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Setting Limits on Supersymmetry Using Simplified Models
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Newer developments on self-modeling curve resolution implementing equality and unimodality constraints.

Samira Beyramysoltan1, Hamid Abdollahi2, Róbert Rajkó3

  • 1Institute of Process Engineering, Faculty of Engineering, University of Szeged, Moszkvai krt. 5-7, Szeged H-6725, Hungary; Department of Chemistry, Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan, Iran.

Analytica Chimica Acta
|May 17, 2014
PubMed
Summary

Analytical self-modeling curve resolution (SMCR) methods were enhanced with computational geometry for analyzing complex data. New algorithms successfully implemented equality and unimodality constraints in the Lawton-Sylvestre method for improved accuracy.

Keywords:
Borgen plotEquality constraintLawton–Sylvestre methodSelf-modeling curve resolution (SMCR)Unimodality constraint

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Area of Science:

  • Analytical Chemistry
  • Chemometrics
  • Computational Geometry

Background:

  • Self-modeling curve resolution (SMCR) methods analyze data using non-negative constraints.
  • The Lawton-Sylvestre method and Borgen plots are foundational for two- and three-component systems.
  • Previous algebraic approaches hindered the general study of Borgen's work.

Purpose of the Study:

  • To revise and simplify analytical SMCR methods.
  • To develop and detail an algorithm for generating Borgen plots.
  • To implement equality and unimodality constraints in the Lawton-Sylvestre method.

Main Methods:

  • Revision of analytical SMCR principles using simple concepts.
  • Development of a computational geometry algorithm for Borgen plot generation.
  • Introduction of a novel procedure for imposing equality constraints in Borgen plots.

Main Results:

  • A developmental algorithm for Borgen plots was detailed.
  • Equality and unimodality constraints were successfully integrated into the Lawton-Sylvestre method.
  • Simulated two- and three-component HPLC-DAD data were analyzed using the enhanced methods.

Conclusions:

  • The study provides a simplified and geometrically-oriented approach to analytical SMCR.
  • The implementation of new constraints enhances the precision of curve resolution.
  • The developed methods offer improved analytical capabilities for complex chemical data.