Background correction least-squares

A total of 185 emission lines for both major and trace elements were attributed from each LIBS broadband spectrum. Then background-corrected, summed, and normalized intensities were calculated for 18 selected emission lines and 153 emission line ratios were generated. Finally, the summed intensities and ratios were used as input variables to multivariate statistical chemometric models. A total of 3100 spectra were used to generate Partial Least Squares Discriminant Analysis (PLS-DA) models and test sets. 

In this work, two methods for the determination of caffeine in energy drinks by derivative spectrophotometry and by partial least-squares multivariate spectropho-tometric calibration (PLS-1) are described. Proposed methods involve background correction methods that interferences from vitamins, taurin and food colours were minimized by treating the sample with basic lead acetate and NaHC03 for the arralysis of caffeine in energy drinks. 

Kinetic analysis can be carried out by least-squares analysis of the logarithm of the integration peak area versus time. Correction for small, interfering serum peaks that co-elute with peptide peaks (subtraction of background) is sometimes necessary. 

Liang, Y.Z., Kvalheim, O.M., Rahmani, A., and Brereton, R.G., A two-way procedure for background correction of chromatographic/spectroscopic data by congruence analysis and least-squares fit of the zero-component regions comparison with doublecentering, Chemom. Intell. Lab. Syst., 18, 265-279, 1993. 

Values for M were calculated using the PAG peak areas determined for several irradiated films as shown in Table I. The area of the PAG peak in each chromatogram was normalized to the area of the internal standard benzene peak and corrected by subtracting the normalized area of the background peak that was determined from the chromatogram of the film exposed to 418 mJ/cm . The PAG concentration M is proportional to the peak area and was normalized by setting the area of the peak for the unexposed film to 1.0. Figure 5 shows a plot of log M versus dose. The solid line is a least-squares fit to the data and G was determined from the slope of this line to be 0.013 (mJ/cm ) . ... 

Fig. 5.59. Background-corrected Raman spectra for ZnCl2 hydrate at 298 K. Solid lines show the peak components obtained by the least-squares fits. (Reprinted from T. Pom, T. Yamaguchi, S. Hayaschi, and H. Ohiaki, J. Am. Chem. Soc.93 2620,1989.)...

Fig. 11.10 Linear sweep semi-integral and semi-differential curves of 10 SM Cd(II) in 1M NaCI at a DME. Average of 25 scans, (a) Linear sweep curve, (b) Linear extrapolation of background current, (c) Background-corrected linear sweep curve, (d) Semi-integral curve, (e) Least-squares fitted semi-integral curve, (f) Semi-differential curve. (Reproduced from [39] with permission of the American Chemical Society).

Rietveld refinement (3,4) permits structural study with powder diffraction data. The entire diffraction pattern is calculated from a model consisting of the unit cell parameters, crystallite size (line width), proposed atomic positions and thermal parameters. The validity of the proposed model is measured by comparison of the observed and calculated intensity at each step-scan increment, including background correction, and the model parameters are systematically refined in order to provide the best agreement in a least squares sense. 

The virial coefficients can be determined from experimental PvT data. When doing so, the theoretical background of the virial coefficients B and C as the first terms of an infinite series should be taken into account. A simple least square fit is not advisable. The correct interpretation and determination of the virial coefficients can be derived from Eq. (2.90) as... 

BAM networks have seen successful application to qualitative analysis of X-ray fluorescence and inductively coupled plasma-atomic emission spec-tra.i - They have also been applied to background prediction and correction of infrared spectra,i 5,i6o giving better results than partial least squares. 

Typical background>corrected, fission-chaln-decayilata are shown in Fig. 1. The data points were least-square fitted to determine the decay constant, alpha. 

To date, the most successful method of combined background correction and peak deconvolution has been the method of digital filtering and least squares fitting of reference peaks to the unknown spectrum [45]. This method is robust, simple to automate, and is applicable to any sample type. 

Detailed spectra were processed with CasaXPS software (V2.3.12, Casa Software Ltd., UK). An iterated Shirley-Sherwood background subtraction was applied before peak fitting using a linear-least-squares algorithm. Minor charging was observed and corrected by referencing the aliphatic carbon to 285.0 eV. Details on the curve-fitting parameters, whieh have been measured on reference compounds, have been pubUshed elsewhere [10, 11],... 

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