2017
DOI: 10.4236/jamp.2017.59155
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The Qualitative and Quantitative Methods of Kovalevskys Case

Abstract: The phase portrait of the functions obtained by Hamilton-Jacobi equations is substantiated, and the classification of singular points is found, and the bifurcation diagram for the problem is studied. The numerical calculation by using Poincaré surface section is used to get the invariant tori for our problem.

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Cited by 4 publications
(2 citation statements)
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References 7 publications
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“…To gather data, the researcher conducted observations and interviews. The observation phase involved the examination of several classes, with the aim of examining the actual practices and techniques used by teachers in the classroom (Fahmy El-Sabaa et al, 2017). During these observations, the researcher not only observed the teachers, but also the learners, in order to gain a more comprehensive understanding of how they respond to the various teaching techniques utilized in the vocabulary instruction process.…”
Section: Methodsmentioning
confidence: 99%
“…To gather data, the researcher conducted observations and interviews. The observation phase involved the examination of several classes, with the aim of examining the actual practices and techniques used by teachers in the classroom (Fahmy El-Sabaa et al, 2017). During these observations, the researcher not only observed the teachers, but also the learners, in order to gain a more comprehensive understanding of how they respond to the various teaching techniques utilized in the vocabulary instruction process.…”
Section: Methodsmentioning
confidence: 99%
“…This involved interpreting the data to identify important findings and drawing conclusions based on the evidence. The validity of the conclusions was then verified by comparing them with the original data and seeking feedback from other researchers in the field (Fahmy El-Sabaa et al, 2017). By utilizing these qualitative methods, the researchers were able to analyze and interpret the data collected through documentation notes and interviews in a rigorous and systematic manner.…”
Section: Data Analysis Techniquementioning
confidence: 99%