Sentence examples for using an expansion of from inspiring English sources

The proofs of the other two are similar by using an expansion of higher order.

This method is based on an indirect Trefftz approach, using an expansion of exact solutions of the governing differential equation to describe the dynamic field variables.

We investigate numerical solution schemes for the semiconductor Boltzmann transport equation using an expansion of the distribution function in spherical harmonics.

The applications of this work are either semi-analytical methods of solution, using an expansion of the solution onto an eigenmode basis of the associated linear problem, or special energy-conserving numerical methods.

Recently developed models for calculating bubble coalescence and breakage frequencies in isothermal bubble columns were adapted to the population balance equation using the bubble mass as the internal coordinate which was discretized using an expansion of the number density function by impulse functions.

Clinical exams, using an expansion of the WHO simplified grading scheme [ 8, 9] were performed on 264 children aged 1 to 6 years who were randomly selected from a single village in Kongwa District.

This algorithm uses an expansion of the moving average representation of a Gaussian random field via a specific orthonormal basis which exploits the scaling behavior of the random field and yields a compact representation of the field despite infrared divergence.

The proof of Theorem 33 for odd number of modes uses an expansion of the translation unitary by the Fourier-transformed Majorana operators, which are m ˜ 2 k : = i ( f ˜ k − f ˜ k † ) and m ˜ 2 k + 1 : = f ˜ k + f ˜ k †. (63).

The health care reform law is supposed to use an expansion of Medicaid as the means to offer health benefits to as many as 17 million people earning up to 133percentt of the federal poverty level, which was $14,856 in 2012.

Migrate uses an expansion of the coalescent theory to estimate migration rates between populations (Nem) and θ (2Neμ), where Ne is the effective population size, m is the constant migration rate between population pairs, and μ is the mutation rate per generation at the locus considered.

The Methods uses an expansion of the Hill functions to derive tractable dynamical equations, with summary analytical expressions provided in Table 2.