Sentence examples for approximation let us from inspiring English sources

In order to derive the sum rate approximation, let us first approximate the two variable function f x, y : = log 1 + x 1 γ + y using first-order Taylor series around E { x } and E { y }. f x, y ≈ f E { x }, E { y } + f x E { x }, E { y } x − E { x } + f y E { x }, E { y } y − E { y }.

With the banded approximation, let us rewrite (14) as r F = H ̄ F b + v ̄ F , (24).

However, a more efficient manner consists of performing a second SVD on the previously estimated set of positive and volume normalized PSFs, and retaining enough singular components for an excellent approximation (let us say, more than 60 80 dB).

With rough approximation, let us assume that the working fluid temperature leaving the DHE equal to the turbine inlet temperature ignoring heat losses in the vertical flow (Akhmadullin and Tyagi 2014).

For example, as a crude (and undoubtedly untrue) approximation, let us assume that isolated plants can achieve exponential growth in the absence of competition.

To study positivity of the numerical approximations let us assume x 0 ≥ 0, y 0 ≥ 0 and a, μ > 0. A straightforward analysis allows us to identify the conditions under which positive iterations x n and y n are obtained.

The average interference powers obtained from Appendix Appendix 1: sum rate using lower bound can be directly used in this approximation, so let us re-visit only the average signal powers where Doppler approximations were involved.

To obtain the approximation ratio, let us first start with the SPCPM algorithm when the weight function h i (u,v) is used.

Thus, we need two initial outer approximation subsets, let us denote them by S ~ 1 0 and S ~ 2 0, respectively.

Let us use the form of the integration by parts formulas (8), (9) for this new approximation.

Here η has finite q-variation, with q∈[1,2) and the last term is a priori not well-defined. There are several approaches to make sense of such a "rough" PDE (or pathwise SPDEs). We shall employ the solution concept based on smooth approximation of η. Let us mention (Caruana et al. 2011) studying a class of linear equations.