Sentence examples for and using the transformation from inspiring English sources

Letting here p k = ∂ L ∂ q k ˙ ( q, q ˙ ), k = 1, 2 …, n. be the momentum variable, and using the transformation ( q, q ˙ ) = ( q, p ) we can write (13) as the Hamiltonian, H ( p, q, t ) = ∑ j = 1 n p j q ˙ j − L ( q, q ˙ ( q, p, t ), t ).

Remark 4.15 If we make the transformations z ↦ z + π 2, z ↦ z + m n π τ 2, z ↦ z + π 2 + m n π τ 2, and using the transformation formulas (1.9 - 1.14) for Theorem 3.1, we can also obtain the corresponding alternating circular summation formulas.

and use the transformation u = v + 1 2, Open image in new window (3.29).

If the drug has two markers assigned then we remove one of the two markers and use the transformations illustrated in Figure  2c and d.

In the second scenario, the attacker has complete knowledge about the fingerprints along with transformation key, that is, the attacker is able to generate cancelable templates from fingerprints (of both sender and receiver) using the transformation keys and algorithm of transformation.

So we correct for the geocenter difference between ITRF2000 and ITRF2008 using the transformation parameters between ITRF2000 and ITRF2008, produced by the International Terrestrial Reference Frame (http://itrf.ensg.ign.fr/ITRF-solutions/).

In other words, is decomposed into,, and by using the transformation matrix.

From [14, equation (14)] and using the PDF transformation for two random variables, related as (here ), we can calculate the PDF of the SNR of two independent and not identically distributed Nakagami-m branches as follows: (12).

From here and using the inverse transformation rule (2), we obtain series solution in the form u ( t ) = ∑ n = 0 ∞ ( − 1 ) n ( 2 n + 1 ) ! t n = sin t, which is the exact solution of equation (8).

From here and using the inverse transformation rule (2), we obtain a series solution in the form u ( t ) = t + t 2 + 1 2 ! t 3 + 1 3 ! t 4 + 1 4 ! t 5 + ⋯ + 1 k ! t k + 1 + ⋯.

We improved the prediction models by including covariates and using the log-transformation to yield a better linear correlation.