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The transient three-dimensional temperature is analyzed exactly by the methods of Laplace and finite cosine transformations.
Simple diffusion of the reactant across a stagnant diffusion layer can be analyzed exactly, but complications arising from homogeneous reactions, variable properties, or ionic migration can modify the impedance, and more detailed analysis is required.
Here ω is the circular frequency; D is the displacement amplitude vector; M and K are the mass and static stiffness matrices; and K is the dynamic stiffness matrix, with coefficients which include trigonometric and hyperbolic functions involving ω and mass because elements (for example, bars or beams) are analyzed exactly by solving their governing differential equations.
Samples were prepared and analyzed exactly as described above.
The velocity distribution of the two-dimensional stagnation flow was first analyzed by Hiemenz (see White [45]) who discovered that this flow can be analyzed exactly by the Navier-Stokes equations.
Because it was impossible to mask patients and staff to treatment and outcome, we used the following measures to minimize bias in assessing results: The database was monitored by third parties with no direct involvement in the study procedures and no interest in outcome, and the data were analyzed exactly according to the statistical analysis plan decided on before the study started.
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Even at 14, she's the smartest person in Verona, capable of analyzing exactly what's happening to her.
Researchers will use an innovative set of tools developed to study gene expression to analyze exactly where early brain development goes awry.
At the end of the week have them analyze exactly what and how many sugars they consumed, and in what form.
That meant building a series of pollution sensor prototypes, measuring their performance under a wide variety of conditions, and analyzing exactly how much air would need to go through the Flow tracker to get accurate pollution measurements.
Plants like Shearon Harris and a three-reactor plant in Oconee County, S.C., are now analyzing exactly how much combustible material is in each location and whether a fire on the floor could grow hot enough to burn a cable in an overhead tray.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com