Sentence examples for rewritten by using from inspiring English sources
They can be rewritten by using the specific (per mass) linear momentum and the specific angular momentum: p^{text{lin.}}_{i} = rho v_{i}, quad p^{text{ang.}}_{i} = rho a_{i} (8).
On the other hand, the relative site amplification factor for two station, G i (f)/G i (f), can be rewritten by using the site amplification factors relative to a common reference station: frac{{G_{i} left( f right)}}{{G_{j} left( f right)}} = frac{{{{G_{i} left( f right)} mathord{left/ {vphantom {{G_{i} left( f right)} {G_{ref} left( f right)}}} right.
The multivariate Mittag-Leffer function can be rewritten by using the Hankel integral representation of (1/Gamma z) ) [5], frac{1}{Gamma z)}=frac{1}{2pi i} int_{Ha epsilon+)} e^{s} s^{-z},ds, where (r>0, Ha epsilon+)={ zin C:|z|=epsilon, 0leq|operatorname{arg} z)|leq pi} cup{ zin C:|z|>epsilon, |operatorname{arg} z)|= pi} ).
Then, the differential equation can be rewritten by using Eq. (19) and its derivative: begin{aligned} left[ 2omega (idot{a}- dot{phi }) + a (Omega ^2 -omega ^2) - ivarepsilon (1-a^2)aomega right] e^{i( omega t + phi (t))}nonumber =alpha e^{i omega t}.
The cooling rate is rewritten as by using Eqs.
Two research directions are pursued in this dissertation: augmenting the expressive power of individual rewrite rules by using new types of patterns, and analyzing the interaction of the rewrite rules.
Tito rewrote history by using foibles and propaganda to distort the integrity and heritage of the region.
One can rewrite (12), by using the q-forward and backward jump operators (10) as Δ x 2 f ( x ) = ( E q + E q − 1 − 2 ) f ( x ).
Then, rewriting it by using the characteristic variables ξ = x + y and η = x − y, we have that the equation of the curve AC can be expressed as ξ = λ , 0 ≤ η ≤ 1. Theorem 1 Let γ ∈ C 1 [ 0, l ] and Q ∈ C 1 ( [ 0, 1 ] × [ 0, 1 ] ).
In order to calculate the unknown coefficients (c_{k}) in linear system (3.5), we rewrite this system by using the above notations in matrix-vector form as mathbf{A}mathbf{c}=mathbf{B} (3.6) where Now we have a linear system of n equations in the n unknown coefficients given by (3.6).
Rewriting Equation (3) by using R ˜ s and R ˜ s i + n instead of R s and R i+n, respectively, another expression of SINR can be written as SINR Rec = w H R ˜ s w w H R ˜ i + n w (22).
