Sentence examples for estimates we use from inspiring English sources

For next estimates, we use the following lemmas.

In order to determine the next two estimates we use the trace formula (2.14).

In these estimates, we use the fractional maximal function as a test function for the capacity.

In our estimates, we use the maximum norm given by ∥ v ∥ ∞ = max [ 0, T ] | v ( t ) |.

In the next section, where we prove our main estimates, we use the following theorem.

In L∞ estimates, we use an improved Morser's technique as in [8 10].

For direct cost estimates, we used average wholesale prices, and the American Medicare and Clinical Laboratory Fee Schedules.

To deduce these estimates we used only the strong ellipticity assumptions for the thermoelastic coefficients.

In numeric estimates, we used τ=150 fs and Φ=1 J/cm2 giving P_{0}= frac{Phi}{tau,c}simeq 0.2~text{GPa}.

Thus, in order to obtain consistent and efficient estimates, we used the Heckman (1979) two-step procedure.

In order to include the effect of initial values in the estimates, we used randomly generated starting values as follows.