Sentence examples for solutions equations from inspiring English sources

Then, according to the solutions (Equations 26, 27, and 28), the surface waves in the z < 0 region would take the following forms: z < 0 : { E x z = A e β z E y z = B e β z E z z = − i k y β B e β z, Open image in new window (33).

Solid lines, stable solutions; dashed lines, unstable solutions (Equations 8 – 14 ).

An important assumption for the analytical solutions, Equations 5 and 8, is that exposures from inhalation, nondietary ingestion, and dermal remain constant.

Inspection of equation 6 immediately reveals that the non-trivial steady-state solutions (equations 4 6) are not biological (P, L ≤ 0) for β ≤ β crit, where β c r i t = δ U A λ B. Because δ P >> δ L, α Q >> α R, we can approximate A ≈ δ P (δ L + α Q ) = δ P B and therefore β c r i t ≈ δ U δ P λ A successful infection is not established (the trivial steady-state occurs) for β ≤ β crit.

For (mneq0), such nodes always occur for even (n-m) in even solutions (equation (20)) and for odd (n-m) in odd solutions (equation (21)).

The two approximate solutions, Equation 22 and Equation 23, are both accurate in the intermediate regime (N s α ) − 1 ≪ z ≪ z −, which allows us to determine the rate γ in Equation 22 by matching the two solutions.

Rayleigh-Ritz displacements are used for deriving the solution equations.

Then the motion differential equation of the particles was educed imitating the damped vibration and the solution equations were gained.

The experimental data were then compared with calculated theoretical data which is calculated form the regular solution equations.

Some additional mathematical analysis shows that the stochastic differential equation (18) and its solution equation (19) have a precise mathematical interpretation.

The Apelblat equation, the λh model, and the ideal solution equation correlate the solubility data well.