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A fast method for approximation of Biot Savart type integrals over the tetrahedral elements is introduced, which uses an analytical expression for the nearest few elements, Gaussian quadratures for moderately distant elements, and a multipole expansion acceleration procedure for distant elements.
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Uniform random spatial distance distribution of point particles in thin films, sheets, and plates is modeled and an exact analytical expression for the nearest-neighbor distance distribution of such point particles is derived.
Therefore, we also examined the correlations between conserved (tag locations conserved between human and chimpanzee) intergenic tag expression and the expression of the nearest protein-coding gene for the following genomic compartments using the data from humans alone: 5′ flanking sense strand, 5′ flanking antisense strand, 3′ flanking sense strand, and 3′ flanking antisense strand.
I look around for the nearest exit.
For example, you might use a fairly complicated expression to determine the nearest gas station to a given moving van.
We also derive a simple analytic expression for the autocorrelation of the acoustic pressure that is valid in the near and far fields.
An expression for the tangential wall-friction coefficient (Ct) indicates two distinct flow regimes as characterized by the near-wall turbulent flow structure.
Moreover, the analytical expression for the band derivatives in the Wannier basis resolves any issues that may occur when evaluating derivatives near band crossings.
An added mass expression for CAP1400 rack near a wall was obtained and the error was evaluated.
The experimental methods use wave decomposition theory to obtain expressions for the incident, reflected and near-field wave spectra for a beam vibrating in flexure in terms of the measured auto- and cross-spectra of an array of closely spaced accelerometers.
In general, there was a direct correlation between the DHS fold change and the expression fold change of the nearest genes for the corresponding peaks, with peaks near promoter regions showing a considerably higher degree of correlation than the rest of the peak populations.
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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