Rapid resolving algorithm of gas chromatographic overlapping peaks based on the asymptotic expansion of integration

The formulation and solution of a boundary value problem is presented, describing the influence of the free convective diffusion on the forced one to a sphere for a wide range of Rayleigh, Ra, and Peclet, Pe, numbers. It is assumed that both the free and forced convection are oriented in the same sense. Numerical results obtained by the method of finite differences were approximated by an empirical formula based on an analytically derived asymptotic expansion for Pe → ∞. The concentration gradient at the surface and the total diffusion current calculated from the empirical formula agree with those obtained from the numerical solution within the limits of the estimated errors.

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A Perturbation Theory of a Quasi-Periodic Motion: An Asymptotic Expansion Method

Progress of Theoretical Physics ◽

10.1143/ptp.62.620 ◽

1979 ◽

Vol 62 (3) ◽

pp. 620-628

Author(s):

A. Ito

Keyword(s):

Perturbation Theory ◽

Asymptotic Expansion ◽

Periodic Motion ◽

Expansion Method ◽

Asymptotic Expansion Method

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Separation of Chromatographic Co-Eluted Compounds by Clustering and by Functional Data Analysis

Metabolites ◽

10.3390/metabo11040214 ◽

2021 ◽

Vol 11 (4) ◽

pp. 214

Author(s):

Aneta Sawikowska ◽

Anna Piasecka ◽

Piotr Kachlicki ◽

Paweł Krajewski

Keyword(s):

Simulated Data ◽

Principal Component ◽

Real Data ◽

Functional Principal Component Analysis ◽

Additional Advantage ◽

Time Alignment ◽

Peak Separation ◽

Biological Mixtures ◽

Overlapping Peaks ◽

Retention Time Alignment

Peak overlapping is a common problem in chromatography, mainly in the case of complex biological mixtures, i.e., metabolites. Due to the existence of the phenomenon of co-elution of different compounds with similar chromatographic properties, peak separation becomes challenging. In this paper, two computational methods of separating peaks, applied, for the first time, to large chromatographic datasets, are described, compared, and experimentally validated. The methods lead from raw observations to data that can form inputs for statistical analysis. First, in both methods, data are normalized by the mass of sample, the baseline is removed, retention time alignment is conducted, and detection of peaks is performed. Then, in the first method, clustering is used to separate overlapping peaks, whereas in the second method, functional principal component analysis (FPCA) is applied for the same purpose. Simulated data and experimental results are used as examples to present both methods and to compare them. Real data were obtained in a study of metabolomic changes in barley (Hordeum vulgare) leaves under drought stress. The results suggest that both methods are suitable for separation of overlapping peaks, but the additional advantage of the FPCA is the possibility to assess the variability of individual compounds present within the same peaks of different chromatograms.

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An order verification method for truncated asymptotic expansion solutions to initial value problems

Alexandria Engineering Journal ◽

10.1016/j.aej.2021.04.068 ◽

2021 ◽

Author(s):

Sudi Mungkasi

Keyword(s):

Asymptotic Expansion ◽

Initial Value Problems ◽

Initial Value ◽

Verification Method

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Application of the topological sensitivity method to the reconstruction of plasma equilibrium domain in a tokamak

Boundary Value Problems ◽

10.1186/s13661-021-01523-8 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Mohamed Abdelwahed ◽

Nejmeddine Chorfi ◽

Maatoug Hassine ◽

Imen Kallel

Keyword(s):

Inverse Problem ◽

Asymptotic Expansion ◽

Numerical Algorithm ◽

Shape Function ◽

Optimization Technique ◽

Plasma Equilibrium ◽

Topological Sensitivity ◽

Sensitivity Method

AbstractThe topological sensitivity method is an optimization technique used in different inverse problem solutions. In this work, we adapt this method to the identification of plasma domain in a Tokamak. An asymptotic expansion of a considered shape function is established and used to solve this inverse problem. Finally, a numerical algorithm is developed and tested in different configurations.

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