where Ω ε = 1 ε Ω.. We also set p k i ′ = 1 ε p k i and define the new approximation in expanded variables as V y) = U εy) + 4 log ε.
By expanding variables at discretized time intervals, an initial boundary value problem is converted into a series of recurrent boundary value problems which can be conveniently solved by EFG/EFG-FE with a self-adaptive computing process.
By expanding variables at a discretized time interval, a non-linear coupled space/time domain problem with initial and boundary values can be converted into a series of recursive linear boundary value problems, the variations of variables can be described more precisely via a self-adaptive computing procedure, and the non-linear iteration can be avoided.
The expanded race variable is only available in the SEER 13 registries database (Surveillance Epidemiology and End Results (SEER) Program, 2007b).
These equations of motion are higher order partial differential equations having variable coefficients, and analytical solutions are obtained by expanding these variable coefficients into infinite power series.
In consideration of previous research finding variations in mass media use among Hispanics according to language,[22] the race/ethnicity variable was expanded into a race/ethnicity/language variable with the categories non-Hispanic white, non-Hispanic black, English-speaking Hispanic, and Spanish-speaking Hispanic.
Expanding the variable X∗in powers of ε = 1/ D X as (23) X ∗ = X 0 + ε X 1 + ε 2 X 2 +.. and substituting the above equation and collecting like powers of ε we have (24) ∂ 2 X 0 ∂ θ 2 = 0 ∂ 2 X 1 ∂ θ 2 + (k sx S + k x ) (X tot − X 0 ) − k − x X 0 = 0 From the first equation, applying periodic boundary conditions, we immediately see that X0 is a constant.
Similarly, further researches can expand other variables rather than the variables in this study into the constructed theoretical structure.
The capacity calculations and the optimisation program are also expanded to incorporate variable rate and power assignments, and the simulations include analyses of schedules with different rate and power objectives.
The Ugt1aI has been greatly expanded into five variable exons (1a1, and 1a3 to la6) (Fig. 3A).
Once the continuous variables (44) have been introduced, it is necessary to estimate U ( 1 / N ) and δ U ( 1 / N ) by expanding such variables around zero.
