Sentence examples for approximations are required from inspiring English sources

Thus, to get an analytical expression, approximations are required.

In particular, for a geodesic circle or helix the resulting minimal surfaces are well-known (catenoid and helicatenoid, respectively), so no approximations are required.

Sought approximations are required to meet the following specific criteria: (i) very low arithmetic complexity, (ii) orthogonality or quasi-orthogonality, and (iii) low-complexity inversion.

These last ten years, several research groups have concentrated their efforts on the development of such sophisticated tools: approximations are required to decrease the CPU time, closely checking that the corresponding loss in accuracy remains acceptable.

In the transformed space, high-order numerical approximations are required for the convective derivatives to inhibit overshadowing of the concurrent contributions by the Leonard stress at all wave-numbers.

To keep the complexity low, some ad-hoc approximations are required, so that the proposed block turbo equalization algorithm for SC turns out to be different from that for OFDM [13].

Special attention has been paid to the implementation of the thermal model because specific approximations were required.

However, the computation of the posterior of a RFS is intractable in general, and therefore the use of approximations is required.

The remaining portion of the results will present the sources that were used for creation of the HIV-1_0.1.5 HIV-1_0.1.5recipes, reveandng some of the challenges for specifying this type of recipe and identifying sev0.1.6gaps in knowledge wherecipesoximations werevealinged.

The second approximation is required to compute the maximum inrush current of a transformer by assuming that the source impedance is not negligible.

The first approximation is required to build an equivalent system for the simultaneous inrush currents of transformers in a distribution feeder.