Sentence examples for shown to be exponential from inspiring English sources

The crack growths were also shown to be exponential.

For algorithms that are allowed access to oracles (whose internal structure is not considered), the speed-up can be shown to be exponential over any classical algorithm in some cases, e.g., Simon's algorithm.

They concluded that the production performance of the reservoir was shown to be exponential in all cases, as long as the bottom-hole pressures in individual wells were maintained constant.

Further, positive harmonic functions on nilpotent hypergroups are shown to be integrals of exponential functions.

The empirical model was shown to be consistent with exponential distribution of active centers characteristic of heterogeneous surfaces.

Incubation was stopped after 16 hours, and the cells were shown to be in the exponential growth phase, with an optical density of 1.5 at 600 nm and a total cell number of approximately 2 × 10 per mL.

Finally, this polycondensate was shown to be microbiologically degradable with exponential microbial growth of 45 CFU (108 mL−1) by using conventional microbiological methods.

They established an exponential decay under the conditions g'(t) ≤ 0 and e αt g(t) ∈ L1 0, ∞) for some large α > 0. This last condition was shown to be necessary condition for exponential decay [7].

OpuCA levels were shown to be significantly lower in exponential phase of growth than observed in stationary phase in L. monocytogenes EGD-e grown at 37°C).

The vegetative B. subtilis phosphoproteome was recently shown to be highly dynamic during exponential growth, with the most significant changes occurring upon entry into the stationary phase [ 30].

In summary, minimum information gain is hence shown to be the underlying law for sub-exponential, exponential and super-exponential population growths.