asymptotic curve


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asymptotic curve

[ā‚sim′täd·ik ′kərv]
(mathematics)
A curve on a surface whose osculating plane at each point is the same as the tangent plane to the surface.
References in periodicals archive ?
In the differential geometry of surfaces, an asymptotic curve is formally defined as a curve on a regular surface such that the normal curvature is zero in the asymptotic direction.
As we can see, the simulation is in exact agreement with theoretical analysis and the asymptotic curve is very tight at high SNR regime, which verifies the correctness of our analysis.
then [alpha] is called a asymptotic curve. If [alpha] is a geodesic curve in M, then we have
--[??] (s) is an asymptotic curve if and only if [k.sub.n] = 0;
The third type of curve is the asymptotic curve, which increases from a value 'a - b' and then steadily approaches a maximum value 'a' known as the asymptote.
Burial rate followed an asymptotic curve over time with a fast initial burial that slowed down with time.
Rohmer and Chabrol proposed an asymptotic curve of accumulated innocence and guilt whose arc might serve to define the "constitutive or original flaw in our natures." It would be a kind of miracle, they point out, if instances of free will were to impact on this curve and "more or less deflect its course." There can be no such "miracle" in Le confessionnal.
The asymptotic curve is distinguishable from the falling rate curve by the fact that as t approaches infinity, [R.sub.f] approaches a finite value in the former case while [R.sub.f] approaches infinity in the latter.
Indeed, an asymptotic curve may come close to describing a key aspect of reality.
Another asymptotic curve would depict the importance of O&M costs as they relate to design costs.
[alpha] is a asymptotic curve if and only if [[kappa].sub.n] = 0.
Comparing the asymptotic curve corresponding to [N.sub.1] = 4, [N.sub.2] = 3 with that corresponding to [N.sub.1] = 3, [N.sub.2] = 3, we find that both curves demonstrate the same decreasing speed.