| Two important characteristics of modern analytical chemistry are the instrumentation of analytical tools and complication of chemical system. Chemometrics is able to achieve useful chemical information as much as possible from the enormous high-order signals generated by the modern analytical instruments, and accordingly provides novel and very powerful research tool for qualitative as well as quantitative analysis of complex multi-component chemical systems. In particular, the second-order calibration methods can offer the so-called"second-order advantage", namely they can allow for the rapid, direct quantitative analysis of the analytes of interest in complex chemical systems even in the existence of unknown interferences. Such methods have shown positive effects on various chemical embranchment subjects, especially pharmaceutical chemistry, biochemistry and food chemistry and provide a variety of powerful techniques to resolve practical difficult problems occurred in these subjects. Studies presented in the thesis primarily focused on the methodologies and applications of second-order calibration methods in chemometrics.(1) In Chapter 2, a novel algorithm named as self-weighted alternating normalized residue fitting (SWANRF) has been proposed for quantitative analysis of excitation-emission matrix fluorescence data. The proposed algorithm can obtain satisfactory solutions for the analyte(s) of interest even in the presence of potentially unknown interference, fully exploiting the second-order advantage. By comparing with the performances of the alternating trilinear decomposition (ATLD), and the parallel factor analysis-alternating least squares (PARAFAC-ALS) algorithms on one simulated and two real fluorescence spectral data arrays, SWANRF can deal with higher collinearity problems, obtain improved convergence rate through shuffling the computational matrices, and partially reextract valid information from the residue and further remove invalid information to the residues. In addition, SWANRF can not only behave more stable independent of the used initial values unlike PARAFAC, but also achieve very smooth profiles at high noise level, where ATLD may be helpless with the actual component and have to resort to additional component(s) to fit noise, yielding rough profiles with a bad grace. Based on these attracted merits, such a novel method may hold great potential to be extended as a promising alternative for the three-way data array analysis and high-order tensorial calibration.(2) In Chapter 3, a novel method, region-based on moving window subspace projection technique (RMWSPT) coupled with Monte Carlo simulation, was developed for the chemical rank estimation of excitation-emission matrix (EEM) fluorescence data arrays. RMWSPT determines the chemical rank by performing truncated singular value decomposition (SVD) on the unfolded matrices of original data array and the subarrays yielded by a moving window, and through employing the subspace projection technique on the difference between the corresponding sub-bands of the significant eigenvectors and those of subarrays. Compared with the traditional methods, it utilizes the information from eigenvectors combined with the projection residuals to estimate the rank of the excitation-emission matrix (EEM) data arrays instead of using the eigenvalues. Two simulated and two real EEM data arrays were analyzed to demonstrate the excellent performance of the RMWSPT. Moreover, its performance was compared with that of other three factor-determining methods, i.e., factor indicator function (IND), the core consistency diagnostic (CORCONDIA) test and two-mode subspace comparison (TMSC) approaches. The results showed that the newly proposed method can accurately and quickly determine the chemical rank to fit the trilinear model, and it can deal with more complex situations in the presence of severe collinearity and trace concentration. The RMWSPT method thus lights a new avenue to determine the chemical rank of EEM data arrays and may hold great potential to be extended as a promising alternative for chemical rank estimation.(3) In Chapter 4, a novel route for the removal of Rayleigh scatter has been proposed, based on the use of a trilinear decomposition algorithm that is not sensitive to the chosen factor number. The Rayleigh scatter is located in the same position in the level-slide as well as the side-slide matrix. This new method constructs a three-way data array containing the Rayleigh scatter along with both of the I-mode and J-mode directions, and then use a trilinear decomposition algorithm to model them to remove the scatter as a response component or factor from the three-way data array constructed. The results obtained from the analysis of simulated and real three-way EEM fluorescence data revealed that the newly proposed approach was simple, not sensitive to the chosen factor number, and able to effectively remove the Rayleigh scatter interference in the analytical system tested.(4) In Chapter 5, a simple, rapid, and effective method for quantitative analysis of 6-methylcoumarin (6-MC) and 7-methoxycoumarin (7-MOC) in cosmetics using EEM fluorescence coupled with second-order calibration. After simple pretreatments, the adopted calibration algorithms exploiting the second-order advantage, i.e., PARAFAC and self-weighted alternating trilinear decomposition (SWATLD), could allow the individual concentrations of the analytes of interest to be evaluated even in the presence of uncalibrated interferences. Moreover, in the analysis of oil control nourishing toner, the standard addition method was suggested to overcome the partial fluorescence quenching of 6-MC induced by the analyte-background interaction, which also yielded satisfactory prediction results. It was found that both algorithms could give accurate results, only the performance of SWATLD was slightly better than that of PARAFAC in the cases suffering from matrix effects. The method proposed lights a new avenue to determine quantitatively 6-MC and 7-MOC in cosmetics, and may hold great potential to be extended as a promising alternative for more practical applications in cosmetic quality control, due to its advantages of easy sample pretreatment, non-toxic and non-destructive analysis, and accurate spectral resolution and concentration prediction, etc.(5) In Chapter 6, a sensitive excitation-emission fluorescence method was proposed to determine testosterone propionate (TP) in several cosmetics with the aid of second-order calibration methods based on the SWATLD,PARAFAC and SWANRF algorithms. TP can be transformed into a highly fluorescent derivative through oxidation reaction with concentrated sulfuric acid (H2SO4). Both algorithms have been recommended to enhance the selectivity and attain TP concentration in cosmetics free from interference from potential interfering matrix contaminants introduced during simple cosmetic pretreatment procedure. Satisfactory results have been achieved for TP in complicated cosmetics, fully exploiting"second-order advantage". The results revealed that such an approach can become a promising alternative for practical applications in cosmetic quality control to achieve higher detector response and enhance the selectivity.(6) In Chapter 7, a new and effective approach for the quantitative analysis of sulpiride, a significant antipsychotic drug, in human urine samples by the incorporation of EEM fluorescence and second-order calibration methodologies based on the alternating fitting residue (AFR) and SWATLD algorithms. With the application of a second-order advantage, the proposed strategy could be utilized for a direct concentration determination of sulpiride with a simple pretreatment step, even in the presence of serious natural fluorescent interferences. The average recoveries of sulpiride in complex urine samples by using AFR and SWATLD with an estimated component number of three were satisfactory. Moreover, the accuracy of the two algorithms was also evaluated. The experimental results demonstrated that both algorithms, as promising quantitative alternatives, have been satisfactorily applied to the determination of sulpiride in human urine.
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