Determination of the degree of polymerization of a polymeric amine from NMR data using a “least-squares” approach

1971 ◽  
Vol 9 (9) ◽  
pp. 657-659 ◽  
Author(s):  
H. Argentar
1998 ◽  
Vol 52 (2) ◽  
pp. 240-249 ◽  
Author(s):  
Hsiaoling Wang ◽  
Chao Wang ◽  
Charles K. Mann ◽  
Thomas J. Vickers

The effect of large, changing concentrations of electrolytes on the behavior of the OH stretching band of water have been investigated with the aim of developing methods for compensating for spectral interferences when solute NH bands are made the basis for mixture analyses. With the use of urea and ammonium salts as analytes, it was found that changing electrolyte concentrations affect the shape of the water band but do not appreciably affect the shapes of either the ammonium ion or urea Raman lines. Chlorides, nitrates, and mixtures of these were used as electrolytes. The identity of the anion had a significant effect on the shape of the OH band. Two methods of compensation were used. One involved factor analyzing the spectra of a set of solutions that contained chlorides and nitrates that are Raman inactive in the vicinity of the OH stretching band. The principal abstract factors were used in place of a water reference for a least-squares mixture analysis. The other method was application of partial least-squares. In addition to urea and ammonium ion, the concentration of KCl and the ionic strength of the system can be determined in the partial least-squares approach with limits of detection better than 0.1 M.


Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 376-377 ◽  
Author(s):  
El‐Sayed M. Abdelrahman

In the article by Gupta, the problem of depth determination of a buried structure from the residual gravity anomaly has been transformed into a problem of finding the solution of a nonlinear equation of the form f(z) = 0. Gupta begins his formulation of the problem with equation (1) from Mettleton (1942) Eq. (1) [Formula: see text]


1996 ◽  
Vol 175 ◽  
pp. 120-121
Author(s):  
E. Ros ◽  
J.M. Marcaide ◽  
J.C. Guirado ◽  
T.P. Krichbaum ◽  
R.A. Preston ◽  
...  

The technique of differential astrometry using the phase-delay VLBI observable promises fractional precisions of ≃2 × 10–9 in the determination of the separation of sources 5° or 6° apart on the sky (Guirado et al. 1995a; Lara et al. 1996). In our present research we seek further improvement in this technique through using triplets of radio sources, which provide a closure constraint in the determination of relative angular positions. This constraint not only eases the resolution of the phase-cycle ambiguities (a major problem in the least-squares approach to astrometry with phase delays), but it also strongly constrains the space of allowable parameter values.


2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.


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