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Chisnell [[13]] provided analytical solutions to the problem of converging shock waves by using the singular points method.
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I'm using the singular because in America they use the singular when they talk about bands.
Enrichment analysis was conducted using the Singular Enrichment Analysis (SEA) tool in the agriGO toolkit [ 84].
The singular points of the extreme poses are solved by using homotopy method as well as the judgment condition of singular points, and thereby the maximum link lengths are achieved.
We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve.
In order to obtain the singular points, the properties of the Jacobian matrix are used.
Using the proposed directional masks in the first step, we detect the neighborhood of the singular points.
Via the Feller boundary classification, the types of singular points are discussed here, and for the system discussed, the singular points only exist in end points.
Based on this observation, an efficient and numerically stable algorithm for computing the singular points is devised, and inversion formulae for the singular points are derived.
The skeleton is determined as the singular points generated as the waves collide.
Biblical Hebrew mostly uses the plural (but functional singular) form Elohim, but more rarely it also uses the singular form Eloah.
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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