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The CSDA (continuous slowing down approximation) range of 687 keV electrons is 0.31 g cm−2 of graphite [ 18], which is equivalent to a wall thickness of approximately 1.8 mm.
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In addition, when the general periodic disturbances fall within the approximation ranges of the periodic basis functions, asymptotic output tracking performance is achieved as well.
No difference in the absorbed doses delivered to the kidney cortex and medulla was assumed due to the long range beta particles emitted by 131I: an average continuous slowing down approximation [CSDA] range of 0.41 mm and a maximum CSDA range of up to 1 mm in water [24].
Different colors indicate different polynomial orders of approximation, ranging from 1 to 5; the transmitting frequency f is equal to 200, 600 kHz, 1 and 2 MHz, respectively.
Approximation error variance was analyzed for various approximation ranges.
This "exact" pressure wave equation is solved semi-analytically by means of the Frobenius method and compared with the conventional approximative wave equation known as the local-plane-wave (LPW) approximation for a range of flow values.
By charting the results, he produced a good approximation of the range of colors one could ever expect to see.
This approximation limits the range of application of the solution to small ambient gradients or relatively high frequencies.
In the present contribution we show that assuming only the surface of the PGM washcoat to be effectively active is a reasonable approximation in the range of operative conditions typical of exhausts aftertreatment systems.
Transient simulations show that steady-state conditions are a reasonable approximation for a range of transient seawater intrusion situations, including two of the three cases considered in this analysis.
To circumvent this problem, a new hybrid PDD method was developed that is based on a linear combination of an additive and a multiplicative PDD approximation, a broad range of orthonormal polynomial bases for Fourier-polynomial expansions of component functions, and a dimension-reduction or sampling technique for estimating the expansion coefficients.
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