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An illustration for the steps followed in this approximation can be found in Algorithm 5.

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Recent advances in Diophantine approximation can be found in the excellent surveys of Moshchevitin [3] and Waldschimidt [4].

A few more applications of sharper estimates and trigonometric Fourier approximation can be found in [19, 29 33], and the references given therein.

When a gamma approximation can be found that adequately fits the data, we may estimate the number of bins that were not sequenced and that could potentially be revealed by additional sequencing.

As an example, consider the mean of the ETL: its true value is given by Eq. (10) and the value of its numerical approximation can be found by iterating Eq. (8).

For special transmission functions such as Fresnel lenses, approximations can be found analytically16,17, but these methods do not generalize to arbitrary target transmission functions, and the accuracy of the approximation is limited.

It follows that the Gromov hyperbolicity can be computed in O(n3.69) time, and a 2-approximation can be found in O(n2.69) time.

The equation can be solved exactly for an atom containing only a single electron (hydrogen), and very close approximations can be found for atoms containing two or three electrons (helium and lithium).

Other sparse reconstruction approaches including greedy algorithms, which iteratively construct sparse approximations, can be found in the literature.

On the other hand, since MMAC uses finite contention windows, only approximations can be found in case of MMAC which are then justified by simulation results.

Fairly crude approximations can be found by looking directly at changes in expenditure on a substitute good that arise as a result of some environmental change.

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