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The Duffing oscillator represents an important model to describe mathematically the nonlinear behaviour of several phenomena occurring in physics and engineering.
Concerning the application of fractional calculus, we can notice that fractional differential equations have played a key role in improving the mathematical modeling of several phenomena occurring in basic technical sciences and engineering.
The tools of fractional calculus have been effectively employed to improve the mathematical modeling of several phenomena occurring in scientific and engineering disciplines such as viscoelasticity [1], electrochemistry [2], electromagnetism [3], biology [4, 5], optimal control [6, 7], diffusion process [8 10], economics [11], chaotic theory [12], variational problems [13], etc.
Afterwards, we analyzed by flow cytometry several phenomena occurring during apoptosis: mitochondrial membrane potential (early apoptotic event), caspase 3 activity (late event), Annexin V staining (in order to detect phosphatidyl serine exposure in apoptotic cells) and propidium iodide staining (a DNA intercalating agent).
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In machining processes several phenomena occur during material cutting.
When concrete flows through certain types of obstacles, such as steel bars, several phenomena occur that should be distinguished.
During the retrace, different force curve is observed as several phenomena occur: (a) multiple small detachment forces shown as a "see-saw" pattern in the atomic force curve and (b) a final detachment force, which is distinctly larger than the small detachment forces and indicates the complete detachment of the tip from the cell surface.
Several epigenetic phenomena, occurring at the transcriptional or post-transcriptional level, have been documented in allopolyploids (polyploids derived from species hybrids) of Arabidopsis thaliana, yet findings in autopolyploids (polyploids derived from the duplication of the genome of a single species) are limited.
In general, they observed that most prodigies do not appear spontaneously; instead, they emerge when several important phenomena occur together (there are exceptions, of course, as in the case of the self-taught mathematician and philosopher Blaise Pascal).
On the occasions when it is necessary to compare several fast, single shot phenomena occurring simultaneously, the only solution is to use an oscilloscope equipped with a c.r.t. with several beams.
The simulation has produced several unique results of the underlying phenomena occurring at various stages of the very low temperature process presented in this paper.
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