Sentence examples for above estimations from inspiring English sources

In this paper, some new estimations about the lower bounds for the rank are deduced, which improve the above estimations.

The remaining problems include the optimality of the above estimations, numerical experiments as well as the corresponding regression problems.

Therefore, from the above estimations, we have lim t → ∞ V 2 ( t ) = 0, lim t → ∞ V 3 ( t ) = 0, and lim t → ∞ V 4 ( t ) = 0, respectively.

Thus, while the above estimations were based on the actual number of diagnostic studies in 2010, the effective doses used for the estimations were taken from the DP study [5].

Also, the estimation errors in above estimations are unavoidable and can be expressed as E x) = f(x) - L x) = frac{{f^{(n)} (xi )}}{3!} cdot prodlimits_{k = 1}^{3} {(x - x_{k} )} (16).

All the above estimations of bioactive compounds were carried out in triplicate and means were plotted.

The bid randomization technique is finally used to develop an algorithm for exploration and exploitation of an auction-based network, furnishing a solution to the above estimation subproblem.

Then, by (3.1) and the above estimation (3.25), we obtain the following result.

The last term in the above estimation is no less than zero because of the assumptions.

However, the actual situation is likely to be far worse than the above estimation.

Note that the above estimation is valid only for examples shown in Fig. 11.