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Polynomials are the preferred class of mathematical functions for the description of curves and surfaces.
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The geometric description of the structures under consideration is performed through the differential geometry which is a convenient and general mathematical tool to have parametric description of curved structures.
Thus, a first version of a complete "modelome" of the mathematical phenomenon "line curvature" has been established by multivariate metamodelling and described in terms of quantitative maps both to the original model parameters in the 38 individual models and to human verbal description of curve shapes.
The interest in projective geometry is in the paths, that is, in the continuous set of points of the image set of curves, rather than in the possible parameter descriptions of curves.
I don't dare hazard my own description of its curves and declivities – but it is strangely beautiful.
The proposed basis functions are suitable for the description of closed curves and surfaces with C∞ continuity at all of their points.
On the basis of calculations, it can be stated that the Brillouin function combined with the rational fraction relationship might yield an appropriate description of magnetization curves.
An equilibrium model provided a good description of breakthrough curves for the bromide tracer but could not adequately describe the colloid data.
A new function is proposed for the description of fatigue curves in both low- and high-cycle fatigue regions, i.e. for the whole region of cycles from tensile strength to permanent fatigue limit (usually described by the Palmgren function).
In the particular case of the space (mathbb W_2(Omega )), which has some additional structure, if compared to arbitrary metric spaces, we would like to give a PDE description of the curves that we obtain as gradient flows, and this will pass through the optimality conditions of the minimization problem (4.10).
The number of concentrations tested was extremely limited and consequently cannot allow accurate description of binding curves.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com