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Using a supplementary variable technique and a plant transformation, a finite phase-type semi-Markov process has been transformed into a finite Markov chain, which is called its associated Markov chain.
Birth size was included as a supplementary variable, because it contained information useful in estimating birth weight.
In order to further substantiate the relationship between lin system diversity and degradation efficiency, principle component analysis (PCA) was performed on the copy number and sequence divergence for these strains, with HCH degradation plotted as a supplementary variable to visualize correlation.
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MCA showed that all supplementary variables belonging to the same category were highly related; this result was used as a justification to generate one outcome variable describing high/low respiratory disease occurrence in cows and pregnant heifers.
Shakuntla et al. (2011) discussed the availability analysis for a pipe manufacturing industry using supplementary variable technique.
By applying the supplementary variable technique, we develop a unified solution to both the single-vacation and multiple-vacation models and for either the PBAS (partial batch acceptance strategy) or the WBAS (whole batch acceptance strategy) service disciplines.
Its main originality lies in the introduction of a supplementary state variable for the crack, which allows describing continuously the state of the crack throughout any complex load sequence.
Due to concern that our main independent variable might result in non-differential misclassification of the responders, we complemented our main analyses with similar analyses using a supplementary independent variable measuring lifetime history of time off work or light duties due to work-related low back injury.
Principle component analysis (PCA) with the copy number and divergence data was then done with the R package FactoMineR [ 75], with HCH degradation plotted as a supplementary discrete variable (0- complete non degrader, 1- partial degrader, 2- full degrader), followed by a plot construction with ggplot2.
A mathematical model of the proposed complex system is designed using Markov process and supplementary variable technique by introducing the concept of the warranty period and the reliability characteristics is analyzed by the deliberation of the Laplace transformation.
By applying the supplementary variable technique, some important performance measures are derived.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com