Sentence examples for are derived by differentiating from inspiring English sources

Explicit expressions of the first and second order derivatives of natural frequencies and eigenvectors with respect to the configuration parameters are derived by differentiating the eigenvalue equation.

can be derived by differentiating the JCCDF in (13) with respect to γ and γ′.

The linear small signal model is derived by differentiating the averaged model around its equilibrium point.

The corresponding PDF can be derived by differentiating (5) with respect to.

The relations for the next order, the snap s = a ¨, can be derived by differentiating yet again.

The shear force and bending moment distributions along the shaft at each mode have been derived by differentiating the mode curves.

The envelope condition (9) was derived by differentiating (4), substituting (3) and integrating between θ and ( underset{raise0.3emhbox{$smash{scriptscriptstyle-}$}}{theta } ) for ( z ( {underset{raise0.3emhbox{$smash{scriptscriptstyle-}$}}{theta } } ) = 0 ).

The optimal packet generation rate of Λ∗(D/2) maximizing the revised transport capacity (16) can be derived by differentiating (16) and finding λ that makes it zero: Λ ∗ ( D / 2 ) = D · log 2 1 + 1 6 ζ θ − 1 2 θ 4 log 2 1 + 1 6 ζ θ − 1 2 θ nπ D 2 L T t + LM 1 ξ + T t, (17).

On the other hand, the CDF of T can be formulated as F T ( x ) = Pr { T < x } = 1 - Pr Z < e B x - 1 N 0 Q pk = 1 - ∑ m = 0 M - 1 M - 1 m ( - 1 ) m e B x - 1 M ( 1 + m ) e B x + m Q pk N 0 + G (19). and the PDF of T can be derived by differentiating (19) with respect to x as f T ( x ) = ∑ m = 0 M - 1 M - 1 m ( - 1 ) m B ̃ M Q pk N 0 exp B ̃ / x exp B ̃ / x + m Q pk N 0 + G 2, x ≥ 0 (20).

The design-sensitivity equations are derived by directly differentiating the equations of motion.

Continuum sensitivity equations are derived by design-differentiating the governing equations of the direct problem.