On the integrability aspects of nonparaxial nonlinear Schrödinger equation and the dynamics of solitary waves

The integrability nature of a nonparaxial nonlinear Schrödinger (NNLS) equation, describing the propagation of ultra-broad nonparaxial beams in a planar optical waveguide, is studied by employing the Painlevé singularity structure analysis. Our study shows that the NNLS equation fails to satisfy the Painlevé test. Nevertheless, we construct one bright solitary wave solution for the NNLS equation by using the Hirota's direct method. Also, we numerically demonstrate the stable propagation of the obtained bright solitary waves even in the presence of an external perturbation in a form of white noise. We then numerically investigate the coherent interaction dynamics of two and three bright solitary waves. Our study reveals interesting energy switching among the colliding solitary waves due to the nonparaxiality.     

多波长系统孤子耦合方程的可积性

多波长系统孤子耦合方程存在Lax对，具有可积性，利用Hirota双线性方法求出了孤子耦合方程的单孤子解和双孤子解. 关键词： Lax对 Hirota双线性变换 可积性     

A novel second-order standard addition analytical method based on data processing with multidimensional partial least-squares and residual bilinearization

In the presence of analyte-background interactions and a significant background signal, both second-order multivariate calibration and standard addition are required for successful analyte quantitation achieving the second-order advantage. This report discusses a modified second-order standard addition method, in which the test data matrix is subtracted from the standard addition matrices, and quantitation proceeds via the classical external calibration procedure. It is shown that this novel data processing method allows one to apply not only parallel factor analysis (PARAFAC) and multivariate curve resolution-alternating least-squares (MCR-ALS), but also the recently introduced and more flexible partial least-squares (PLS) models coupled to residual bilinearization (RBL). In particular, the multidimensional variant N-PLS/RBL is shown to produce the best analytical results. The comparison is carried out with the aid of a set of simulated data, as well as two experimental data sets: one aimed at the determination of salicylate in human serum in the presence of naproxen as an additional interferent, and the second one devoted to the analysis of danofloxacin in human serum in the presence of salicylate.     

Fast chromatographic method for the determination of dyes in beverages by using high performance liquid chromatography—Diode array detection data and second order algorithms

A fast chromatographic methodology is presented for the analysis of three synthetic dyes in non-alcoholic beverages: amaranth (E123), sunset yellow FCF (E110) and tartrazine (E102). Seven soft drinks (purchased from a local supermarket) were homogenized, filtered and injected into the chromatographic system. Second order data were obtained by a rapid LC separation and DAD detection. A comparative study of the performance of two second order algorithms (MCR-ALS and U-PLS/RBL) applied to model the data, is presented. Interestingly, the data present time shift between different chromatograms and cannot be conveniently corrected to determine the above-mentioned dyes in beverage samples. This fact originates the lack of trilinearity that cannot be conveniently pre-processed and can hardly be modelled by using U-PLS/RBL algorithm. On the contrary, MCR-ALS has shown to be an excellent tool for modelling this kind of data allowing to reach acceptable figures of merit. Recovery values ranged between 97% and 105% when analyzing artificial and real samples were indicative of the good performance of the method. In contrast with the complete separation, which consumes 10 mL of methanol and 3 mL of 0.08 mol L⁻¹ ammonium acetate, the proposed fast chromatography method requires only 0.46 mL of methanol and 1.54 mL of 0.08 mol L⁻¹ ammonium acetate. Consequently, analysis time could be reduced up to 14.2% of the necessary time to perform the complete separation allowing saving both solvents and time, which are related to a reduction of both the costs per analysis and environmental impact.     

Bilinearization and soliton solutions of N=1 supersymmetric coupled dispersionless integrable system

An N=1 supersymmetric generalization of coupled dispersionless (SUSY-CD) integrable system has been proposed by writing its superfield Lax representation. It has been shown that under a suitable variable transformation, the SUSY-CD integrable system is equivalent to N=1 supersymmetric sine-Gordon equation. A superfield bilinear form of SUSY-CD integrable system has been proposed by using super Hirota operator. Explicit expressions of superfield soliton solutions of SUSY-CD integrable system have been obtained by using the Hirota method.     

Non-autonomous bright matter wave solitons in spinor Bose–Einstein condensates

We investigate the dynamics of bright matter wave solitons in spin-1 Bose–Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross–Pitaevskii (3-GP) equations using Hirota?s method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite–Gaussian-like potential strength. Our study shows that these non-autonomous solitons undergo non-trivial collisions involving condensate switching.     

序贯数论优化法用于“灰色”体系多组分同时定量分析

将序贯为九论优化法,结合采用约束背影双线性比模型用于多组分“灰色”体系同时测定,且对ＳＮＴＯ的收缩比和收敛判据进行了改进。结果表明,ＳＮＴＯ法是一种实用的全局优化方法,收缩比和收敛判据的改进可大大缩短计算时间。     

Adsorptive stripping square wave voltammetry (Ad-SSWV) accomplished with second-order multivariate calibration determination of fenitrothion and its metabolites in river water samples

A method, using stripping square wave voltammetry (Ad-SSWV), for the simultaneous determination of fenitrothion (FEN) and its metabolites: fenitrooxon (OXON) and 3-methyl-4-nitrophenol (3-MET) in environmental samples is reported. All three compounds produce, at mercury electrode (HMDE), an electrochemical signal due to an adsorptive-reductive process. The electrochemical approach shows a very high overlap degree for FEN and OXON voltammograms, however the adsorption kinetic profile could be used as an additional differential variable between both analytes. Second-order multivariate calibration has been tested to solve the mixture of the three compounds. The second-order assayed methods were parallel factor analysis (PARAFAC), unfolded partial least squares (U-PLS), multidimensional partial least squares (N-PLS) and the latest ones were used in combination with the residual bilinearization procedure RBL. U-PLS/RBL model was stated as the best second-order algorithm for the simultaneous determination of these three compounds up to 50 ng mL⁻¹ for each analyte. The detection limits and recovery values were 1.6 ng mL⁻¹ and 92 ± 7% for FEN; 3.7 ng mL⁻¹ and 101 ± 9% for OXON and 0.6 ng mL⁻¹ and 97 ± 8% for 3-MET.     

Determination of atenolol in human urine by emission-excitation fluorescence matrices and unfolded partial least-squares with residual bilinearization

A second-order multivariate calibration method based on a combination of unfolded partial least-squares (U-PLS) with residual bilinearization (RBL) has been applied to second-order data obtained from excitation-emission fluorescence matrices for determining atenolol in human urine, even in the presence of background interactions and fluorescence inner filter effects, which are both sample dependent. Atenolol is a cardioselective beta-blocker, which is considered a doping agent in shoot practice, so that its determination in urine can be required for monitoring the drug. Loss of trilinearity due to analyte-background interactions which may vary between samples, as well as inner filter effects, precludes the use of methods like parallel factor analysis (PARAFAC) that cannot handle trilinearity deviations, and justifies the employment of U-PLS. Successful analysis required to include the background in the calibration set. Unexpected components appear in new urine samples, different from those used in calibration set, requiring the second-order advantage which is obtained from a separate procedure known as residual bilinearization (RBL). Satisfactory results were obtained for artificially spiked urines, and also for real urine samples. They were statistically compared with those obtained applying a reference method based on high-performance liquid chromatography (HPLC).     

基于遗传算法优化的约束背景双线性分解算法用于改进高效液相色谱灰色分析体系的校正结果

该文采用约束背景双线性分解算法(CBBL)对以高效液相色谱(HPLC)方法分离分析的灰色分析体系进行了多元校正研究。针对采用包括CBBL在内的矩阵校正方法处理HPLC灰色分析体系的固有缺陷,即在相关组分的色谱保留时间重现性较低的情形下多元校正的结果不理想,对CBBL方法进行了改进,即将待测组分的浓度与组分的色谱保留时间同时作为优化的参量引入CBBL,并采用遗传算法(GA)优化CBBL,对于模拟的组分保留时间飘移严重的HPLC灰色分析体系及保留时间重现性不佳的多种酚类化合物组成的实际HPLC灰色分析体系进行了多元校正分析,成功克服了经典CBBL的固有缺陷,取得了较理想的多元校正结果。另外,该研究所建议的方法的校正结果也显著优于传统的残差双线性分解法(RBL)以及秩消失因子分析法(RAFA)。