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In either case, a law may be valid even though it obtains only under special circumstances or as a convenient approximation.
A rubber band can't be stretched indefinitely, because although it seems smooth and continuous, that's merely a convenient approximation: it's really made of atoms, and if you stretch it too much, it snaps.
Consequently, the conventional approach of finding the postbuckling path of a shell as the lower festoon curve of postbuckling paths of individual harmonic modes is not valid and is at best a convenient approximation.
Kelly's analysis identifies a common value in the limit of an infinite tree, which serves as a convenient approximation for large finite trees.
To deal with this shortcoming, the following parametric model that was previously derived in [36] offers a convenient approximation of (10): begin{array}{*{20}l} widetilde{P}(S,N,delta)= 0.5expleft[-frac{delta (N-{S}/{delta})^{H}}{S (1-delta)}right] text{for} Ngeq {S}/{delta}.
Because it allows an objective definition of the utility threshold, the piecewise model can serve as a convenient approximation for curvilinear attribute-pressure relationships (resembling Figs. 1b-c) that continuously accelerate or decelerate (i.e., the second derivative is never equal to zero).
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Why? Basically, because infinity is an extremely convenient approximation for which we haven't discovered convenient alternatives.
Thus, the linear regression model that we use in this paper was a parsimonious and convenient approximation of the reality and it is useful for testing statistically our hypothesis that social patterning of BMI had changed over time.
A parabolic potential, V = 1 2 ω | x | 2 Open image in new window is often used as a realistic and, at the same time, computationally convenient approximation.
We compare the drag force with the Brinkman force evaluated using the composite sphere hydrodynamic radius, showing that this convenient approximation is reasonable when the Brinkman screening length of the embedding porous medium is large compared to the core radius; otherwise, the Brinkman force can significantly underestimate the force.
into several kernels in order to show the kind of singularities we are dealing with and to find afterwards the most convenient approximation formulas.
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