Sentence examples for using the same notations from inspiring English sources

Using the same notations as in [15], the covariance matrix can be written as, where is a Toeplitz matrix with coefficients given in (2) and defined in (9).

In the following, we will compute the coordinates which describe the center manifold (C_{0}) at (mu=0) by using the same notations as the ideas in Hassard et al. [15].

Moreover, we have p ( x ∗, x ∗ ) = 0. Proof Using the same notations as in the proof of Corollary 3.1, one can show easily from (16) that for all x, y ∈ X, we have.

In the remainder of this section, we follow the ideas in Hassard et al. [18] using the same notations as there to compute the coordinates describing the center manifold (C_{0}) at (mu =0).

Recalling that Gs,nis modeled as a lognormal r.v., we have, using the same notations as in Section II, F G s, n x ∕ u = Q μ d B - 1 0 log x u ∕ σ d B, where Q ( z ) = 1 / 2 π ∫ z ∞ exp ( − t 2 / 2 ) d t is the complementary error function of Gaussian statistics.

Using the same notations as for FastML and RefineFast, RefineML aims to find the which maximizes the likelihood of the subtree between A p and.

Well-known methods such as the force density method, dynamic relaxation, updated reference strategy and others are discussed by mathematically structuring and presenting them in the same way, using the same notation and combining terminology.

The method will be based on the specification of components in a standardized way, so that both customers and manufacturers can refer to them by using the same notation.

using the same notation as before.

The new metrics were designed by extending those defined in [9] by using the same notation.

Using the same notation as above, we denote this reference point by (A^{Jm}).