Sentence examples for by computing the first from inspiring English sources

This must be determined by other means; we checked this numerically by computing the first Lyapunov coefficient.

The existence of limit cycles appearing through local Hopf bifurcation and its stability is also examined and validated numerically by computing the first Lyapunov number.

The sequence obtained by computing the second difference of the sequence of approximations is more stationary than the sequence obtained by computing the first difference of approximations or than the sequence of approximations itself.

In order to understand the convergence property of SO-DCTS algorithm with Gaussian delay, we first quantify the overall impact of uncertainty by computing the first two moments of the disagreement vector.

Let us first study the behavior of (M(1 - sqrt {gamma })) for small γ, by computing the first order Taylor expansion of (M(1 - sqrt {gamma })) around γ=0.

Firstly, by computing the first several singular point quantities with Mathematica and vanishing them, the same center conditions at degenerate singular point (Theorem 3.2) and at infinity (Theorem 4.2) are obtained.

In this scheme, the average size of the undersampling noise can be obtained by computing the second-order correlation function of the ghost imaging system.

We also estimate the state price density function by computing the second derivative of the estimated call price function for both of the maturities.

In the following, by computing the fourth moment of ξ n, k and σ n, m, we obtain the strong limit properties (in the sense of a.e). of them by the Chebyshev inequality and the Borel-Cantelli lemma.

This can be achieved by computing the second part of the precoding matrix such that [13] Im H q F q G q = 0 ∈ C M R q × d q, (11).

In this regard, insight about the activation process can be obtained by computing the mean first passage time (MFPT) for transitions between the low and the high state.