Sentence examples for geometric observation from inspiring English sources

A simple geometric observation yields the following corollary.

A geometric observation shows (2Bsubset B(x,3r)) for all (x in B).

This geometric observation becomes important when we try to understand changes in neural dynamics.

end{aligned} Since both x and y are in B, (zin(4B ^{c}), by a purely geometric observation, we must have (|x-z|geq2|x-y|).

Because k + 1 ≥ 3, a simple geometric observation yields Re { ( k + 1 ) w ( z 0 ) − 3 1 − w ( z 0 ) } ≥ 0, hence Re { z 0 f ‴ ( z 0 ) f ″ ( z 0 ) } ≥ 0. This contradicts the assumption (2.1).

By simple geometric observation, we have 1 | R | ∫ Q n R w ( y ) dy = C 1 | x - x 0 | n ∫ Q w ( y ) dy = C | x - x 0 | n w ( Q ).

For example, unlike the doubling measure spaces, we need delicate geometric observations (see (2.19) for example).

Our algorithm is based on a number of interesting geometric observations and approximation techniques on smooth curves, and can be easily implemented for practical purpose.

Five years later Fr Sidgreaves began the first series of monthly geometric observations, which continued until May 1919.

For specific measures, there exist automatic methods that identify such a point, some of them being theoretically sound [ 21], while others are based on heuristic geometric observations [ 20, 37].

Hence, to avoid sample dilution a number of approaches are used, e.g. use of different geometric arrangements for observation of fluorescence or use of mathematical corrections [ 10].