scholarly journals A Dynamical Determination of the Astronomical Unit by a Least-Squares Fit to the Orbit of Pioneer V.

1960 ◽  
Vol 65 ◽  
pp. 493
Author(s):  
J. B. McGuire ◽  
D. D. Morrison ◽  
L. Wong
Keyword(s):  
Least Squares ◽  
Astronomical Unit ◽  
Least Squares Fit

Reply by the author to G. D. Garland.

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1460-1460
Author(s):  
B. A. Sissons
Keyword(s):  
Least Squares ◽  
Standard Error ◽  
Gravitational Constant ◽  
Gravity Data ◽  
Residual Distribution ◽  
Density Measurements ◽  
Least Squares Fit ◽  
Least Squares Adjustment ◽  
Sufficient Precision

Although the Tokaanu experiment does contradict the proposal that the gravitational constant G increases with scale, the result is not significant. The standard error in the least‐squares adjustment is at least 1 percent, which exceeds the predicted variation in G. The uncertainty in mean density is nearer 5 percent. Gravity data with sufficient precision to test for a scale effect in G are obtainable; the main problem appears to be the uncertainty in density determinations. Stacey et al (1981) made a least‐squares determination of G using gravity and density measurements from a mine. However, the pattern of residuals obtained indicated the presence of anomalous masses not adequately accounted for by their density averaging. The method I have used which models the spatial variation in density offers the possibility of obtaining a least‐squares fit for G with a satisfactory residual distribution. However, the problem of the effect on bulk density of joints and voids not sampled in hand specimens remains.

Background Correction in Raman Spectroscopic Determination of Dimethylsulfone, Sulfate, and Bisulfate

1985 ◽  
Vol 39 (3) ◽  
pp. 463-470 ◽  
Author(s):  
Yong-Chien Ling ◽  
Thomas J. Vickers ◽  
Charles K. Mann
Keyword(s):  
Least Squares ◽  
Simulated Data ◽  
Background Correction ◽  
Data Sets ◽  
Raman Spectroscopic ◽  
Dimethyl Sulfone ◽  
Quantitative Measurements ◽  
Least Squares Fit ◽  
Background Curvature

A study has been made to compare the effectiveness of thirteen methods of spectroscopic background correction in quantitative measurements. These include digital filters, least-squares fitting, and cross-correlation, as well as peak area and height measurements. Simulated data sets with varying S/N and degrees of background curvature were used. The results were compared with the results of corresponding treatments of Raman spectra of dimethyl sulfone, sulfate, and bisulfate. The range of variation of the simulated sets was greater than was possible with the experimental data, but where conditions were comparable, the agreement between them was good. This supports the conclusion that the simulations were valid. Best results were obtained by a least-squares fit with the use of simple polynomials to generate the background correction. Under the conditions employed, limits of detection were about 80 ppm for dimethyl sulfone and sulfate and 420 ppm for bisulfate.

On the determination of accurate intensities from powder diffraction data. II. Estimation of intensities of overlapping reflections

1992 ◽  
Vol 25 (2) ◽  
pp. 237-243 ◽  
Author(s):  
J. Jansen ◽  
R. Peschar ◽  
H. Schenk
Keyword(s):  
Least Squares ◽  
Direct Methods ◽  
Real Data ◽  
Powder Diffraction Data ◽  
Comparative Tests ◽  
Patterson Function ◽  
Structure Factors ◽  
Least Squares Fit ◽  
Overlapping Peaks

Even the best least-squares algorithm to extract intensities from a powder diagram will not be able to determine the separate intensities of completely overlapping peaks. In this paper a new method (DOREES) is presented to determine these intensities more accurately by applying relations between structure factors derived from direct methods and the Patterson function. The intensities obtained from the least-squares fit are used as a starting set for DOREES. Comparative tests on both artificially generated and real data show that DOREES improves the intensity set considerably.

Determination of Pyridostigmine Bromide in Presence of its Related Impurities by Four Modified Classical Least Square Based Models: A Comparative Study

2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem
Keyword(s):  
Comparative Study ◽  
Least Squares ◽  
Orthogonal Projection ◽  
Predictive Ability ◽  
Least Square ◽  
Projection To Latent Structures ◽  
Preprocessing Method ◽  
Spectral Residual ◽  
Latent Structures

: 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.

scholarly journals Application of Derivative, Derivative Ratio, and Multivariate Spectral Analysis and Thin-Layer Chomatography-Densitometry for Determination of a Ternary Mixture Containing Drotaverine Hydrochloride, Caffeine, and Paracetamol

2007 ◽  
Vol 90 (2) ◽  
pp. 391-404 ◽  
Author(s):  
Fadia H Metwally ◽  
Yasser S El-Saharty ◽  
Mohamed Refaat ◽  
Sonia Z El-Khateeb
Keyword(s):  
Thin Layer ◽  
Least Squares ◽  
Ternary Mixture ◽  
Principal Component Regression ◽  
Pharmaceutical Preparations ◽  
Principal Component ◽  
Standard Addition ◽  
Drotaverine Hydrochloride ◽  
Assay Precision

Abstract New selective, precise, and accurate methods are described for the determination of a ternary mixture containing drotaverine hydrochloride (I), caffeine (II), and paracetamol (III). The first method uses the first (D1) and third (D3) derivative spectrophotometry at 331 and 315 nm for the determination of (I) and (III), respectively, without interference from (II). The second method depends on the simultaneous use of the first derivative of the ratio spectra (DD1) with measurement at 312.4 nm for determination of (I) using the spectrum of 40 μg/mL (III) as a divisor or measurement at 286.4 and 304 nm after using the spectrum of 4 μg/mL (I) as a divisor for the determination of (II) and (III), respectively. In the third method, the predictive abilities of the classical least-squares, principal component regression, and partial least-squares were examined for the simultaneous determination of the ternary mixture. The last method depends on thin-layer chromatography-densitometry after separation of the mixture on silica gel plates using ethyl acetatechloroformmethanol (16 + 3 + 1, v/v/v) as the mobile phase. The spots were scanned at 281, 272, and 248 nm for the determination of (I), (II), and (III), respectively. Regression analysis showed good correlation in the selected ranges with excellent percentage recoveries. The chemical variables affecting the analytical performance of the methodology were studied and optimized. The methods showed no significant interferences from excipients. Intraday and interday assay precision and accuracy values were within regulatory limits. The suggested procedures were checked using laboratory-prepared mixtures and were successfully applied for the analysis of their pharmaceutical preparations. The validity of the proposed methods was further assessed by applying a standard addition technique. The results obtained by applying the proposed methods were statistically analyzed and compared with those obtained by the manufacturer's method.

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