Sentence examples for by the foregoing from inspiring English sources

The behaviour of the viscosity of a mixture can also be explained by the foregoing calculation.

Butter becomes rancid by the foregoing process and by hydrolysis, which liberates volatile and malodorous acids, particularly butyric acid.

The following two conclusions seem to be fairly strongly supported by the foregoing discussion.

Of course, these morphological changes of mature DCs may be regulated by the foregoing different and sometimes overlapping pathways.

Computed values are compared with those predicted by the foregoing numerical methods and by the classical plane wave theory, and the former agree very well with the results of the present study.

Case I: If 0 < a ≤ β n ≤ b < 1 and 0 ≤ α n ≤ 1, then by the foregoing discussion and by Lemma 2.10, we have lim n → ∞ d ( T y n, x n ) = 0.

The Handmaid's Tale by Margaret Atwood The foregoing fences have been very literal ones; Atwood's seminal feminist dystopian novel gives us both literal and metaphorical borders.

For example, features of back scarp (scarp, sharp slope or cliff), landslide valley or collapsed valley (depression or gully), landslide mass (hilly block), landslide bench and sliding surfaces can be known by using the foregoing geophysical prospecting methods.

By combining the foregoing observations, we have c ≤ lim inf n → ∞ d ( y n, x ) ≤ lim sup n → ∞ d ( y n, x ) ≤ c, so that c = lim n → ∞ d ( y n, x ) = lim n → ∞ d ( α n T x n ⊕ ( 1 − α n ) x n, x ).

By pursuing the foregoing four objectives, Erdogan is running the risk of destabilizing Turkey and neighboring states: 1) By attacking ISIS targets in Northern Syria, ostensibly in retaliation for the killed Turkish soldier, Ankara is breaking its secret understanding with ISIS to refrain from mutual attacks.

By means of the foregoing observations we make the following.