amplitude. The incremental wear in each point of contact area is calculated using the Reye–Archard–Khrushchov wear criterion. For applying this criterion, the distributions of pressure and relative displacements of bodies are required. These are calculated using the method of dimensionality reduction (MDR).     

Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems.     

Rapid determination of catecholamines in urine samples by nonaqueous microchip electrophoresis with LIF detection

A method was developed for the rapid separation of catecholamines by nonaqueous microchip electrophoresis (NAMCE) with LIF detection, A homemade pump‐free negative pressure sampling device was used for rapid bias‐free sampling in NAMCE, the injection time was 0.5 s and the electrophoresis separation conditions were optimized. Under the optimized conditions, the samples were separated completely in <1 min. The average migration times of the epinephrine (E), dopamine (DA), and norepinephrine (NE) were 34.26, 43.81, and 50.07 s, with an RSD of 1.05, 1.26, and 0.89% (n = 7), respectively. The linearity of the method ranged from 0.0125 to 2.0 mg/L for E and 0.025～4.0 mg/L for DA and NE, with correlation coefficients ranging between 0.9978 and 0.9986. The detection limits of E, DA, and NE were 2.5, 5.0, and 5.0 μg/L, respectively. The recoveries of E, DA, and NE in spiked urine samples were between 86 and 103%, with RSDs of 4.5～6.8% (n = 5). The proposed NAMCE with LIF detection combined with a pump‐free negative pressure sampling device is a simple, inexpensive, energy efficient, miniaturized system that can be successfully applied for the determination of catecholamines in urine samples.     

Development of a sensitive and reliable high performance liquid chromatography method with fluorescence detection for high-throughput analysis of multi-class mycotoxins in Coix seed

As an edible and medicinal plant, Coix seed is readily contaminated by more than one group of mycotoxins resulting in potential risk to human health. A reliable and sensitive method has been developed to determine seven mycotoxins (aflatoxins B₁, B₂, G₁, G₂, zearalenone, α-zearalenol, and β-zearalenol) simultaneously in 10 batches of Coix seed marketed in China. The method is based on a rapid ultrasound-assisted solid–liquid extraction (USLE) using methanol/water (80/20) followed by immunoaffinity column (IAC) clean-up, on-line photochemical derivatization (PCD), and high performance liquid chromatography coupled with fluorescence detection (HPLC-FLD). Careful optimization of extraction, clean-up, separation and detection conditions was accomplished to increase sample throughput and to attain rapid separation and sensitive detection. Method validation was performed by analyzing samples spiked at three different concentrations for the seven mycotoxins. Recoveries were from 73.5% to 107.3%, with relative standard deviations (RSDs) lower than 7.7%. The intra- and inter-day precisions, expressed as RSDs, were lower than 4% for all studied analytes. Limits of detection and quantification ranged from 0.01 to 50.2 μg kg⁻¹, and from 0.04 to 125.5 μg kg⁻¹, respectively, which were below the tolerance levels for mycotoxins set by the European Union. Samples that tested positive were further analyzed by HPLC tandem electrospray ionization mass spectrometry for confirmatory purposes. This is the first application of USLE-IAC-HPLC-PCD-FLD for detecting the occurrence of multi-class mycotoxins in Coix seed.     

A Correlation of the Drag Force Coefficient on a Sphere with Interface Slip at Low and Intermediate Reynolds Numbers

The hydrodynamics of a sphere with interface slip has been numerically investigated for flows of Reynolds number ranging 0 < Re ≤ 75. A simple correlation of the drag force coefficient in the present of interface slip has been derived based on our numerical simulations. The correlation takes the slip coefficient and Reynolds number as two input parameters. By comparing results found in the literature, we believe that the present correlation is more accurate; it provides a source for future experiment study and for numerical simulations of large multi-particle system where the interface slip is important.     

Ammonium Determination in Water Samples by Using Opa-Nac Reagent: A Comparative Study with Nessler and Ammonium Selective Electrode Methods

A selective and sensitive method based on the ammonium derivatisation with o -phthaldialdehyde (OPA) and N -acetyl-cysteine (NAC) has been developed for ammonium determination in real water samples. The proposed procedure has been compared with ammonium reference methods such as Nessler reagent method and ammonium selective electrode. All procedures have been chemometrically tested and compared in terms of the main analytical properties. These procedures have been used to determine ammonium in unknown water samples. The OPA-NAC reagent method does not present any systematic error (proportional or constant), while Nessler reagent presents both of them for some samples assayed. The ammonium selective electrode is free of corrigible systematic errors, however presents amine interference. The OPA-NAC ammonium method is able to achieve a detection limit (LOD) of 0.07 mg/L in the sample, with a linear dynamic range up to 1.4 mg/L of ammonium.     

基于CA和LS-SVM的TE过程多模型建模

针对TE化工过程高度非线性、复杂性的特点,本文提出了一种基于相关分析和最小二乘支持向量机对TE过程进行多模型建模方法,以提高模型性能。首先对TE过程采用相关分析法划分为3个子系统,对每个子系统分别采用基于C-均值聚类的最小二乘支持向量机建模和基于k均值聚类的最小二乘支持向量机多模型建模。实验表明,基于K-均值聚类的多模型建模能简化计算、提高模型精度、并且能更好的预测模型输出。     

Development and validation of high-performance liquid chromatography method for analysis of β-CCT and its related substances

Compound 2β-carbomethoxy-3β-(4-chlorophenyl)tropane (β-CCT) is a key intermediate for the synthesis of some clinical dopamine transporter (DAT) imaging agents. Potential impurities from synthesis process of β-CCT and degradation during storage might have detrimental effect on the final imaging agents. Thus, it is necessary to guarantee the quality of β-CCT. In this study, a rapid, sensitive and accurate high-performance liquid chromatography (HPLC) method was developed and validated for the analysis of β-CCT and its related substances. The chromatographic separation was achieved on a reverse-phase phenomenex? Gemini C18 column with an isocratic mobile phase consisted of methanol, water and TFA (30:70:0.1 v/v/v). The flow rate was 1.0 mL/min at 30 °C and samples were monitored at 220 nm. The method was validated concerning system suitability, linearity, accuracy, precision, specificity, robustness and stability. The limit of detection (LOD) and the limit of quantification (LOQ) of β-CCT were 0.5 and 1.5 μg/mL, respectively. The linearity range of β-CCT was 1.5–450 μg/mL with a good linear correlation coefficient (R² = 0.9999) between the peak response and concentration. Specificity investigation through forced degradation experiments displayed that β-CCT was stable in acidic, thermal and photolytic degradation conditions, but significantly unstable in alkaline and oxidative conditions. With the developed chromatographic method, possible impurity α-CCT from synthetic process and potential degradation products could be well separated from β-CCT. Good recovery and precision were manifested in the assay method. These results indicated that the present method would be suitable for not only the quality assurance of β-CCT in regular production sample assays but also the monitoring and determination of its related substances.     

Development of GC–MS/MS method for environmental monitoring of 49 pesticide residues in food commodities in Al-Rass,Al-Qassim region,Saudi Arabia

The harmful effects of pesticide residues are a threat to our health. Therefore, the current study aimed to validate a simple method for the determination of pesticide residues in commonly consumed fruits and vegetables from Al-Rass, Al-Qassim region, Saudi Arabia. A total of 1430 samples were collected from a local market and then analyzed for monitoring of 49 pesticide residues. A quick, easy, cheap, effective, rugged, and safe (QuEChERS) multi-residue extraction method followed by gas chromatography equipped with triple-quadrupole mass spectrometry (GC–MS/MS) was successfully implemented. This 17-min-run analytical method detects and quantifies pesticide residues with acceptable validation performance parameters in terms of sensitivity, selectivity, linearity, the limit of quantification, accuracy, and precision. The linear range of the calibration curves ranged from 10 to 300 µg/L, all the pesticide LODs ranged from 0.0005 to 0.0024 mg/kg, and the pesticide LOQs ranged from 0.0011 to 0.0047 mg/kg. The recovery values at the three fortification levels ranged from 78 % to 107 %, and the precision values (expressed as RSD%) were less than 20 % for all of the investigated analytes. The results showed that 138 (9.65 %) of the analyzed samples were contaminated with pesticide residues, 40 (2.80 %) of the analyzed samples exceeded the maximum residue limit (MRL) of the European Commission regulations (EC) for pesticides residues, 98 (6.85 %) of the analyzed samples were contaminated with residues below the MRL, and 1292 (90.35 %) of the analyzed samples were pesticide residue-free. Coriander contained the highest percentage (46.88 %) of pesticide residues, particularly tetradifon that representing 18.75 % noncompliance with the MRL, followed by parsley, with 20.59 % pesticide residues (10.29 % non-compliance). Multiple pesticide residues were observed most frequently in tomatoes and dates which were contaminated with buprofezin and ethion respectively.