Sentence examples for approximation forward from inspiring English sources
For each source, only data at detectors that were more than one transport mean free path away from the source were used in order to avoid singularities in the diffusion approximation (forward model).
In the undepleted pump beam approximation, Raman forward and backward scatterings evolve exponentially [29] with the exponential factor being respectively ( {g_R}^f L P/{A}_{eff}^R ) and ( {g_R}^b;{L}_{eff} P/{A}_{eff}^R ).
The underlying intuition of CSMP is to obtain the cosparsity estimation and the signal approximation in the forward process and refine them in the backward process.
Calculations using FWEM are presented for two propagation problems and comparisons to data computed with analytical and theoretical solutions and show this forward approximation to be highly accurate.
Theorem 3. Using the Gaussian mixture approximations for the forward and the backward filter introduced in Sections 3.1 and 3.3, respectively, a closed form expression of is obtained as follows: (32).
However, all of the backward time methods are approximations to a forward Wright-Fisher process, and are meant to model natural processes that clearly occur in forward time, so this method is adequate for exploring most relevant models of positive selection and demography.
We instead adopt a forward difference approximation in the following manner.
The derivative boundary condition is discretized using a forward difference approximation.
The forward difference approximation to the time derivative is stable when the time step is sufficiently small relative to the ratio between the permittivity and the conductivity.
We employed ab initio electronic structure calculations with DFT and the generalized gradient approximation (GGA) [16] put forward by Perdew–Burke Ernzerhof (PBE) [17].
The corrector step is then obtained by replacing the space derivative by rearward difference, while the time derivative is preserved using forward difference approximation, to obtain Eq. 4.
