Sentence examples for using the above transformations from inspiring English sources

By using the above transformations, the governing partial differential equations are transformed into a system of non-dimensional nonlinear and coupled ordinary differential equations as follows: f ‴ + f f ″ − f ′ 2 − A ( f ′ + 1 2 η f ″ ) − M 1 + m 2 ( f ′ + m g ) = 0, (10).

Using the above transformations and with the help of Eq. (4), Eqs.

By using the above transformation, the original equation can be converted into Hirota's bilinear form, G ( D t, D x ; f ) = 0, where the D-operator is defined by [1] D t n D x m f ( x, y ) ⋅ g ( x, t ) = ( ∂ ∂ t − ∂ ∂ t ′ ) n ( ∂ ∂ x − ∂ ∂ x ′ ) m [ f ( x, t ) g ( x ′, t ′ ) ] | x ′ = x, t ′ = t.

Using the above transformation in equations (31 - 33 31 - 33tegrandng wintegrating to z from z = 0 to z = 1, the system of equations may be withten as [ − ( s Va + 1 + M ) − 36 5 Da ˜ 1 12 respect− 1 6 Rn α 2 J toW − 1 2 + N B Le J Φ Θ + 2 N A N B Le J T Θ − J 2 N b Le J T Φ 1 ε J Φ W N A Le J 2 1 Le J 2 + s σ ] [ W 0 Θ 0 Φ 0 ] = [ 0 0 0 ], (38).

By using the above elementary invertible linear transformations, the augmented matrix [ A | T ] transforms into row-echelon form, which yields (2.3) from the last low.

Tobacco BY-2 cells expressing apoaequorin in the nucleoplasm were established by transformation using the above strain according to (16).

Using the above method: 10x/2 = 5x.

All masks were then propagated onto each individual's DTI scalar maps using the inverse of the above transformations.

The author of this paper used the above resources to analyse land use changes in the region of Wielkopolska (Poland) in the period of system transformation (1989 2005).

Learn how to use the above commands.

The performance of a prediction model can be measured by r L 2, the squared correlation between each individual's predicted risk Gi and their liability value (r L 2 can be computed from r O 2, the squared correlation between Gi and case/control status, using the transformation above).