Sentence examples for expanding variables from inspiring English sources

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.

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.

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.

In addition, we have shown that, although the discrete lattice model has numerical solutions which are smooth at large times, the apparently simple expedient of Taylor expanding the variables and truncating the resulting expansion simply leads to the wrong result.

Gaining insight into the modified migration model used here could be useful to care professionals in other HIC settings for identifying context-dependent knowledge about any sociocultural factors relevant for immigrant women in their communities, and also for expanding sociocultural variables into maternal death reporting.

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.

Similarly, further researches can expand other variables rather than the variables in this study into the constructed theoretical structure.

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.

Their approach was to expand the variables in a way similar to Equation 12 but using a small number of arbitrarily chosen 'modes' rather than orthogonal polynomials.

Entering all these variables, along with control variables into a linear regression to find unique contributions of these variables onto each subtype of aggression, we entered them into a linear regression, expanding the predictor variables by the MAYSI subscales of traumatic events and drug and alcohol abuse.