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Two approximate high frequency solutions are presented, one based on Kirchhoff's approximation and the other in the spirit of the geometrical theory of diffraction, and are compared with Munt's [2] exact solution by the Wiener-Hopf technique.
The design of continuous observers, approximate high gain observers, and observers for systems with bad input points are treated and illustrated with examples.
Although these solutions resemble the approximate, "high frequency", WKB form of solution of the wave equation, they have the interesting property that they are exact, regardless of the scale of the acoustic disturbance relative to that of the inhomogeneity.
Deep-sea hydrothermal vent H2S (>1500 m water depth) have δ34S values that approximate high temperature equilibrium exchange with seawater sulfate (Figure 14).
Although the ACIP recommendations specified 15 years of age to approximate high school entry, we combined 14 and 15 year olds to represent high school entry because census data estimate that 64% and 22% of 9th graders are 14 and 15 years of age, respectively [ 1, 13].
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Exact and approximate high-order transmission conditions (HOTC) are obtained for the model problem of a multi-layer planar structure.
A set of approximate high-level relationships are presented for the determination of frequency and buckling parameters of polar orthotropic circular plates with edges elastically restrained against rotation.
At render time, when blocks are tiled to produce a high-resolution volume, we accurately compute low-order scattering, with modular flux transfer used to approximate higher-order scattering.
For the design of wind-power facilities, the highest and lowest astronomical tides (HAT and LAT, respectively) are needed for the tidal-water levels regarding international designs; however, the approximate highest high water and approximate lowest low water AHHW and ALLW, respectively, have been used in Korea.
As shall be seen, the problem amounts to finding the roots of an approximate high-degree polynomial equation derived from the log-likelihood function.
Even there, though, the solution is simple: Use a higher film speed, either literally with 400-speed film or digitally by adjusting the setting on the camera to ISO 400 to approximate high-speed film.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com