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As a result, analytical models often require many simplifying assumptions.
As a result, analytical analyses agree well with experimental results.
As a result, analytical errors have reduced over time and more accurate analyses have become possible.
As the result, analytical expressions for the eigenmodes and the eigenfrequencies of the system are obtained.
As a result, analytical sensitivities with respect to location design variables are achieved as easily as for pseudo-density variables.
As a result, analytical measurements from a colorimeter or a spectrophotometer are frequently relied upon to indicate color differences and establish a path for correction.
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These are referred to as simulation results, analytical results are attained using the exact capacity expression derived in Equation (28).
The resulting analytical solutions are verified against the results of 3-D dynamic FEM analyses.
For actual results, analytical and/or numerical approaches can be used to interpret the SWTT back-production.
The resulting analytical cohort comprised 492 960 participants.
The resulting analytical sample for the adherence analyses included 1404 patients.
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